Using a fractional model to measure the impact of antioxidant information, price, and liking on purchase intent for specialty potatoes

Food Quality and Preference 46 (2015) 66–78

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Food Quality and Preference journal homepage: www.elsevier.com/locate/foodqual

Using a fractional model to measure the impact of antioxidant information, price, and liking on purchase intent for specialty potatoes Catherine A. Durham a,⇑, Linda J. Wechsler b,1, Michael T. Morrissey b a b

Applied Economics, Food Innovation Center, Oregon State University, 1207 NW Naito Parkway, USA Food Science and Technology, Food Innovation Center, Oregon State University, 1207 NW Naito Parkway, USA

a r t i c l e

i n f o

Article history: Received 14 January 2015 Received in revised form 1 July 2015 Accepted 8 July 2015 Available online 8 July 2015 Keywords: Purchase intent Fractional Ordinal Health interest Antioxidants Potato Consumer test

a b s t r a c t A procedure for analyzing categorical purchase intent data from consumer tests is demonstrated using data from a test of fresh market specialty potato varieties. Due to the probabilistic nature of purchase intent a fractional model is based, just as a binary choice analysis using probit or logit would be, on a non-linear cumulative distribution function. The results from a fractional model are compared to an ordinal model. Participants in the consumer test evaluated six unreleased varieties and one commonly available variety of potato, the Yukon Gold. Four of the new varieties had colored red or purple flesh rated highly for antioxidant content. The effect of antioxidant information and other variables on the probability of purchase for red and purple potatoes was compared to the effect on the yellow potatoes using a fractional model and an ordinal model. Other variables include liking, price, gender, age, education, income, potato usage frequency, health interest, and food interest. As expected hedonic ratings and price had significant positive and negative effects respectively on purchase intent for both categories of potatoes. Antioxidant information, whether simple or detailed, increased purchase intent for the colorful potato varieties. Interactive variables between health interest and antioxidant information level demonstrate the impact of personal health interest in conjunction with the information. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Moskowitz, Muñoz, and Gacula (2008) report that purchase intent questions are typically not used by sensory analysts because it requires that the participant make a decision that goes beyond the sensory properties, nevertheless, purchase intent is of critical interest to marketers and quite often included in consumers tests. Other factors; such as price, convenience, advertising and promotions have all been demonstrated as important in actual purchasing. They note that a purchase intent question will provide little information not provided in a liking question unless accompanied by the knowledge they may receive at point of purchase. The marketing literature has extensively examined the ability of surveyed purchase intent responses to predict actual purchases using follow-up surveys. They have provided simple linear relationships that provide a downward modification of surveyed

⇑ Corresponding author. E-mail addresses: [email protected] (C.A. Durham), Michael. [email protected] (M.T. Morrissey). 1 Present address: Oregon Manufacturing Extension Partnership, 12909 SW 68th Parkway, Suite 140, Portland, OR 97223, USA. http://dx.doi.org/10.1016/j.foodqual.2015.07.007 0950-3293/Ó 2015 Elsevier Ltd. All rights reserved.

purchase intent which can be further adjusted with additional information about the product for example-durables versus non-durables. More complex models are based on the initial purchase intent and then modified with information about the marketing efforts planned. One of the most successful (Clancy, Krieg, & Wolf, 2006, p. 45) of the simulated test marketing systems, BASES, begins with the 5-point categorical purchase intent scale. In this paper we describe an approach to utilize categorical purchase intent questions accompanied by point of purchase type information in a consumer test to capture information about the impact of credence attributes such as nutritional information and consumer characteristics as well as sensory attributes. Two possible analytical methods, a fractional approach treating the categories as purchase intent probabilities and an ordinal approach treating them as an ordered choice, are described and compared in terms of ability to predict purchase intent and in what each tells us about how much each explanatory factor changes purchase intent. In comparison to alternatives these approaches fit well within a consumer test and provide a rigorous analytical procedure. Both approaches work well, but one provides for more direct interpretation and lends itself more readily to graphical representation.

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There are other useful approaches to examining choices with respect to complex purchase intent decisions. If the need is to examine several credence product attributes simultaneously such as brand, price, label details, and ingredient levels a choice experiment such as that utilized in Enneking, Neumann, and Henneberