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Modeling preference of commercial toasted white corn tortilla chips using proportional odds models
Food Quality and Preference 14 (2003) 603–614 www.elsevier.com/locate/foodqual
Modeling preference of commercial toasted white corn tortilla chips using proportional odds models J-F. Meullenet*, R. Xiong, J.A. Hankins, P. Dias, S. Zivanovic, M.A. Monsoor, T. Bellman-Horner, Z. Liu, H. Fromm Department of Food Science, University of Arkansas, 2650 N Young Avenue, Fayetteville, AR 72704, USA Received 31 August 2001; received in revised form 21 July 2002; accepted 27 August 2002
Abstract Eleven commercial toasted white corn tortilla chip products from the United States were evaluated by a group of 80 consumers of age 18–35 and by a trained sensory panel. Proportional odds models in conjunction with principal components were used for internal and external preference modeling of tortilla chip consumer overall acceptance. The internal preference modeling showed that flavor was the most important attribute to consumer overall acceptance followed by the interaction of appearance by flavor and texture. The external preference modeling showed that one flavor attribute (salt aftertaste) and one texture attribute (crispness) contributed significantly to increase consumer overall acceptance, whereas one appearance attribute (instrumental color a*) significantly lowered consumer overall acceptance. The information reported in this study is important to the tortilla chip industry to produce tortilla chips with greater consumer acceptability. This study implies that proportional odds model using principal components is an alternative tool for consumer preference modeling. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Tortilla chips; Consumer testing; Descriptive analysis; Preference modeling; Proportional odds models
1. Introduction US households are very fond of salty snacks, including tortilla chips. According to Dies (2000), 76% of US households purchase tortilla chips every 32 days. In 1996, tortilla and potato chips accounted for five of the top 10 products of the salty snack category (Anonymous, 1998). In the USA, tortilla chips have a 20% market share of salty snack purchases, second only to potato chips (Lisser, 1993). In 1996, tortilla chips enjoyed their highest sales in 10 years, and yellow tortilla chips gained in popularity (Wellman, 1997). A few studies have been carried out to evaluate sensory properties of tortilla chips. Buttery and Ling (1995, 1998) characterized the flavor volatiles of corn tortilla chips, while Hawrysh, Erin, Kim, and Hardin (1995) examined the sensory and chemical stability of tortilla chips fried in canola oil, corn oil, and partially hydro* Corresponding author. Tel.: +1-501-575-6822; fax: +1-501-5756936. E-mail address: [email protected] (J.-F. Meullenet).
genated soybean oil. Stinson and Tomassetti (1995) showed that flavor and texture acceptability of low-fat tortilla chips increased when natural corn flavor was added. However, the consumer preference pattern of this product is not yet clearly defined. The knowledge of the consumer’s attitude and preference patterns of tortilla chip products is of importance to develop a new product or to improve existing products. Consumer preference of tortilla chips can be studied using external and internal preference modeling techniques that have been employed for many foods (Arditti, 1997; Meullenet et al., 2001). Internal preference modeling uses only the consumer data to determine consumer preference patterns, while external preference modeling relates consumer preference data to descriptive sensory information and/or instrumental data (Lawlor & Delahunty, 2000). In the preference study, consumer acceptance responses are usually ordinal categories. Ordinary least square (OLS) regression can be used for preference modeling when the ordinal response (Y) is treated as a continuous variable. As a result, OLS regression models the mean scores of the
0950-3293/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0950-3293(02)00154-4
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ther like nor dislike the product. The proportional odds assumption is crucial to a proportional odds model, which limits its use in some situations. Another limitation of the proportional odds model is that it requires a large number of observations to model the structure of the response. This study was conducted to determine preferences for tortilla chips and to quantify specific sensory characteristics in tortilla chips presently on the market. The specific objectives of this paper were to apply proportional odds models to internal and external preference modeling and to identify the key sensory characteristics that determine consumer acceptance of eleven tortilla chip products by using descriptive analysis and proportional odds models.
ordinal response and the information on the structure (frequencies) of the ordinal response is lost. From the marketing point of view, the information from the structure of the ordinal response is often more meaningful and useful than that from the mean scores of the response. OLS regression requires that the distribution of error is normal. However, for the limited number of response categories used in consumer testing or if the nine or seven response categories are collapsed to five or three categories, the normal distribution assumption might not be satisfied. In addition, OLS regression may produce extreme predictions that may be out of the categorical range. These drawbacks have limited the use of OLS regression in preference modeling. Proportional odds models do not have these limitations and could be an alternative for preference modeling. Proportional odds models are widely used in categorical data analysis in health science (Agresti, 1990) and have been recently applied to sensory data from study on consumer acceptance of canola oil (Vaisey-Genser et al., 1994), qualitative studies of food choice (Tepper, Choi, & Nayga, 1997) and consumer acceptance of oca cultivars (Sangketkit, Savage, Martin, Searle, & Mason, 2000). The major advantages of the proportional odds model analysis are that it can apply to ordinal categorical responses, model the structure (frequencies) of the categorical responses and estimate the mean scores of the responses. Its invariance to choice of response categories is also an advantage (Agresti, 1990). Since the logit transformation in the proportional odds model exaggerates differences at the ends of the scale, compared to the middle, it suggests that differences between categories in the middle of the scale are quite minor, but more influential at either extreme of the scale. This may be considered being a merit because the two ends of the scale represent two different groups of consumers who either like or dislike the product and the middle of the scale represents an ‘undecided’ group of consumers who nei-
2. Materials and methods 2.1. Samples A broad range of commercially available tortilla chips was purchased at local supermarkets. The original group of tortilla chips, which included yellow and white corn chips, was evaluated for salt and fat content. The tortilla chips were then screened based on color, salt and fat content. Eleven commercially available tortilla chip products were selected for this study (Table 1). All samples selected were toasted white corn chips. Large bags of each type of tortilla chips were purchased 1–2 days before testing. The samples were randomly coded with a three-digit number and stored to prevent fractioning of chips. The coded samples were presented to panelists on white plastic plates 6-inches in diameter. Approximately 5–6 large chips or 6–8 bite size chips were placed on each plate. Each bag of chips was immediately resealed using a bag clip to preserve freshness.
Table 1 Commercial baked pure white corn tortilla chip products Product name
Abbreviation
Shape
Producer
Salt content (%)a
Best Yet White Corn Green Mountain Gringo Guy’s Restaurant Rounds Medallion White Corn Mission Strips Mission Triangle Oak Creek Farms White Corn Santita’s Tom’s White Corn Tostito’s Bite Size Tostito’s Restaurant Style
BYW GMG GUY MED MIS MIT OAK SAN TOM TOB TOR
Triangle Strip Round Triangle Strip Triangle Round Triangle Triangle Round Triangle
Fleming Companies, Inc. Green Mountain Gringo Guy’s Snack Foods Medallion Food Corporation Mission Food Corporation Mission Food Corporation Oak Creek Farms Frito-Lay Tom’s Foods Inc. Frito-Lay Frito-Lay
4 5 3 2 4 4 2 5 5 5 3
a
Expressed as percent daily intake: percent daily value are based on a 2000 calorie diet. The size of serving is 28 g.
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605
Eleven tortilla chip samples were evaluated for appearance, flavor and texture by a group of nine Spectrum1 trained panelists (Meilgaard, Civille, & Carr, 1999). Panel orientation was conducted to develop a descriptive lexicon for appearance, flavor and texture attributes specific to tortilla chips, using the Spectrum1 Method (Sensory Spectrum Inc., Chatham, NJ) and a numerical scale from 0 to 15 with one significant digit (Meilgaard et al., 1999). Lexicon and references used were too lengthy to publish here but can be found in an article by Meullenet et al. (in press) or are available upon request. The texture ballot analyzed four major categories of product texture characteristics: surface, first bite, chewdown, and residual, for a total of 15 texture attributes. The flavor profile (i.e. basic tastes, aromatics, feeling factors, and aftertaste), consisted of 23 attributes. The appearance ballot consisted of five attributes. Texture, flavor and appearance evaluations were carried out under controlled conditions over two 3-h sessions, two 2.5-h sessions and two 2-h sessions, respectively. During each session, the samples were randomly presented to panelists assigned to an individual booth and provided with a paper ballot and references. Crackers (Nabisco Premium Unsalted) and water were provided to each panelist as a means for cleansing and rinsing their palates between each sample. A 10-min break was scheduled at each session. The texture and flavor evaluations were performed in duplicate, while the appearance evaluation was performed by presenting 10 chips. The panelists were asked to evaluate all the chips and to give an average score for each attribute. This method was used because of the large variation in appearance within each product.
the caller consumed tortilla chips on a regular basis, considered to be every 2 weeks or twice a month. The screener was used for every caller until 80 eligible participants were identified. A $20 gift card was offered as an incentive and was paid upon completion of the 2-day test. A completely randomized design was used across the 11 samples for the 80 consumers (Meilgaard et al., 1999). Each consumer was seated in an individual testing booth with controlled lighting and positive airflow, and was presented with five tortilla chip samples on the first day of the test and with six tortilla chip samples on the second day. The consumers were provided with 5–6 large chips or 6–8 bite size chips for each sample, presented on coded white 6-inch diameter plastic plates. Each sample was assigned a random three-digit code to be entered on the ballot as a means of identifying the sample. Each consumer was asked to evaluate appearance, overall impression, flavor, and texture of each sample on a nine-point hedonic scale with 1=Dislike extremely and 9=Like extremely (Table 2). Consumers were also asked to rate the amount of salt on a fivepoint just-about-right scale with 1=Much too low, 5=Much too high (Table 2). The purchase intent of consumers toward the product was rated using a fivepoint scale with 1=definitely would buy and 5=definitely would not buy (Table 2). Demographic data including consumer gender, age group (1=18–20, 2=21–23, 3=24–26, 4=27–29, 5=30–32, 6=33–35 years of age), consumption frequency (1=6 times or more/week, 2=3–5 times/week, 3=1–2 times/week, 4=1–3 times/month, 5=less than 1 time/month) and preference toward brands (0=not preferred, 1=preferred) and preferred shape (1=Triangle, 2=Round, 3=Strip, 4=Bite sized, 5=no preference) of tortilla chips, were also gathered.
2.3. Consumer testing
2.4. Color measurements
Based on the work of Dies (2000) who reported that 76% of US households purchase tortilla chips every 32 days, we assumed that 75% of the population in Northwest Arkansas (i.e. where the test was conducted) consumes tortilla chip products on a regular basis. The minimum sample size necessary to get a representative sample of the population was calculated to be 73 consumers using the formula Z pð1 pÞ=C2p (in this case, Z value Za=1.96 associated with 95% confidence level, the proportion P=0.75, and the confidence interval C2p 4 10%) (Rea & Parker, 1992). Since the consumer test was performed over a 2-day period, 80 consumers were selected in anticipation of second day no shows. The consumer panel was recruited by posting advertisements requesting participation in a salty snack consumer test. Consumers of these snack products between the ages of 18 and 35 interested in participating were asked to call. A phone screener was used to determine if
Five whole chips were randomly selected from each sample. The color of each whole chip was instrumentally evaluated using a Minolta CR-300 colorimeter (Minolta Co., Ltd., Osaka, Japan) with a 50 mm measuring head. The measuring head was placed into the center of each whole chip. Color values were measured in triplicate and recorded as averaged L*=whiteness (0=black, 100=white), a* (a*=greenness, +a*=redness) and b* (b*=blueness, +b*=yellowness). L*, a* and b*, referred as to instrumental color L*, a* and b*, respectively, were used as appearance attributes for external preference modeling.
2.2. Descriptive analysis
2.5. Statistical analysis The consumer response scores (Y) (overall acceptance and acceptance of appearance, flavor and texture, purchase intent, etc.) of tortilla chips were ordered values in
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Table 2 Frequency (%) of consumer overall acceptance and consumer acceptance of appearance, flavor, texture and saltiness for 11 tortilla chip productsa
Attribute
Scaleb
% of the number of consumers for white corn tortilla chipsc BYW
GMG
GUY
MED
MIS
MIT
OAK
SAN
TOB
TOM
TOR
Overall acceptance
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 0.0 3.8 11.3 13.8 13.8 30.0 26.3 1.3
5.0 5.0 8.8 13.8 10.0 23.8 16.3 13.8 3.8
1.3 2.5 6.3 17.5 7.5 21.3 22.5 20.0 1.3
3.8 7.5 7.5 18.8 8.8 20.0 25.0 6.3 2.5
1.3 2.5 6.3 12.5 3.8 18.8 26.3 22.5 6.3
0.0 3.8 2.5 10.0 5.0 8.8 36.3 25.0 8.8
6.3 3.8 6.3 17.7 7.6 16.5 27.8 10.1 3.8
0.0 0.0 0.0 7.5 6.3 7.5 33.8 38.8 6.3
0.0 0.0 3.8 3.8 3.8 12.5 18.8 43.8 13.8
5.0 1.3 3.8 6.3 12.5 12.5 30.0 21.3 7.5
0.0 2.5 1.3 2.5 5.0 15.0 26.3 30.0 17.5
Appearance
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 0.0 3.0 16.0 4.0 13.0 21.0 21.0 2.0
1.0 0.0 4.0 11.0 11.0 12.0 19.0 17.0 4.0
0.0 1.0 5.0 10.0 6.0 14.0 22.0 18.0 4.0
0.0 4.0 2.0 13.0 8.0 9.0 27.0 13.0 4.0
0.0 3.0 6.0 15.0 6.0 13.0 12.0 15.0 10.0
0.0 0.0 4.0 7.0 5.0 12.0 20.0 24.0 8.0
1.0 2.0 1.0 6.0 11.0 10.0 27.0 12.0 9.0
0.0 0.0 0.0 2.0 5.0 8.0 26.0 32.0 7.0
0.0 1.0 2.0 6.0 4.0 6.0 16.0 29.0 16.0
1.0 1.0 0.0 6.0 6.0 13.0 19.0 27.0 7.0
0.0 2.0 1.0 7.0 3.0 9.0 19.0 27.0 12.0
Flavor
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 0.0 6.3 13.8 10.0 13.8 22.5 28.8 5.0
5.1 7.6 7.6 16.5 12.7 17.7 16.5 12.7 3.8
1.3 1.3 8.8 22.5 8.8 21.3 17.5 16.3 2.5
7.5 10.0 8.8 18.8 6.3 22.5 15.0 10.0 1.3
2.5 3.8 7.5 6.3 6.3 23.8 21.3 21.3 7.5
0.0 1.3 6.3 6.3 8.8 15.0 25.0 27.5 10.0
8.9 11.4 6.3 19.0 10.1 13.9 17.7 8.9 3.8
0.0 0.0 1.3 6.3 7.5 8.8 27.5 36.3 12.5
0.0 0.0 2.5 3.8 3.8 17.5 21.3 33.8 17.5
1.3 5.0 5.0 16.3 15.0 12.5 16.3 21.3 7.5
0.0 2.5 0.0 6.3 3.8 18.8 20.0 35.0 13.8
Texture
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 1.3 2.5 12.5 1.3 12.5 28.8 31.3 10.0
3.8 6.3 6.3 26.6 8.9 15.2 21.5 10.1 1.3
0.0 0.0 8.8 16.3 11.3 13.8 27.5 20.0 2.5
1.3 7.5 1.3 18.8 8.8 15.0 27.5 17.5 2.5
0.0 1.3 3.8 5.0 8.8 17.5 22.5 31.3 10.0
0.0 1.3 5.0 15.0 5.0 15.0 25.0 25.0 8.8
1.3 2.6 5.1 7.7 9.0 19.2 28.2 21.8 5.1
0.0 0.0 0.0 3.8 7.5 13.8 23.8 35.0 16.3
0.0 0.0 0.0 2.5 5.1 16.5 17.7 38.0 20.3
0.0 3.8 2.5 11.4 15.2 11.4 21.5 27.8 6.3
0.0 1.3 1.3 0.0 6.3 8.8 23.8 38.8 20.0
Amount of salt
Much too low (1) Low (2) Just right (3) High (4) Much too high (5)
3.8 31.3 48.8 13.8 2.5
20.0 46.3 32.5 1.3 0.0
8.8 41.3 36.3 13.8 0.0
31.3 41.3 15.0 12.5 0.0
1.3 10.1 63.3 20.3 5.1
5.0 10.0 60.0 18.8 6.3
10.1 44.3 38.0 6.3 1.3
0.0 12.5 62.5 22.5 2.5
2.5 22.5 62.5 12.5 0.0
8.8 32.5 46.3 11.3 1.3
3.8 23.8 65.0 7.5 0.0
Purchase intent
Definitely would not buy (1) Probably would not buy (2) Maybe/maybe not buy (3) Probably would buy (4) Definitely would buy (5)
6.3 22.5 30.0 31.3 10.0
21.3 35.0 28.8 12.5 2.5
16.3 23.8 28.8 27.5 3.8
30.0 22.5 28.8 16.3 2.5
6.3 18.8 27.5 36.3 11.3
6.3 19.0 20.3 36.7 17.7
24.1 27.8 27.8 11.4 8.9
0.0 13.8 27.5 25.0 23.8
10.0 21.3 30.0 22.5 16.3
2.5 12.5 17.5 42.5 25.0
2.5 13.8 23.8 27.5 32.5
a
Total observations (n=80 consumers) for each tortilla chip sample. Frequency (%)=100number of consumers rating the category/n. A nine-point hedonic scale for consumer overall acceptance and acceptance of appearance, flavor and texture, a five-point Just About Right scale for the amount of salt (saltiness), and a five-point scale for purchase intent. c Sample name abbreviations can be found in Table 1. b
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a set of nine or five categories. Since the order of the categories is meaningful, the responses are ordinal categorical variables. Each of ordinal categorical variables has ordered categories and a frequency associated with each category. Both proportional odds models and OLS regression models can apply to the ordinal categorical variables, depending upon how the ordinal categorical variables are treated and what is required to be modeled. When the ordinal categorical responses are simply treated as continuous variables and modeling of the mean scores of the responses is of interest, OLS regression can apply if its assumptions are met. It was found in this study that the response scores (Y) for some of the products tested did not follow a normal distribution and therefore were not appropriate for significance testing using a standard analysis of variance or OLS regression (Jones & Wang, 2000). When the ordinal categorical responses are treated as ordinal categorical variables and the frequencies of the categories of the responses are of interest, proportional odds models are appropriate. The proportional odds models can also predict the mean scores of the response, which provides a basis for comparison with OLS regression models. Another advantage of proportional odds models is invariance to choice of response categories (Agresti, 1990). This means that when nine categories and three categories which were collapsed from the nine categories are used in parallel, similar conclusions will be reached (Agresti, 1990). This feature is useful in the case where nine categories need to be collapsed into three categories such as (dislike, neither dislike nor like, like) to determine the probability of ‘like’ or ‘dislike’. The proportional odds models are widely used to analyze the structure (frequencies) of ordered categorical data, do not require the normality assumption and can be mathematically expressed as (SAS OnlineDoc); Agresti, 1990]: ijk logit ijk ¼ log ¼ k þ X0ij 1 ijk
ijk where log is the log (i.e. loge) odds of 1 ijk response Yij (scores) being in category k or below (k=1,2,. . .,K1, with K=9 for a nine-point scale and K=5 for a five-point scale), also referred as to the logit. ijk=P(Y4k|Xij) is the probability that the categorical score (response Yij) rated by the ith consumer (i=1,2,. . .,80) will be in category k or below for tortilla chip product j (j=1,2,. . .,11), given a vector of independent variables/covariates Xij. k is an intercept parameter representing the logits of the cumulative response when the explanatory variables/covariates Xij are zero and 1424. . .4K1. is a vector of unknown parameters representing the effect of Xij on the response Y. The proportional odds assumption is
crucial for the proportional odds model (Jones & Wang, 2000). It is that, after fitting an intercept term for each logit, the effect of changing a value or level of a covariate is the same for each of the (K1) types of logit. Proportional odds models were fitted to the data using PROC LOGISTIC of SAS. The highest end of the rating scale (Y=9, i.e. Y=‘Like extremely’ for acceptance; Y=5, i.e. ‘Would buy definitely’ for purchase intent, or ‘Much too high’ for saltiness) was used to associate with the lowest level in the SAS response profile table, the probability of ‘Y=90 or ‘Y=50 was modeled in the proportional odds models. PROC LOGISTIC provides a Chi-square statistic (2) to test proportional odds assumption. The goodness-of-fit of a logistic model is measured using either the likelihood ratio (G2) or Pearson Chi-square statistic (2). Only G2 was used in this study. The null hypothesis for the goodness-of-fit test of a proportional odds model is that the expected cumulative frequencies from the proportional odds model agrees with the observed cumulative frequencies, namely that the model fits the data. The statistic G 2, defined as P 2 observed logðobserved=expectedÞ, is used as a goodness-of-fit test statistic to compare observed and expected cumulative frequencies. G2 is approximately a chi-square distribution with a degree of freedom (DF) (in PROC LOGISTIC of SAS, degree of freedom is computed as DF=mkq, where m is the number of subpopulation profiles determined by the number of distinct observations, k+1 is the number of response levels, q is the number of parameter estimated) (SAS OnlineDoc, SAS Version 8, SAS Institute Inc., Cary, NC). The P-value for G2 with DF is usually used for testing the null hypothesis. If the P-value for G2 from a proportional odds model is less than the pre-selected significance level (usually 0.05), the null hypothesis is rejected, indicating that the model does not fit. Otherwise, the null hypothesis is accepted, that is, the model fits. The pre-selected significance level of 0.05 was used in this study. If the model fits the data, it can be used to calculate the fitted/expected mean frequencies/probabilities of all levels of a response Y. For an ordinal response (more than two levels) such as consumer overall acceptance and acceptance of appearance, flavor or texture, the expected mean frequency/probability (Pk of observing level k) for product j (j=1,2,. . .,11) is calculated as follows: j1 ¼ P Yij ¼ 1 j Xij ¼ j2 ¼ P Yij ¼ 2 j Xij ¼
1 1þe
ð1 þ0 Xij Þ
1þe
ð2 þ0 Xij Þ
1
1
1þe
ð1 þ0 Xij Þ
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j3 ¼ P Yij ¼ 3 j Xij ¼
1 1þe
ð3 þ0 Xij Þ
1
1þe
ð2 þ0 Xij Þ
... jðK1Þ ¼ P Yij ¼ ðK 1Þ j Xij 1
¼ 1þe
ðK1 þ0 Xij Þ
1
1þe
jK ¼ P Yij ¼ K j Xij ¼ 1
ðK2 þ0 Xij Þ
1 1þe
ðK1 þ0 Xij Þ
By using the expected mean frequency/probability, the fitted/expected mean scores ðY j Þ of consumer response for product j (j=1,2,. . .,11) are calculated as: Y j ¼ j1 1 þ j2 2 þ j3 3 þ . . . þ jðK1Þ ðK 1Þ þ jK K ¼
K X jk k
and external preference modeling, principal components (continuous variables), together with the categorical variable of product shape (round, triangle and strip), were used as covariates (Xij) in the proportional odds models because the original sensory variables (that were continuous variables) were correlated. For internal preference modeling, principal components were extracted from consumer acceptance scores of appearance, flavor, texture and their interactions. For external preference modeling, principal components were extracted from the descriptive attributes prior to performing preference modeling of consumer overall acceptance and acceptance of appearance, flavor and texture. The SELECTION=BACKWARD option in PROC LOGISTIC was used to select significant covariates (principal components) (P < 0.05). The likelihood ratio G2=D1D0 (D1=deviance for the simple model, D0=deviance for the complex model) and backward elimination method were also used to select significant sensory variables (P < 0.05) in the significant principal components. Only the ‘optimal’ proportional odds models were reported in this paper.
k¼1
3. Results and discussion This equation implies that although the proportional odds model fits the cumulative probabilities of the response, the fitted mean scores of the response for each product can be derived indirectly from the fitted model. If OLS regression applies to the same response, the fitted mean scores for each product can also be obtained directly from the OLS regression model. R2 (coefficient of determination) and RMSE (root mean square error) are used in OLS regression to assess the goodness-of-fit of the model and can be calculated out using the observed and fitted mean scores of the response. Since the fitted mean scores of the response can be obtained from both OLS regression and proportional odds model, their goodness-of-fit can be compared using R2 and RMSE (denoted hereafter as R2score and RMSEscore). This provides a means for comparing proportional odds model with other regression models in terms of only the mean scores of the response. For modeling of the consumer overall acceptance and purchase intent, the product variable (11 tortilla chips products) together with demographic variables (gender, age group, preferred brand, preferred shape and consumption frequency) were used as covariates (Xij) in the proportional odds models. The covariates such as product, gender, preferred brand and preferred shape were categorical variables in the proportional odds models. Since the covariates of consumption frequency and age group were ordinal categorical variables, they were treated as continuous variables in the proportional odds models (i.e. assuming linear effects of the ordinal categorical variables on the response). However, for internal
3.1. Consumer acceptance The frequency of the consumer overall acceptance and acceptance of appearance, flavor, texture and amount of salt is presented in Table 2. It was evident that TOR had the highest overall acceptance frequency of ‘Like extremely’, followed by TOB. The consumer acceptance of appearance, flavor and texture of TOB was rated as ‘Like extremely’ by 16.0, 17.5 and 20.3% of the consumers, respectively. In contrast, only 4.0, 1.4 and 2.5% of the consumers rated the acceptance of appearance, flavor and texture of MED as ‘Like extremely’, respectively. In terms of the amount of salt, 60 to 65% of the consumers rated five products (MIT, MIS, TOB, TOR and SAN) as ‘Just about right’, whereas MED had the lowest rate (i.e. 15%). It was found that the ‘Just about right’ rates were associated with the salt content (Table 1). A salt content of 4% was found to be ‘Just about right’ for saltiness acceptance. TOR had the highest rate (i.e. 32.5%) of purchase intent as ‘Definitely would buy’, while MED again had the lowest rate (2.5%). The Chi-square (2) for testing the proportional odds assumption was 84.93, which was not significant with respect to a Chi-square distribution with 84 degrees of freedom (DF) (P=0.45). This suggests that the proportional odds assumption was satisfied. The likelihood ratio G2 was 2886.13 (DF=5836) with P 1.0, indicating that the proportional odds model adequately fitted the data. The parameterization used in the SAS system
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is one that leaves out the parameter for the baseline (TOR in this case) with which each product is compared. Hence, a positive parameter estimate () in Table 3 means that the compared product is preferred to TOR, and a negative value means that TOR was preferred. Based on the b estimates, SAN (0.24) was the most preferred product, while MED (1.47) was the least preferred one. It was evident from Table 3 that the probabilities (P > Chi-square) for the products BYW, MIT SAN, TOB and TOM were greater than 0.05, indicating that the products were not significantly different from TOR, while those for the remaining products were less than 0.05, suggesting significant difference in overall acceptance between the products and TOR. The odds ratios in Table 3 compare each product with TOR. Other odds ratios can be obtained. For example, the odds ratio between MED (least preferred) and SAN (most preferred) was 0.18, indicating that the odds of consumers liking rate for MED was 0.18 times the odds for SAN. The positive parameter estimate for age group suggested that age group was positively associated with liking. The odds ratio for age group means that the odds of consumer liking rate would increased by 8% for one unit increase in age group if holding other covariates constant. ‘Older’ consumers tended to give higher acceptance scores for tortilla chips than ‘younger’ ones. The odds ratios for
preferred brand showed that the odds of consumers liking non-preferred brand products were 0.58 times the odds of liking preferred brands. This indicated that although the chip samples were randomly presented without any indication of brand names, consumers could have recognized their preferred brand samples, maybe through shape, size, color, smell and texture of chips, which they are familiar with. Tostita’s brand was selected as a preferred brand by 90% of consumers. Similarly, Mission brand, Guy’s brand, Santita’s brand and the remaining brands were selected as a preferred brand by 41.2, 15.0, 12.5 and 0 to 1.2%, respectively. The proportional odds model also adequately fitted for purchase intent (P=0.33 for 2 of 39.15, DF=36; G2=2239.32, DF=2912, P 1.0). Product, preferred brand and gender were significant contributors to consumer purchase intent (Table 3). The odds that consumers ‘would buy’ non-preferred brand products were 0.50 times the odds that consumers ‘would buy’ preferred brands. The odds ratios for gender showed that the odds of ‘would buy’ the chips were 25.7% smaller for females than for males. The estimates indicated that consumers would buy SAN most if the effects of gender and preferred brand were partialed out, and MED was the least likely to be purchased. In this study, it was found that the proportional odds assumption was not satisfied with acceptance of appearance, flavor, tex-
Table 3 Parameter estimates and statistics for proportional odds models for consumer overall acceptance and purchase intent (see Appendix) Parametera
1 2 3 4 5 6 7 8 Product: BYW Product: GMG Product: GUY Product: MED Product: MIS Product: MIT Product: OAK Product: SAN Product: TOB Product: TOM Product: TOR Age group Preferred brand: No Preferred brand: Yes Gender: Female Gender: Male a
DF
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0
Overall acceptance
Purchase intent
Estimate
S.E.
Chi-square
P >Chi-square
2.17 0.24 1.01 1.76 2.22 3.19 3.94 4.80 0.47 1.28 1.00 1.47 0.73 0.33 1.21 0.24 0.18 0.43 0 0.07 0.54 0
0.26 0.24 0.24 0.25 0.25 0.27 0.29 0.34 0.34 0.34 0.32 0.34 0.30 0.30 0.34 0.33 0.29 0.34 – 0.04 0.20 –
67.43 0.98 17.09 50.18 76.92 142.82 186.35 201.49 1.99 14.44 9.66 18.95 5.92 1.18 12.84 0.56 0.41 1.62 – 4.50 6.90 –
<0.0001 0.3226 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.1586 0.0001 0.0019 <0.0001 0.015 0.2764 0.0003 0.4537 0.5223 0.203 – 0.0338 0.0086 –
Sample name abbreviations can be found in Table 1.
Odds ratio
0.62 0.28 0.37 0.23 0.48 0.72 0.30 1.28 1.20 0.65 1.00 1.08 0.58 1.00
Estimate
S.E.
Chi-square
P >Chi-square
Odds ratio
0.76 0.87 2.12 3.58
0.22 0.22 0.23 0.25
11.84 15.44 84.85 205.95
0.0006 <0.0001 <0.0001 <0.0001
0.37 1.53 1.01 1.59 0.46 0.24 1.41 0.35 0.01 0.40 0
0.34 0.34 0.33 0.34 0.30 0.30 0.34 0.33 0.29 0.34 –
1.21 20.06 9.54 21.59 2.29 0.62 16.91 1.16 0.00 1.42 –
0.2708 <0.0001 0.002 <0.0001 0.1299 0.43 <0.0001 0.2808 0.9687 0.2339 –
0.69 0.22 0.37 0.20 0.63 0.79 0.24 1.42 0.99 0.67 1.00
0.69 0 0.30 0
0.21 – 0.12 –
11.08 – 5.72 –
0.0009 – 0.0167 –
0.50 1.00 0.74 1.00
610
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ture and saltiness. This may be due to non-parallelism of the logits of each cumulative response among the chip products, suggesting the limitations of proportional odds models. 3.2. Prediction of overall acceptance from attribute acceptance: internal preference model The model for consumer overall acceptance using the principal components as covariates is presented in Table 4. The proportional odds assumption was satisfied (P=0.35 for 2 of 15.42 with DF=14). The goodness-of-fit statistic (G2=913.53, DF=1918, P 1.0) indicated that the model fitted the data well. Two principal components (PC1o and PC2o) were statistically significant. From the principal components analysis, PC1o and PC2o could be expressed as 0.60Flavor+0.53Texture+0.60AppearanceFlavor and 0.40Flavor+0.85Texture0.35AppearanceFlavor, respectively. Keep in mind that the important sensory variables (i.e. Flavor, Texture, and Appearance by Flavor) associated with the principal components were selected using the likelihood ratio (G2) and backward elimination. The parameter estimates for PC1o and PC2o were 2.56 and 0.76, respectively. In order to examine the effects of the original sensory variables on consumer overall acceptance, 2.56PC1o0.76PC2o was re-expressed as: 1.83Flavor+0.72Texture+1.81Appearance Flavor. The regression coefficients in this expression clearly show that the most influential sensory variable was flavor (1.83), followed by the interaction (1.81) of appearance by flavor and texture (0.72). The positive coefficients suggested that consumer overall acceptance had a positive association with the sensory variables of
flavor, appearance and texture. Based on the predicted mean probabilities, the predicted mean scores of consumer overall acceptance were calculated to be compared with the observed mean scores for the 11 tortilla chips (Fig. 1). The corresponding R2Score and RMSEScore values were 0.99 and 0.06 (Fig. 1), respectively, also indicating that the model predicted the mean scores well for consumer overall acceptance. R2score and RMSEscore are useful for comparison of the proportional odds model with other regression models in terms of fitting the mean scores of the response. For example, R2score and RMSEscore can be used to assess the goodness-of-fit of the proportional odds model for the mean scores against the goodness-of-fit of partial least squares regression model that is a popular tool for preference modeling (Meullenet et al., 2001). For purchase intent, the proportional odds model fitted adequately (G2=892.03, DF=1916, P 1.0; P=0.27 for 2 of 7.59, DF=6, Table 4). The model included two principal components, PC1p=0.48Appearance+0.61Flavor+0.63FlavorTexture, PC2p=0.88Appearance0.38Flavor0.30FlavorTexture. The parameter estimates () suggested that PC1p had more effect on the purchase intent than PC2p, which can be re-expressed as that flavor (1.46) was the most influential variable on consumer’s purchase intent (Table 4). The R2Score and RMSEScore values for purchase intent scores were 0.98 and 0.11, respectively. 3.3. Prediction of overall acceptance from descriptive profiles: external preference model Descriptive intensity means (data not shown, but reported by Meullenet et al., in press) for visual
Table 4 Parameter estimates and statistics for proportional odds model for internal preference mapping (see Appendix) Parametera
DF
Overall acceptance Estimate
S.E.
Purchase intent Chi-square
P >Chi-square
Odds ratio
Estimate
S.E.
Chi-square
1 6.22 0.24 658.96 <0.0001 3.91 0.17 542.23 1 2 1 2.75 0.15 347.59 <0.0001 1.09 0.11 96.44 1 0.42 0.12 12.39 0.0004 1.63 0.12 175.57 3 4 1 2.53 0.15 277.73 <0.0001 4.64 0.21 493.68 5 1 3.88 0.19 435.41 <0.0001 1 6.28 0.26 576.95 <0.0001 6 7 1 7.84 0.32 594.36 <0.0001 8 1 9.40 0.40 544.35 <0.0001 PC1o 1 2.56 0.10 719.52 <0.0001 12.96 1 0.76 0.10 54.85 <0.0001 0.47 PC2o Associated with the original sensory variables: 2.56PC1o0.76PC2o=1.83Flavor+0.72Texture+1.81AppearanceFlavor PC1p 2.04 0.09 573.03 PC2p 0.53 0.09 35.41 Associated with the original sensory variables: 2.04PC1p+0.53PC2p=0.52Appearance+1.46Flavor+1.43FlavorTexture a
P>Chi-square
Odds ratio
<0.0001 <0.0001 <0.0001 <0.0001
<0.0001 <0.0001
7.70 0.59
PC=principal component. PCi means the ith principal component. Subscripts (o and p) stand for overall acceptance and purchase intent, PC2o=0.40Flavor+0.85Texture0.35AppearanceFlavor, respectively. PC1o=0.60Flavor+0.53Texture+0.60Appearance Flavor, PC1p=0.48Appearance+0.61Flavor+0.63FlavorTexture, PC2p=0.88Appearance0.38Flavor0.30FlavorTexture.
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acceptance. The R2Score and RMSEScore values for the average scores of consumer purchase intent were 0.97 and 0.09, respectively, suggesting that the mean scores of purchase intent could be accurately predicted by the proportional odds model using salt aftertaste, crispness and instrumental color a*. 3.4. Prediction of tortilla chip flavor acceptance from flavor descriptors
Fig. 1. Predicted versus observed average consumer overall acceptance. Predicted average scores were obtained from consumer appearance, flavor and texture acceptance using a proportional odds model. Sample name abbreviations can be found in Table 1.
appearance, flavor, and texture attributes were used for external preference modeling. The modeling results showed that the proportional odds model adequately fitted the data for overall acceptance (2=9.25, DF=14, P=0.81; G2=89.99, DF=94, P=0.60). The parameter estimates are listed in Table 5. Two (PC1o and PC2o) out of three principal components were selected as important covariates, which equivalently says that one flavor descriptive attribute (salt aftertaste), one appearance attribute (instrumental color a*) and one texture descriptive attribute (crispness) were statistically significant contributors to the consumer overall acceptance of tortilla chips (Table 5). Appearance, flavor and texture descriptive attributes were included in the external preference model, confirming modeling results from the above internal preference modeling. It should not be surprising that salt aftertaste was the most important flavor attribute to the acceptance because American consumers like salt. Crispness was one of the most important texture attributes for chips including tortilla chips. As expected, it increased consumer overall acceptance, but its contribution to the overall acceptance was lower than that of salt aftertaste. Instrumental color a* negatively contributed consumer overall acceptance. The R2Score and RMSEScore values for the average scores of consumer overall acceptance were 0.95 and 0.16 (Fig. 2), respectively, indicating that the model could accurately predicted the mean scores of overall acceptance. The proportional odds model (Table 5) including two principal components (PC1p and PC2p) also adequately fitted the data for purchase intent (2=8.49, DF=6, P=0.20; G2=45.05, DF=46, P=0.48). Since salt aftertaste, crispness and instrumental color (a*) were associated with the principal components, they were also significant contributors to consumer purchase intent. These variables played similar roles in the model for purchase intent as they did in the model for overall
The proportional odds assumption was satisfied for flavor external preference modeling (2=27.56, DF=28, P=0.49). The likelihood ratio (G2=73.66, DF=84, P=0.78) indicated that the proportional odds model could adequately fit the flavor data. The first, third, fifth and sixth principal components (PC1f, PC3f, PC5f, PC6f) were selected as significant predictors in the model (Table 5). By replacing the principal components with the original sensory variables, it was found that toasted corn, salt aftertaste, toasted grain aftertaste and sweet aftertaste contributed to increased consumer acceptance of flavor while cardboard and grain complex decreased consumer flavor acceptance (Table 5). The R2Score and RMSEScore values for the average scores of consumer flavor acceptance were 0.99 and 0.09, respectively. 3.5. Prediction of tortilla chip texture acceptance from texture descriptors The proportional odds model also adequately fitted the texture data (2=31.79, DF=21, P=0.06; G2=85.29, DF=77, P=0.24). The first, second and third principal components (PC1t, PC2t, PC3t) were selected out of seven principal components as significant predictors in the model, indicating that the seven sensory texture variables were highly correlated. The texture descriptive variables/attributes of hardness, toothpack, crispness, oily film, moisture absorption, persist of crisp, loose particles were significant contributors to the consumer acceptance of tortilla chip texture (Table 5). The R2Score and RMSEScore values for the average scores of consumer texture acceptance for the tortilla chip products were 0.93 and 0.19, respectively. 3.6. Prediction of tortilla chip appearance acceptance from visual appearance descriptors The proportional odds model adequately fitted the data for appearance acceptance (2=40.47, DF=35, P=0.24; G2=90.78, DF=83, P=0.26). Two principal components (PC1a and PC2a) and product shape were selected as significant predictors in the model. When PC1a and PC2a were expressed by the original sensory variables, it was found that degree of whiteness
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Table 5 Parameter estimates for the proportional odds model for external preference modeling (see Appendix) Parametera
DF
Overall acceptanceb
Appearance acceptancec
Texture acceptancee
Purchase intentf
Chi-square
P > Chi- square
Estimate
Chi-square
P > Chi- square
Estimate
Chi-square
P >Chi- square
Estimate
Chi-square
P >Chi- square
Estimate
Chi-square
P >Chi- square
2.12 0.38 0.74 1.40 1.90 3.21 4.23 5.98
267.33 16.02 58.05 177.84 271.84 358.93 272.92 105.13
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
2.70 0.94 0.01 0.80 1.26 2.20 2.92 3.96
429.79 147.42 0.01 110.99 230.71 407.53 421.12 315.98
< 0.0001 < 0.0001 0.9248 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
2.45 0.61 0.47 1.19 1.71 2.90 3.72 5.37
415.11 69.85 42.89 215.12 336.34 409.47 329.43 142.33
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
2.01 0.40 0.83 2.26
388.08 31.108 117.76 413.11
< 0.0001 < 0.0001 < 0.0001 < 0.0001
0.17 0.25 0.85 0.30 0.73 0.00
6.79 11.73 14.90 2.95 19.52 –
0.0092 0.0006 0.0001 0.0860 < 0.0001 – 0.35 0.22 0.35 1.68
95.25 10.53 6.96 35.44
< 0.0001 0.0012 0.0083 < 0.0001 0.26 0.11 0.47
40.39 5.88 72.71
< 0.0001 0.0154 < 0.0001 125.85 17.90
< 0.0001 < 0.0001
1 1 1 1 1 1 1 1
2.84 0.93 0.30 1.04 1.49 2.46 3.21 4.07
415.84 147.08 17.84 176.28 290.76 419.67 390.25 289.04
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
PC1o PC2o
1 1
0.50 0.20
106.58 9.42
< 0.0001 0.0021
PC2a PC3a PC4a Shape: round Shape: strip Shape: triangle
1 1 1 1 1 0
PC1f PC3f PC5f PC6f
1 1 1 1
PC1t PC2t PC3t
1 1 1
PC1p PC2p
1 1
0.55 0.28
PC=principal component, PCi=ith principal component, Subscripts (o, a, f, t and p) stand for acceptance of overall, appearance, flavor and texture, purchase intent, respectively. Information on Shape can be found in Table 1. Overall acceptance: PC1o=0.51SaltAftertaste+0.67Crispness0.55a*, PC2o=0.75SaltAftertaste0.03Crispness+0.66a*, 0.5PC1o+0.2PC2o=0.41SaltAftertaste+0.32Crispness0.14a*. c Appearance acceptance: PC2a=0.18DegreeOfWhiteness+0.06GrainFlecks0.32CharMarks+0.93a*, PC3a=0.65DegreeOfWhiteness+0.08GrainFlecks+0.75CharMarks+0.13a*, PC4a=0.52 DegreeOfWhiteness+0.77GrainFlecks+0.34CharMarks+0.17a*, 0.85PC2a+0.78PC3a+0.43PC4a=0.24DegreeOfWhiteness0.68GrainFlecks0.42CharMarks0.33a*. d Flavor acceptance: PC1f=0.46ToastedCorn+0.49SaltAftertaste0.45ToastedGrainAftertaste0.24SweetAftertaste0.39Cardboard+0.36GrainComplex, PC3f=0.16ToastedCorn+0.44SaltAftertaste0.40 ToastedGrain Aftertaste+0.69SweetAftertaste+0.06Cardboard0.37GrainComplex, PC5f=0.30ToastedCorn+0.74SaltAftertaste0.53ToastedGrainAftertaste0.26SweetAftertaste+0.09Cardboard0.03 GrainComplex, PC6f=0.48Toast0.48ToastedCorn+0.02SaltAftertaste0.41ToastedGrainAftertaste0.10SweetAftertaste+0.51Cardboard+0.57GrainComplex, 0.35PC1f+0.22PC3f+0.35PC5f1.68PC6f=0.84 ToastedCorn+ 0.50SaltAftertaste+0.63 ToastedGrainAftertaste+0.14SweetAftertaste0.95Cardboard0.93GrainComplex. e Texture acceptance: PC1t=0.34Hardness+0.17Toothpack+0.51Crispness+0.37OilyFilm0.43MoistAbsorption+0.51PersistOfCrisp+0.11LooseParticles, PC2t=0.43Hardness +0.56Toothpack0.32Crispness0.08OilyFilm0.29MoistAbsorption+0.12PersistOfCrisp+0.55LooseParticles, PC3t=0.45Hardness +0.33Toothpack+0.33Crispness0.54OilyFilm+0.40MoistAbsorption0.10PersistOfCrisp+0.35 LooseParticles, 0.26PC1t0.11PC2t+0.47PC3t=0.35Hardness +0.14Toothpack+0.32Crispness0.15OilyFilm+0.11MoistAbsorption+0.08PersistOfCrisp+0.13LooseParticles. f Purchase intent: PC1p=0.51SaltAftertaste+0.67Crispness0.55a*, PC2p=0.75SaltAftertaste0.03Crispness+0.66a*, 0.55PC1p+0.28PC2p=0.49SaltAftertaste+0.36Crispness0.12a*. b
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Estimate 1 2 3 4 5 6 7 8
a
Flavor acceptanced
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the consumer panel was drawn from the local population and may not be totally representative of the national population.
5. Uncited reference Shtatland et al., 2000
Acknowledgements Fig. 2. Predicted versus observed average consumer overall acceptance. Predicted average scores were obtained from sensory descriptive attributes using a proportional odds model. Sample name abbreviations can be found in Table 1.
The authors would like to thank Dr. James Dunn, Department of Mathematics, University of Arkansas for the assistance with the proportional odds modeling.
Appendix increased appearance acceptance, while grain flecks, char marks and instrumental color (a*) had negative impact on appearance acceptance. Product shape also played an important role in determining appearance acceptance. Triangle tortilla chips were most preferred by consumers, while strip chips were least preferred (Table 5). The R2Score and RMSEScore values for the mean scores of consumer appearance acceptance for the chips were 0.85 and 0.17, respectively.
4. Conclusions The present study demonstrated that proportional odds models offer sensory scientists an alternative choice for internal/external preference modeling. Use of principal components in proportional odds model can avoid the collinearity problem caused by correlation between sensory variables. Proportional odds models can model the structure of ordinal categorical responses and estimate the mean scores of the responses. Comparison of proportional odds model analysis with other regression models need to be performed in more details. The internal preference modeling revealed that flavor was the most important attribute to consumer overall acceptance. The external preference modeling showed potential for predicting consumer overall acceptance of tortilla chips using three descriptive attributes of salt aftertaste, crispness and instrumental color value a* as predictors. The research reported here provides useful information for developing an understanding of the drivers of tortilla chips consumer acceptance. The results must be interpreted within the limits of experimental conditions. In a real purchase situation, consumers probably pay less attention to information than in an experimental situation, and they can choose a product with a lower expected quality but with an attractive price (Siret & Issanchou, 2000). In addition,
*==EXAMPLES OF FITTING PROPORTIONAL ODDS MODELS TO OVERALL ACCEPTANCE DATA USING SAS PROCEDURES; *==THE RESULTS ARE PRESENTED IN TABLES 3,4 AND 5, RESPECTIVELY; *THE DATA FORMAT USED (ONLY A PORTION OF THE VARIABLES IS LISTED HERE); DATA ChipsData; INFILE ‘‘C:n>ChipsData.txt‘‘; INPUT Panlist Product$ Overall Appearance Flavor Texture Gender$ AgeGroup$ ConsumptionFrequency$ PreferredShape$ PreferredBrand$ AftertasteSalt Crispiness Color_a ProductShape$; RUN; *THE MODEL FOR OVERALL ACCEPTANCE (THE RESULTS ARE IN TABLE 3); PROC LOGISTIC DATA=ChipsData DESCENDING; CLASS Product Gender ConsumptionFrequency PreferredShape PreferredBrand/ PARAM=GLM; MODEL Overall=Product Gender PreferredShape PreferredBrand AgeGroup ConsumptionFrequency/ SELECTION=Backward SLS=0.05 SLE=0.10 LINK=Logit RSQUARE LACKFIT SCALE=None AGGREGATE;
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TITLE1 ‘POM: Overall acceptance=Product & Demographical Variables’; RUN;
*THE OPTIMAL MODEL FOR INTERNAL PREFERENCE MODELING FOR OVERALL ACCEPTANCE (THE RESULTS ARE IN TABLE 4); *--PRIN1:THE 1ST PRINCIPAL COMPONENT, PRIN2:THE 2ND PRINCIPAL COMPONENT,. . .; PROC PRINCOMP DATA=ChipsData OUT=PCSEx OUTSTAT=StatEx; VAR Flavor Texture Appearance*Flavor; RUN; PROC LOGISTIC DATA=PCSEx DESCENDING OUT=ParamsEx; MODEL Overall=PRIN1-PRIN3/ SELECTION=Backward SLS=0.05 SLE=0.10 LINK=Logit RSQUARE LACKFIT SCALE=None AGGREGATE; TITLE1 ‘Internal Preference Modeling For Overall Acceptance’; OUTPUT OUT=PredOverallEx(KEEP=Product _LEVEL_ Pred) P=Pred; RUN;
*THE OPTIMAL MODEL FOR EXTERNAL PREFERENCE MODELING FOR OVERALL ACCEPTANCE (THE RESULTS ARE IN TABLE 5); PROC PRINCOMP DATA=ChipsData OUT=PCSIn OUTSTAT=StatIn; VAR AftertasteSalt Crispiness Color_a; RUN; PROC LOGISTIC DATA=PCSIn DESCENDING OUT=ParamsEx; CLASS ProductShape/PARAM=GLM; MODEL Overall=PRIN1-PRIN3 ProductShape/SELECTION=Backward SLS=0.05 SLE=0.10 LINK=Logit RSQUARE LACKFIT SCALE=None AGGREGATE; TITLE1 ‘External Preference Modeling For Overall Acceptance’; OUTPUT OUT=PredOverallIn(KEEP=Product _LEVEL_ Pred) P=Pred; RUN;
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Modeling preference of commercial toasted white corn tortilla chips using proportional odds models J-F. Meullenet*, R. Xiong, J.A. Hankins, P. Dias, S. Zivanovic, M.A. Monsoor, T. Bellman-Horner, Z. Liu, H. Fromm Department of Food Science, University of Arkansas, 2650 N Young Avenue, Fayetteville, AR 72704, USA Received 31 August 2001; received in revised form 21 July 2002; accepted 27 August 2002
Abstract Eleven commercial toasted white corn tortilla chip products from the United States were evaluated by a group of 80 consumers of age 18–35 and by a trained sensory panel. Proportional odds models in conjunction with principal components were used for internal and external preference modeling of tortilla chip consumer overall acceptance. The internal preference modeling showed that flavor was the most important attribute to consumer overall acceptance followed by the interaction of appearance by flavor and texture. The external preference modeling showed that one flavor attribute (salt aftertaste) and one texture attribute (crispness) contributed significantly to increase consumer overall acceptance, whereas one appearance attribute (instrumental color a*) significantly lowered consumer overall acceptance. The information reported in this study is important to the tortilla chip industry to produce tortilla chips with greater consumer acceptability. This study implies that proportional odds model using principal components is an alternative tool for consumer preference modeling. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Tortilla chips; Consumer testing; Descriptive analysis; Preference modeling; Proportional odds models
1. Introduction US households are very fond of salty snacks, including tortilla chips. According to Dies (2000), 76% of US households purchase tortilla chips every 32 days. In 1996, tortilla and potato chips accounted for five of the top 10 products of the salty snack category (Anonymous, 1998). In the USA, tortilla chips have a 20% market share of salty snack purchases, second only to potato chips (Lisser, 1993). In 1996, tortilla chips enjoyed their highest sales in 10 years, and yellow tortilla chips gained in popularity (Wellman, 1997). A few studies have been carried out to evaluate sensory properties of tortilla chips. Buttery and Ling (1995, 1998) characterized the flavor volatiles of corn tortilla chips, while Hawrysh, Erin, Kim, and Hardin (1995) examined the sensory and chemical stability of tortilla chips fried in canola oil, corn oil, and partially hydro* Corresponding author. Tel.: +1-501-575-6822; fax: +1-501-5756936. E-mail address: [email protected] (J.-F. Meullenet).
genated soybean oil. Stinson and Tomassetti (1995) showed that flavor and texture acceptability of low-fat tortilla chips increased when natural corn flavor was added. However, the consumer preference pattern of this product is not yet clearly defined. The knowledge of the consumer’s attitude and preference patterns of tortilla chip products is of importance to develop a new product or to improve existing products. Consumer preference of tortilla chips can be studied using external and internal preference modeling techniques that have been employed for many foods (Arditti, 1997; Meullenet et al., 2001). Internal preference modeling uses only the consumer data to determine consumer preference patterns, while external preference modeling relates consumer preference data to descriptive sensory information and/or instrumental data (Lawlor & Delahunty, 2000). In the preference study, consumer acceptance responses are usually ordinal categories. Ordinary least square (OLS) regression can be used for preference modeling when the ordinal response (Y) is treated as a continuous variable. As a result, OLS regression models the mean scores of the
0950-3293/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0950-3293(02)00154-4
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ther like nor dislike the product. The proportional odds assumption is crucial to a proportional odds model, which limits its use in some situations. Another limitation of the proportional odds model is that it requires a large number of observations to model the structure of the response. This study was conducted to determine preferences for tortilla chips and to quantify specific sensory characteristics in tortilla chips presently on the market. The specific objectives of this paper were to apply proportional odds models to internal and external preference modeling and to identify the key sensory characteristics that determine consumer acceptance of eleven tortilla chip products by using descriptive analysis and proportional odds models.
ordinal response and the information on the structure (frequencies) of the ordinal response is lost. From the marketing point of view, the information from the structure of the ordinal response is often more meaningful and useful than that from the mean scores of the response. OLS regression requires that the distribution of error is normal. However, for the limited number of response categories used in consumer testing or if the nine or seven response categories are collapsed to five or three categories, the normal distribution assumption might not be satisfied. In addition, OLS regression may produce extreme predictions that may be out of the categorical range. These drawbacks have limited the use of OLS regression in preference modeling. Proportional odds models do not have these limitations and could be an alternative for preference modeling. Proportional odds models are widely used in categorical data analysis in health science (Agresti, 1990) and have been recently applied to sensory data from study on consumer acceptance of canola oil (Vaisey-Genser et al., 1994), qualitative studies of food choice (Tepper, Choi, & Nayga, 1997) and consumer acceptance of oca cultivars (Sangketkit, Savage, Martin, Searle, & Mason, 2000). The major advantages of the proportional odds model analysis are that it can apply to ordinal categorical responses, model the structure (frequencies) of the categorical responses and estimate the mean scores of the responses. Its invariance to choice of response categories is also an advantage (Agresti, 1990). Since the logit transformation in the proportional odds model exaggerates differences at the ends of the scale, compared to the middle, it suggests that differences between categories in the middle of the scale are quite minor, but more influential at either extreme of the scale. This may be considered being a merit because the two ends of the scale represent two different groups of consumers who either like or dislike the product and the middle of the scale represents an ‘undecided’ group of consumers who nei-
2. Materials and methods 2.1. Samples A broad range of commercially available tortilla chips was purchased at local supermarkets. The original group of tortilla chips, which included yellow and white corn chips, was evaluated for salt and fat content. The tortilla chips were then screened based on color, salt and fat content. Eleven commercially available tortilla chip products were selected for this study (Table 1). All samples selected were toasted white corn chips. Large bags of each type of tortilla chips were purchased 1–2 days before testing. The samples were randomly coded with a three-digit number and stored to prevent fractioning of chips. The coded samples were presented to panelists on white plastic plates 6-inches in diameter. Approximately 5–6 large chips or 6–8 bite size chips were placed on each plate. Each bag of chips was immediately resealed using a bag clip to preserve freshness.
Table 1 Commercial baked pure white corn tortilla chip products Product name
Abbreviation
Shape
Producer
Salt content (%)a
Best Yet White Corn Green Mountain Gringo Guy’s Restaurant Rounds Medallion White Corn Mission Strips Mission Triangle Oak Creek Farms White Corn Santita’s Tom’s White Corn Tostito’s Bite Size Tostito’s Restaurant Style
BYW GMG GUY MED MIS MIT OAK SAN TOM TOB TOR
Triangle Strip Round Triangle Strip Triangle Round Triangle Triangle Round Triangle
Fleming Companies, Inc. Green Mountain Gringo Guy’s Snack Foods Medallion Food Corporation Mission Food Corporation Mission Food Corporation Oak Creek Farms Frito-Lay Tom’s Foods Inc. Frito-Lay Frito-Lay
4 5 3 2 4 4 2 5 5 5 3
a
Expressed as percent daily intake: percent daily value are based on a 2000 calorie diet. The size of serving is 28 g.
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605
Eleven tortilla chip samples were evaluated for appearance, flavor and texture by a group of nine Spectrum1 trained panelists (Meilgaard, Civille, & Carr, 1999). Panel orientation was conducted to develop a descriptive lexicon for appearance, flavor and texture attributes specific to tortilla chips, using the Spectrum1 Method (Sensory Spectrum Inc., Chatham, NJ) and a numerical scale from 0 to 15 with one significant digit (Meilgaard et al., 1999). Lexicon and references used were too lengthy to publish here but can be found in an article by Meullenet et al. (in press) or are available upon request. The texture ballot analyzed four major categories of product texture characteristics: surface, first bite, chewdown, and residual, for a total of 15 texture attributes. The flavor profile (i.e. basic tastes, aromatics, feeling factors, and aftertaste), consisted of 23 attributes. The appearance ballot consisted of five attributes. Texture, flavor and appearance evaluations were carried out under controlled conditions over two 3-h sessions, two 2.5-h sessions and two 2-h sessions, respectively. During each session, the samples were randomly presented to panelists assigned to an individual booth and provided with a paper ballot and references. Crackers (Nabisco Premium Unsalted) and water were provided to each panelist as a means for cleansing and rinsing their palates between each sample. A 10-min break was scheduled at each session. The texture and flavor evaluations were performed in duplicate, while the appearance evaluation was performed by presenting 10 chips. The panelists were asked to evaluate all the chips and to give an average score for each attribute. This method was used because of the large variation in appearance within each product.
the caller consumed tortilla chips on a regular basis, considered to be every 2 weeks or twice a month. The screener was used for every caller until 80 eligible participants were identified. A $20 gift card was offered as an incentive and was paid upon completion of the 2-day test. A completely randomized design was used across the 11 samples for the 80 consumers (Meilgaard et al., 1999). Each consumer was seated in an individual testing booth with controlled lighting and positive airflow, and was presented with five tortilla chip samples on the first day of the test and with six tortilla chip samples on the second day. The consumers were provided with 5–6 large chips or 6–8 bite size chips for each sample, presented on coded white 6-inch diameter plastic plates. Each sample was assigned a random three-digit code to be entered on the ballot as a means of identifying the sample. Each consumer was asked to evaluate appearance, overall impression, flavor, and texture of each sample on a nine-point hedonic scale with 1=Dislike extremely and 9=Like extremely (Table 2). Consumers were also asked to rate the amount of salt on a fivepoint just-about-right scale with 1=Much too low, 5=Much too high (Table 2). The purchase intent of consumers toward the product was rated using a fivepoint scale with 1=definitely would buy and 5=definitely would not buy (Table 2). Demographic data including consumer gender, age group (1=18–20, 2=21–23, 3=24–26, 4=27–29, 5=30–32, 6=33–35 years of age), consumption frequency (1=6 times or more/week, 2=3–5 times/week, 3=1–2 times/week, 4=1–3 times/month, 5=less than 1 time/month) and preference toward brands (0=not preferred, 1=preferred) and preferred shape (1=Triangle, 2=Round, 3=Strip, 4=Bite sized, 5=no preference) of tortilla chips, were also gathered.
2.3. Consumer testing
2.4. Color measurements
Based on the work of Dies (2000) who reported that 76% of US households purchase tortilla chips every 32 days, we assumed that 75% of the population in Northwest Arkansas (i.e. where the test was conducted) consumes tortilla chip products on a regular basis. The minimum sample size necessary to get a representative sample of the population was calculated to be 73 consumers using the formula Z pð1 pÞ=C2p (in this case, Z value Za=1.96 associated with 95% confidence level, the proportion P=0.75, and the confidence interval C2p 4 10%) (Rea & Parker, 1992). Since the consumer test was performed over a 2-day period, 80 consumers were selected in anticipation of second day no shows. The consumer panel was recruited by posting advertisements requesting participation in a salty snack consumer test. Consumers of these snack products between the ages of 18 and 35 interested in participating were asked to call. A phone screener was used to determine if
Five whole chips were randomly selected from each sample. The color of each whole chip was instrumentally evaluated using a Minolta CR-300 colorimeter (Minolta Co., Ltd., Osaka, Japan) with a 50 mm measuring head. The measuring head was placed into the center of each whole chip. Color values were measured in triplicate and recorded as averaged L*=whiteness (0=black, 100=white), a* (a*=greenness, +a*=redness) and b* (b*=blueness, +b*=yellowness). L*, a* and b*, referred as to instrumental color L*, a* and b*, respectively, were used as appearance attributes for external preference modeling.
2.2. Descriptive analysis
2.5. Statistical analysis The consumer response scores (Y) (overall acceptance and acceptance of appearance, flavor and texture, purchase intent, etc.) of tortilla chips were ordered values in
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Table 2 Frequency (%) of consumer overall acceptance and consumer acceptance of appearance, flavor, texture and saltiness for 11 tortilla chip productsa
Attribute
Scaleb
% of the number of consumers for white corn tortilla chipsc BYW
GMG
GUY
MED
MIS
MIT
OAK
SAN
TOB
TOM
TOR
Overall acceptance
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 0.0 3.8 11.3 13.8 13.8 30.0 26.3 1.3
5.0 5.0 8.8 13.8 10.0 23.8 16.3 13.8 3.8
1.3 2.5 6.3 17.5 7.5 21.3 22.5 20.0 1.3
3.8 7.5 7.5 18.8 8.8 20.0 25.0 6.3 2.5
1.3 2.5 6.3 12.5 3.8 18.8 26.3 22.5 6.3
0.0 3.8 2.5 10.0 5.0 8.8 36.3 25.0 8.8
6.3 3.8 6.3 17.7 7.6 16.5 27.8 10.1 3.8
0.0 0.0 0.0 7.5 6.3 7.5 33.8 38.8 6.3
0.0 0.0 3.8 3.8 3.8 12.5 18.8 43.8 13.8
5.0 1.3 3.8 6.3 12.5 12.5 30.0 21.3 7.5
0.0 2.5 1.3 2.5 5.0 15.0 26.3 30.0 17.5
Appearance
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 0.0 3.0 16.0 4.0 13.0 21.0 21.0 2.0
1.0 0.0 4.0 11.0 11.0 12.0 19.0 17.0 4.0
0.0 1.0 5.0 10.0 6.0 14.0 22.0 18.0 4.0
0.0 4.0 2.0 13.0 8.0 9.0 27.0 13.0 4.0
0.0 3.0 6.0 15.0 6.0 13.0 12.0 15.0 10.0
0.0 0.0 4.0 7.0 5.0 12.0 20.0 24.0 8.0
1.0 2.0 1.0 6.0 11.0 10.0 27.0 12.0 9.0
0.0 0.0 0.0 2.0 5.0 8.0 26.0 32.0 7.0
0.0 1.0 2.0 6.0 4.0 6.0 16.0 29.0 16.0
1.0 1.0 0.0 6.0 6.0 13.0 19.0 27.0 7.0
0.0 2.0 1.0 7.0 3.0 9.0 19.0 27.0 12.0
Flavor
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 0.0 6.3 13.8 10.0 13.8 22.5 28.8 5.0
5.1 7.6 7.6 16.5 12.7 17.7 16.5 12.7 3.8
1.3 1.3 8.8 22.5 8.8 21.3 17.5 16.3 2.5
7.5 10.0 8.8 18.8 6.3 22.5 15.0 10.0 1.3
2.5 3.8 7.5 6.3 6.3 23.8 21.3 21.3 7.5
0.0 1.3 6.3 6.3 8.8 15.0 25.0 27.5 10.0
8.9 11.4 6.3 19.0 10.1 13.9 17.7 8.9 3.8
0.0 0.0 1.3 6.3 7.5 8.8 27.5 36.3 12.5
0.0 0.0 2.5 3.8 3.8 17.5 21.3 33.8 17.5
1.3 5.0 5.0 16.3 15.0 12.5 16.3 21.3 7.5
0.0 2.5 0.0 6.3 3.8 18.8 20.0 35.0 13.8
Texture
Dislike extremely (1) Dislike very much (2) Dislike moderately (3) Dislike slightly (4) Neither dislike or like (5) Like slightly (6) Like moderately (7) Like very much (8) Like extremely (9)
0.0 1.3 2.5 12.5 1.3 12.5 28.8 31.3 10.0
3.8 6.3 6.3 26.6 8.9 15.2 21.5 10.1 1.3
0.0 0.0 8.8 16.3 11.3 13.8 27.5 20.0 2.5
1.3 7.5 1.3 18.8 8.8 15.0 27.5 17.5 2.5
0.0 1.3 3.8 5.0 8.8 17.5 22.5 31.3 10.0
0.0 1.3 5.0 15.0 5.0 15.0 25.0 25.0 8.8
1.3 2.6 5.1 7.7 9.0 19.2 28.2 21.8 5.1
0.0 0.0 0.0 3.8 7.5 13.8 23.8 35.0 16.3
0.0 0.0 0.0 2.5 5.1 16.5 17.7 38.0 20.3
0.0 3.8 2.5 11.4 15.2 11.4 21.5 27.8 6.3
0.0 1.3 1.3 0.0 6.3 8.8 23.8 38.8 20.0
Amount of salt
Much too low (1) Low (2) Just right (3) High (4) Much too high (5)
3.8 31.3 48.8 13.8 2.5
20.0 46.3 32.5 1.3 0.0
8.8 41.3 36.3 13.8 0.0
31.3 41.3 15.0 12.5 0.0
1.3 10.1 63.3 20.3 5.1
5.0 10.0 60.0 18.8 6.3
10.1 44.3 38.0 6.3 1.3
0.0 12.5 62.5 22.5 2.5
2.5 22.5 62.5 12.5 0.0
8.8 32.5 46.3 11.3 1.3
3.8 23.8 65.0 7.5 0.0
Purchase intent
Definitely would not buy (1) Probably would not buy (2) Maybe/maybe not buy (3) Probably would buy (4) Definitely would buy (5)
6.3 22.5 30.0 31.3 10.0
21.3 35.0 28.8 12.5 2.5
16.3 23.8 28.8 27.5 3.8
30.0 22.5 28.8 16.3 2.5
6.3 18.8 27.5 36.3 11.3
6.3 19.0 20.3 36.7 17.7
24.1 27.8 27.8 11.4 8.9
0.0 13.8 27.5 25.0 23.8
10.0 21.3 30.0 22.5 16.3
2.5 12.5 17.5 42.5 25.0
2.5 13.8 23.8 27.5 32.5
a
Total observations (n=80 consumers) for each tortilla chip sample. Frequency (%)=100number of consumers rating the category/n. A nine-point hedonic scale for consumer overall acceptance and acceptance of appearance, flavor and texture, a five-point Just About Right scale for the amount of salt (saltiness), and a five-point scale for purchase intent. c Sample name abbreviations can be found in Table 1. b
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a set of nine or five categories. Since the order of the categories is meaningful, the responses are ordinal categorical variables. Each of ordinal categorical variables has ordered categories and a frequency associated with each category. Both proportional odds models and OLS regression models can apply to the ordinal categorical variables, depending upon how the ordinal categorical variables are treated and what is required to be modeled. When the ordinal categorical responses are simply treated as continuous variables and modeling of the mean scores of the responses is of interest, OLS regression can apply if its assumptions are met. It was found in this study that the response scores (Y) for some of the products tested did not follow a normal distribution and therefore were not appropriate for significance testing using a standard analysis of variance or OLS regression (Jones & Wang, 2000). When the ordinal categorical responses are treated as ordinal categorical variables and the frequencies of the categories of the responses are of interest, proportional odds models are appropriate. The proportional odds models can also predict the mean scores of the response, which provides a basis for comparison with OLS regression models. Another advantage of proportional odds models is invariance to choice of response categories (Agresti, 1990). This means that when nine categories and three categories which were collapsed from the nine categories are used in parallel, similar conclusions will be reached (Agresti, 1990). This feature is useful in the case where nine categories need to be collapsed into three categories such as (dislike, neither dislike nor like, like) to determine the probability of ‘like’ or ‘dislike’. The proportional odds models are widely used to analyze the structure (frequencies) of ordered categorical data, do not require the normality assumption and can be mathematically expressed as (SAS OnlineDoc); Agresti, 1990]: ijk logit ijk ¼ log ¼ k þ X0ij 1 ijk
ijk where log is the log (i.e. loge) odds of 1 ijk response Yij (scores) being in category k or below (k=1,2,. . .,K1, with K=9 for a nine-point scale and K=5 for a five-point scale), also referred as to the logit. ijk=P(Y4k|Xij) is the probability that the categorical score (response Yij) rated by the ith consumer (i=1,2,. . .,80) will be in category k or below for tortilla chip product j (j=1,2,. . .,11), given a vector of independent variables/covariates Xij. k is an intercept parameter representing the logits of the cumulative response when the explanatory variables/covariates Xij are zero and 1424. . .4K1. is a vector of unknown parameters representing the effect of Xij on the response Y. The proportional odds assumption is
crucial for the proportional odds model (Jones & Wang, 2000). It is that, after fitting an intercept term for each logit, the effect of changing a value or level of a covariate is the same for each of the (K1) types of logit. Proportional odds models were fitted to the data using PROC LOGISTIC of SAS. The highest end of the rating scale (Y=9, i.e. Y=‘Like extremely’ for acceptance; Y=5, i.e. ‘Would buy definitely’ for purchase intent, or ‘Much too high’ for saltiness) was used to associate with the lowest level in the SAS response profile table, the probability of ‘Y=90 or ‘Y=50 was modeled in the proportional odds models. PROC LOGISTIC provides a Chi-square statistic (2) to test proportional odds assumption. The goodness-of-fit of a logistic model is measured using either the likelihood ratio (G2) or Pearson Chi-square statistic (2). Only G2 was used in this study. The null hypothesis for the goodness-of-fit test of a proportional odds model is that the expected cumulative frequencies from the proportional odds model agrees with the observed cumulative frequencies, namely that the model fits the data. The statistic G 2, defined as P 2 observed logðobserved=expectedÞ, is used as a goodness-of-fit test statistic to compare observed and expected cumulative frequencies. G2 is approximately a chi-square distribution with a degree of freedom (DF) (in PROC LOGISTIC of SAS, degree of freedom is computed as DF=mkq, where m is the number of subpopulation profiles determined by the number of distinct observations, k+1 is the number of response levels, q is the number of parameter estimated) (SAS OnlineDoc, SAS Version 8, SAS Institute Inc., Cary, NC). The P-value for G2 with DF is usually used for testing the null hypothesis. If the P-value for G2 from a proportional odds model is less than the pre-selected significance level (usually 0.05), the null hypothesis is rejected, indicating that the model does not fit. Otherwise, the null hypothesis is accepted, that is, the model fits. The pre-selected significance level of 0.05 was used in this study. If the model fits the data, it can be used to calculate the fitted/expected mean frequencies/probabilities of all levels of a response Y. For an ordinal response (more than two levels) such as consumer overall acceptance and acceptance of appearance, flavor or texture, the expected mean frequency/probability (Pk of observing level k) for product j (j=1,2,. . .,11) is calculated as follows: j1 ¼ P Yij ¼ 1 j Xij ¼ j2 ¼ P Yij ¼ 2 j Xij ¼
1 1þe
ð1 þ0 Xij Þ
1þe
ð2 þ0 Xij Þ
1
1
1þe
ð1 þ0 Xij Þ
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j3 ¼ P Yij ¼ 3 j Xij ¼
1 1þe
ð3 þ0 Xij Þ
1
1þe
ð2 þ0 Xij Þ
... jðK1Þ ¼ P Yij ¼ ðK 1Þ j Xij 1
¼ 1þe
ðK1 þ0 Xij Þ
1
1þe
jK ¼ P Yij ¼ K j Xij ¼ 1
ðK2 þ0 Xij Þ
1 1þe
ðK1 þ0 Xij Þ
By using the expected mean frequency/probability, the fitted/expected mean scores ðY j Þ of consumer response for product j (j=1,2,. . .,11) are calculated as: Y j ¼ j1 1 þ j2 2 þ j3 3 þ . . . þ jðK1Þ ðK 1Þ þ jK K ¼
K X jk k
and external preference modeling, principal components (continuous variables), together with the categorical variable of product shape (round, triangle and strip), were used as covariates (Xij) in the proportional odds models because the original sensory variables (that were continuous variables) were correlated. For internal preference modeling, principal components were extracted from consumer acceptance scores of appearance, flavor, texture and their interactions. For external preference modeling, principal components were extracted from the descriptive attributes prior to performing preference modeling of consumer overall acceptance and acceptance of appearance, flavor and texture. The SELECTION=BACKWARD option in PROC LOGISTIC was used to select significant covariates (principal components) (P < 0.05). The likelihood ratio G2=D1D0 (D1=deviance for the simple model, D0=deviance for the complex model) and backward elimination method were also used to select significant sensory variables (P < 0.05) in the significant principal components. Only the ‘optimal’ proportional odds models were reported in this paper.
k¼1
3. Results and discussion This equation implies that although the proportional odds model fits the cumulative probabilities of the response, the fitted mean scores of the response for each product can be derived indirectly from the fitted model. If OLS regression applies to the same response, the fitted mean scores for each product can also be obtained directly from the OLS regression model. R2 (coefficient of determination) and RMSE (root mean square error) are used in OLS regression to assess the goodness-of-fit of the model and can be calculated out using the observed and fitted mean scores of the response. Since the fitted mean scores of the response can be obtained from both OLS regression and proportional odds model, their goodness-of-fit can be compared using R2 and RMSE (denoted hereafter as R2score and RMSEscore). This provides a means for comparing proportional odds model with other regression models in terms of only the mean scores of the response. For modeling of the consumer overall acceptance and purchase intent, the product variable (11 tortilla chips products) together with demographic variables (gender, age group, preferred brand, preferred shape and consumption frequency) were used as covariates (Xij) in the proportional odds models. The covariates such as product, gender, preferred brand and preferred shape were categorical variables in the proportional odds models. Since the covariates of consumption frequency and age group were ordinal categorical variables, they were treated as continuous variables in the proportional odds models (i.e. assuming linear effects of the ordinal categorical variables on the response). However, for internal
3.1. Consumer acceptance The frequency of the consumer overall acceptance and acceptance of appearance, flavor, texture and amount of salt is presented in Table 2. It was evident that TOR had the highest overall acceptance frequency of ‘Like extremely’, followed by TOB. The consumer acceptance of appearance, flavor and texture of TOB was rated as ‘Like extremely’ by 16.0, 17.5 and 20.3% of the consumers, respectively. In contrast, only 4.0, 1.4 and 2.5% of the consumers rated the acceptance of appearance, flavor and texture of MED as ‘Like extremely’, respectively. In terms of the amount of salt, 60 to 65% of the consumers rated five products (MIT, MIS, TOB, TOR and SAN) as ‘Just about right’, whereas MED had the lowest rate (i.e. 15%). It was found that the ‘Just about right’ rates were associated with the salt content (Table 1). A salt content of 4% was found to be ‘Just about right’ for saltiness acceptance. TOR had the highest rate (i.e. 32.5%) of purchase intent as ‘Definitely would buy’, while MED again had the lowest rate (2.5%). The Chi-square (2) for testing the proportional odds assumption was 84.93, which was not significant with respect to a Chi-square distribution with 84 degrees of freedom (DF) (P=0.45). This suggests that the proportional odds assumption was satisfied. The likelihood ratio G2 was 2886.13 (DF=5836) with P 1.0, indicating that the proportional odds model adequately fitted the data. The parameterization used in the SAS system
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is one that leaves out the parameter for the baseline (TOR in this case) with which each product is compared. Hence, a positive parameter estimate () in Table 3 means that the compared product is preferred to TOR, and a negative value means that TOR was preferred. Based on the b estimates, SAN (0.24) was the most preferred product, while MED (1.47) was the least preferred one. It was evident from Table 3 that the probabilities (P > Chi-square) for the products BYW, MIT SAN, TOB and TOM were greater than 0.05, indicating that the products were not significantly different from TOR, while those for the remaining products were less than 0.05, suggesting significant difference in overall acceptance between the products and TOR. The odds ratios in Table 3 compare each product with TOR. Other odds ratios can be obtained. For example, the odds ratio between MED (least preferred) and SAN (most preferred) was 0.18, indicating that the odds of consumers liking rate for MED was 0.18 times the odds for SAN. The positive parameter estimate for age group suggested that age group was positively associated with liking. The odds ratio for age group means that the odds of consumer liking rate would increased by 8% for one unit increase in age group if holding other covariates constant. ‘Older’ consumers tended to give higher acceptance scores for tortilla chips than ‘younger’ ones. The odds ratios for
preferred brand showed that the odds of consumers liking non-preferred brand products were 0.58 times the odds of liking preferred brands. This indicated that although the chip samples were randomly presented without any indication of brand names, consumers could have recognized their preferred brand samples, maybe through shape, size, color, smell and texture of chips, which they are familiar with. Tostita’s brand was selected as a preferred brand by 90% of consumers. Similarly, Mission brand, Guy’s brand, Santita’s brand and the remaining brands were selected as a preferred brand by 41.2, 15.0, 12.5 and 0 to 1.2%, respectively. The proportional odds model also adequately fitted for purchase intent (P=0.33 for 2 of 39.15, DF=36; G2=2239.32, DF=2912, P 1.0). Product, preferred brand and gender were significant contributors to consumer purchase intent (Table 3). The odds that consumers ‘would buy’ non-preferred brand products were 0.50 times the odds that consumers ‘would buy’ preferred brands. The odds ratios for gender showed that the odds of ‘would buy’ the chips were 25.7% smaller for females than for males. The estimates indicated that consumers would buy SAN most if the effects of gender and preferred brand were partialed out, and MED was the least likely to be purchased. In this study, it was found that the proportional odds assumption was not satisfied with acceptance of appearance, flavor, tex-
Table 3 Parameter estimates and statistics for proportional odds models for consumer overall acceptance and purchase intent (see Appendix) Parametera
1 2 3 4 5 6 7 8 Product: BYW Product: GMG Product: GUY Product: MED Product: MIS Product: MIT Product: OAK Product: SAN Product: TOB Product: TOM Product: TOR Age group Preferred brand: No Preferred brand: Yes Gender: Female Gender: Male a
DF
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0
Overall acceptance
Purchase intent
Estimate
S.E.
Chi-square
P >Chi-square
2.17 0.24 1.01 1.76 2.22 3.19 3.94 4.80 0.47 1.28 1.00 1.47 0.73 0.33 1.21 0.24 0.18 0.43 0 0.07 0.54 0
0.26 0.24 0.24 0.25 0.25 0.27 0.29 0.34 0.34 0.34 0.32 0.34 0.30 0.30 0.34 0.33 0.29 0.34 – 0.04 0.20 –
67.43 0.98 17.09 50.18 76.92 142.82 186.35 201.49 1.99 14.44 9.66 18.95 5.92 1.18 12.84 0.56 0.41 1.62 – 4.50 6.90 –
<0.0001 0.3226 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.1586 0.0001 0.0019 <0.0001 0.015 0.2764 0.0003 0.4537 0.5223 0.203 – 0.0338 0.0086 –
Sample name abbreviations can be found in Table 1.
Odds ratio
0.62 0.28 0.37 0.23 0.48 0.72 0.30 1.28 1.20 0.65 1.00 1.08 0.58 1.00
Estimate
S.E.
Chi-square
P >Chi-square
Odds ratio
0.76 0.87 2.12 3.58
0.22 0.22 0.23 0.25
11.84 15.44 84.85 205.95
0.0006 <0.0001 <0.0001 <0.0001
0.37 1.53 1.01 1.59 0.46 0.24 1.41 0.35 0.01 0.40 0
0.34 0.34 0.33 0.34 0.30 0.30 0.34 0.33 0.29 0.34 –
1.21 20.06 9.54 21.59 2.29 0.62 16.91 1.16 0.00 1.42 –
0.2708 <0.0001 0.002 <0.0001 0.1299 0.43 <0.0001 0.2808 0.9687 0.2339 –
0.69 0.22 0.37 0.20 0.63 0.79 0.24 1.42 0.99 0.67 1.00
0.69 0 0.30 0
0.21 – 0.12 –
11.08 – 5.72 –
0.0009 – 0.0167 –
0.50 1.00 0.74 1.00
610
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ture and saltiness. This may be due to non-parallelism of the logits of each cumulative response among the chip products, suggesting the limitations of proportional odds models. 3.2. Prediction of overall acceptance from attribute acceptance: internal preference model The model for consumer overall acceptance using the principal components as covariates is presented in Table 4. The proportional odds assumption was satisfied (P=0.35 for 2 of 15.42 with DF=14). The goodness-of-fit statistic (G2=913.53, DF=1918, P 1.0) indicated that the model fitted the data well. Two principal components (PC1o and PC2o) were statistically significant. From the principal components analysis, PC1o and PC2o could be expressed as 0.60Flavor+0.53Texture+0.60AppearanceFlavor and 0.40Flavor+0.85Texture0.35AppearanceFlavor, respectively. Keep in mind that the important sensory variables (i.e. Flavor, Texture, and Appearance by Flavor) associated with the principal components were selected using the likelihood ratio (G2) and backward elimination. The parameter estimates for PC1o and PC2o were 2.56 and 0.76, respectively. In order to examine the effects of the original sensory variables on consumer overall acceptance, 2.56PC1o0.76PC2o was re-expressed as: 1.83Flavor+0.72Texture+1.81Appearance Flavor. The regression coefficients in this expression clearly show that the most influential sensory variable was flavor (1.83), followed by the interaction (1.81) of appearance by flavor and texture (0.72). The positive coefficients suggested that consumer overall acceptance had a positive association with the sensory variables of
flavor, appearance and texture. Based on the predicted mean probabilities, the predicted mean scores of consumer overall acceptance were calculated to be compared with the observed mean scores for the 11 tortilla chips (Fig. 1). The corresponding R2Score and RMSEScore values were 0.99 and 0.06 (Fig. 1), respectively, also indicating that the model predicted the mean scores well for consumer overall acceptance. R2score and RMSEscore are useful for comparison of the proportional odds model with other regression models in terms of fitting the mean scores of the response. For example, R2score and RMSEscore can be used to assess the goodness-of-fit of the proportional odds model for the mean scores against the goodness-of-fit of partial least squares regression model that is a popular tool for preference modeling (Meullenet et al., 2001). For purchase intent, the proportional odds model fitted adequately (G2=892.03, DF=1916, P 1.0; P=0.27 for 2 of 7.59, DF=6, Table 4). The model included two principal components, PC1p=0.48Appearance+0.61Flavor+0.63FlavorTexture, PC2p=0.88Appearance0.38Flavor0.30FlavorTexture. The parameter estimates () suggested that PC1p had more effect on the purchase intent than PC2p, which can be re-expressed as that flavor (1.46) was the most influential variable on consumer’s purchase intent (Table 4). The R2Score and RMSEScore values for purchase intent scores were 0.98 and 0.11, respectively. 3.3. Prediction of overall acceptance from descriptive profiles: external preference model Descriptive intensity means (data not shown, but reported by Meullenet et al., in press) for visual
Table 4 Parameter estimates and statistics for proportional odds model for internal preference mapping (see Appendix) Parametera
DF
Overall acceptance Estimate
S.E.
Purchase intent Chi-square
P >Chi-square
Odds ratio
Estimate
S.E.
Chi-square
1 6.22 0.24 658.96 <0.0001 3.91 0.17 542.23 1 2 1 2.75 0.15 347.59 <0.0001 1.09 0.11 96.44 1 0.42 0.12 12.39 0.0004 1.63 0.12 175.57 3 4 1 2.53 0.15 277.73 <0.0001 4.64 0.21 493.68 5 1 3.88 0.19 435.41 <0.0001 1 6.28 0.26 576.95 <0.0001 6 7 1 7.84 0.32 594.36 <0.0001 8 1 9.40 0.40 544.35 <0.0001 PC1o 1 2.56 0.10 719.52 <0.0001 12.96 1 0.76 0.10 54.85 <0.0001 0.47 PC2o Associated with the original sensory variables: 2.56PC1o0.76PC2o=1.83Flavor+0.72Texture+1.81AppearanceFlavor PC1p 2.04 0.09 573.03 PC2p 0.53 0.09 35.41 Associated with the original sensory variables: 2.04PC1p+0.53PC2p=0.52Appearance+1.46Flavor+1.43FlavorTexture a
P>Chi-square
Odds ratio
<0.0001 <0.0001 <0.0001 <0.0001
<0.0001 <0.0001
7.70 0.59
PC=principal component. PCi means the ith principal component. Subscripts (o and p) stand for overall acceptance and purchase intent, PC2o=0.40Flavor+0.85Texture0.35AppearanceFlavor, respectively. PC1o=0.60Flavor+0.53Texture+0.60Appearance Flavor, PC1p=0.48Appearance+0.61Flavor+0.63FlavorTexture, PC2p=0.88Appearance0.38Flavor0.30FlavorTexture.
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acceptance. The R2Score and RMSEScore values for the average scores of consumer purchase intent were 0.97 and 0.09, respectively, suggesting that the mean scores of purchase intent could be accurately predicted by the proportional odds model using salt aftertaste, crispness and instrumental color a*. 3.4. Prediction of tortilla chip flavor acceptance from flavor descriptors
Fig. 1. Predicted versus observed average consumer overall acceptance. Predicted average scores were obtained from consumer appearance, flavor and texture acceptance using a proportional odds model. Sample name abbreviations can be found in Table 1.
appearance, flavor, and texture attributes were used for external preference modeling. The modeling results showed that the proportional odds model adequately fitted the data for overall acceptance (2=9.25, DF=14, P=0.81; G2=89.99, DF=94, P=0.60). The parameter estimates are listed in Table 5. Two (PC1o and PC2o) out of three principal components were selected as important covariates, which equivalently says that one flavor descriptive attribute (salt aftertaste), one appearance attribute (instrumental color a*) and one texture descriptive attribute (crispness) were statistically significant contributors to the consumer overall acceptance of tortilla chips (Table 5). Appearance, flavor and texture descriptive attributes were included in the external preference model, confirming modeling results from the above internal preference modeling. It should not be surprising that salt aftertaste was the most important flavor attribute to the acceptance because American consumers like salt. Crispness was one of the most important texture attributes for chips including tortilla chips. As expected, it increased consumer overall acceptance, but its contribution to the overall acceptance was lower than that of salt aftertaste. Instrumental color a* negatively contributed consumer overall acceptance. The R2Score and RMSEScore values for the average scores of consumer overall acceptance were 0.95 and 0.16 (Fig. 2), respectively, indicating that the model could accurately predicted the mean scores of overall acceptance. The proportional odds model (Table 5) including two principal components (PC1p and PC2p) also adequately fitted the data for purchase intent (2=8.49, DF=6, P=0.20; G2=45.05, DF=46, P=0.48). Since salt aftertaste, crispness and instrumental color (a*) were associated with the principal components, they were also significant contributors to consumer purchase intent. These variables played similar roles in the model for purchase intent as they did in the model for overall
The proportional odds assumption was satisfied for flavor external preference modeling (2=27.56, DF=28, P=0.49). The likelihood ratio (G2=73.66, DF=84, P=0.78) indicated that the proportional odds model could adequately fit the flavor data. The first, third, fifth and sixth principal components (PC1f, PC3f, PC5f, PC6f) were selected as significant predictors in the model (Table 5). By replacing the principal components with the original sensory variables, it was found that toasted corn, salt aftertaste, toasted grain aftertaste and sweet aftertaste contributed to increased consumer acceptance of flavor while cardboard and grain complex decreased consumer flavor acceptance (Table 5). The R2Score and RMSEScore values for the average scores of consumer flavor acceptance were 0.99 and 0.09, respectively. 3.5. Prediction of tortilla chip texture acceptance from texture descriptors The proportional odds model also adequately fitted the texture data (2=31.79, DF=21, P=0.06; G2=85.29, DF=77, P=0.24). The first, second and third principal components (PC1t, PC2t, PC3t) were selected out of seven principal components as significant predictors in the model, indicating that the seven sensory texture variables were highly correlated. The texture descriptive variables/attributes of hardness, toothpack, crispness, oily film, moisture absorption, persist of crisp, loose particles were significant contributors to the consumer acceptance of tortilla chip texture (Table 5). The R2Score and RMSEScore values for the average scores of consumer texture acceptance for the tortilla chip products were 0.93 and 0.19, respectively. 3.6. Prediction of tortilla chip appearance acceptance from visual appearance descriptors The proportional odds model adequately fitted the data for appearance acceptance (2=40.47, DF=35, P=0.24; G2=90.78, DF=83, P=0.26). Two principal components (PC1a and PC2a) and product shape were selected as significant predictors in the model. When PC1a and PC2a were expressed by the original sensory variables, it was found that degree of whiteness
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Table 5 Parameter estimates for the proportional odds model for external preference modeling (see Appendix) Parametera
DF
Overall acceptanceb
Appearance acceptancec
Texture acceptancee
Purchase intentf
Chi-square
P > Chi- square
Estimate
Chi-square
P > Chi- square
Estimate
Chi-square
P >Chi- square
Estimate
Chi-square
P >Chi- square
Estimate
Chi-square
P >Chi- square
2.12 0.38 0.74 1.40 1.90 3.21 4.23 5.98
267.33 16.02 58.05 177.84 271.84 358.93 272.92 105.13
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
2.70 0.94 0.01 0.80 1.26 2.20 2.92 3.96
429.79 147.42 0.01 110.99 230.71 407.53 421.12 315.98
< 0.0001 < 0.0001 0.9248 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
2.45 0.61 0.47 1.19 1.71 2.90 3.72 5.37
415.11 69.85 42.89 215.12 336.34 409.47 329.43 142.33
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
2.01 0.40 0.83 2.26
388.08 31.108 117.76 413.11
< 0.0001 < 0.0001 < 0.0001 < 0.0001
0.17 0.25 0.85 0.30 0.73 0.00
6.79 11.73 14.90 2.95 19.52 –
0.0092 0.0006 0.0001 0.0860 < 0.0001 – 0.35 0.22 0.35 1.68
95.25 10.53 6.96 35.44
< 0.0001 0.0012 0.0083 < 0.0001 0.26 0.11 0.47
40.39 5.88 72.71
< 0.0001 0.0154 < 0.0001 125.85 17.90
< 0.0001 < 0.0001
1 1 1 1 1 1 1 1
2.84 0.93 0.30 1.04 1.49 2.46 3.21 4.07
415.84 147.08 17.84 176.28 290.76 419.67 390.25 289.04
< 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001
PC1o PC2o
1 1
0.50 0.20
106.58 9.42
< 0.0001 0.0021
PC2a PC3a PC4a Shape: round Shape: strip Shape: triangle
1 1 1 1 1 0
PC1f PC3f PC5f PC6f
1 1 1 1
PC1t PC2t PC3t
1 1 1
PC1p PC2p
1 1
0.55 0.28
PC=principal component, PCi=ith principal component, Subscripts (o, a, f, t and p) stand for acceptance of overall, appearance, flavor and texture, purchase intent, respectively. Information on Shape can be found in Table 1. Overall acceptance: PC1o=0.51SaltAftertaste+0.67Crispness0.55a*, PC2o=0.75SaltAftertaste0.03Crispness+0.66a*, 0.5PC1o+0.2PC2o=0.41SaltAftertaste+0.32Crispness0.14a*. c Appearance acceptance: PC2a=0.18DegreeOfWhiteness+0.06GrainFlecks0.32CharMarks+0.93a*, PC3a=0.65DegreeOfWhiteness+0.08GrainFlecks+0.75CharMarks+0.13a*, PC4a=0.52 DegreeOfWhiteness+0.77GrainFlecks+0.34CharMarks+0.17a*, 0.85PC2a+0.78PC3a+0.43PC4a=0.24DegreeOfWhiteness0.68GrainFlecks0.42CharMarks0.33a*. d Flavor acceptance: PC1f=0.46ToastedCorn+0.49SaltAftertaste0.45ToastedGrainAftertaste0.24SweetAftertaste0.39Cardboard+0.36GrainComplex, PC3f=0.16ToastedCorn+0.44SaltAftertaste0.40 ToastedGrain Aftertaste+0.69SweetAftertaste+0.06Cardboard0.37GrainComplex, PC5f=0.30ToastedCorn+0.74SaltAftertaste0.53ToastedGrainAftertaste0.26SweetAftertaste+0.09Cardboard0.03 GrainComplex, PC6f=0.48Toast0.48ToastedCorn+0.02SaltAftertaste0.41ToastedGrainAftertaste0.10SweetAftertaste+0.51Cardboard+0.57GrainComplex, 0.35PC1f+0.22PC3f+0.35PC5f1.68PC6f=0.84 ToastedCorn+ 0.50SaltAftertaste+0.63 ToastedGrainAftertaste+0.14SweetAftertaste0.95Cardboard0.93GrainComplex. e Texture acceptance: PC1t=0.34Hardness+0.17Toothpack+0.51Crispness+0.37OilyFilm0.43MoistAbsorption+0.51PersistOfCrisp+0.11LooseParticles, PC2t=0.43Hardness +0.56Toothpack0.32Crispness0.08OilyFilm0.29MoistAbsorption+0.12PersistOfCrisp+0.55LooseParticles, PC3t=0.45Hardness +0.33Toothpack+0.33Crispness0.54OilyFilm+0.40MoistAbsorption0.10PersistOfCrisp+0.35 LooseParticles, 0.26PC1t0.11PC2t+0.47PC3t=0.35Hardness +0.14Toothpack+0.32Crispness0.15OilyFilm+0.11MoistAbsorption+0.08PersistOfCrisp+0.13LooseParticles. f Purchase intent: PC1p=0.51SaltAftertaste+0.67Crispness0.55a*, PC2p=0.75SaltAftertaste0.03Crispness+0.66a*, 0.55PC1p+0.28PC2p=0.49SaltAftertaste+0.36Crispness0.12a*. b
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Estimate 1 2 3 4 5 6 7 8
a
Flavor acceptanced
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the consumer panel was drawn from the local population and may not be totally representative of the national population.
5. Uncited reference Shtatland et al., 2000
Acknowledgements Fig. 2. Predicted versus observed average consumer overall acceptance. Predicted average scores were obtained from sensory descriptive attributes using a proportional odds model. Sample name abbreviations can be found in Table 1.
The authors would like to thank Dr. James Dunn, Department of Mathematics, University of Arkansas for the assistance with the proportional odds modeling.
Appendix increased appearance acceptance, while grain flecks, char marks and instrumental color (a*) had negative impact on appearance acceptance. Product shape also played an important role in determining appearance acceptance. Triangle tortilla chips were most preferred by consumers, while strip chips were least preferred (Table 5). The R2Score and RMSEScore values for the mean scores of consumer appearance acceptance for the chips were 0.85 and 0.17, respectively.
4. Conclusions The present study demonstrated that proportional odds models offer sensory scientists an alternative choice for internal/external preference modeling. Use of principal components in proportional odds model can avoid the collinearity problem caused by correlation between sensory variables. Proportional odds models can model the structure of ordinal categorical responses and estimate the mean scores of the responses. Comparison of proportional odds model analysis with other regression models need to be performed in more details. The internal preference modeling revealed that flavor was the most important attribute to consumer overall acceptance. The external preference modeling showed potential for predicting consumer overall acceptance of tortilla chips using three descriptive attributes of salt aftertaste, crispness and instrumental color value a* as predictors. The research reported here provides useful information for developing an understanding of the drivers of tortilla chips consumer acceptance. The results must be interpreted within the limits of experimental conditions. In a real purchase situation, consumers probably pay less attention to information than in an experimental situation, and they can choose a product with a lower expected quality but with an attractive price (Siret & Issanchou, 2000). In addition,
*==EXAMPLES OF FITTING PROPORTIONAL ODDS MODELS TO OVERALL ACCEPTANCE DATA USING SAS PROCEDURES; *==THE RESULTS ARE PRESENTED IN TABLES 3,4 AND 5, RESPECTIVELY; *THE DATA FORMAT USED (ONLY A PORTION OF THE VARIABLES IS LISTED HERE); DATA ChipsData; INFILE ‘‘C:n>ChipsData.txt‘‘; INPUT Panlist Product$ Overall Appearance Flavor Texture Gender$ AgeGroup$ ConsumptionFrequency$ PreferredShape$ PreferredBrand$ AftertasteSalt Crispiness Color_a ProductShape$; RUN; *THE MODEL FOR OVERALL ACCEPTANCE (THE RESULTS ARE IN TABLE 3); PROC LOGISTIC DATA=ChipsData DESCENDING; CLASS Product Gender ConsumptionFrequency PreferredShape PreferredBrand/ PARAM=GLM; MODEL Overall=Product Gender PreferredShape PreferredBrand AgeGroup ConsumptionFrequency/ SELECTION=Backward SLS=0.05 SLE=0.10 LINK=Logit RSQUARE LACKFIT SCALE=None AGGREGATE;
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TITLE1 ‘POM: Overall acceptance=Product & Demographical Variables’; RUN;
*THE OPTIMAL MODEL FOR INTERNAL PREFERENCE MODELING FOR OVERALL ACCEPTANCE (THE RESULTS ARE IN TABLE 4); *--PRIN1:THE 1ST PRINCIPAL COMPONENT, PRIN2:THE 2ND PRINCIPAL COMPONENT,. . .; PROC PRINCOMP DATA=ChipsData OUT=PCSEx OUTSTAT=StatEx; VAR Flavor Texture Appearance*Flavor; RUN; PROC LOGISTIC DATA=PCSEx DESCENDING OUT=ParamsEx; MODEL Overall=PRIN1-PRIN3/ SELECTION=Backward SLS=0.05 SLE=0.10 LINK=Logit RSQUARE LACKFIT SCALE=None AGGREGATE; TITLE1 ‘Internal Preference Modeling For Overall Acceptance’; OUTPUT OUT=PredOverallEx(KEEP=Product _LEVEL_ Pred) P=Pred; RUN;
*THE OPTIMAL MODEL FOR EXTERNAL PREFERENCE MODELING FOR OVERALL ACCEPTANCE (THE RESULTS ARE IN TABLE 5); PROC PRINCOMP DATA=ChipsData OUT=PCSIn OUTSTAT=StatIn; VAR AftertasteSalt Crispiness Color_a; RUN; PROC LOGISTIC DATA=PCSIn DESCENDING OUT=ParamsEx; CLASS ProductShape/PARAM=GLM; MODEL Overall=PRIN1-PRIN3 ProductShape/SELECTION=Backward SLS=0.05 SLE=0.10 LINK=Logit RSQUARE LACKFIT SCALE=None AGGREGATE; TITLE1 ‘External Preference Modeling For Overall Acceptance’; OUTPUT OUT=PredOverallIn(KEEP=Product _LEVEL_ Pred) P=Pred; RUN;
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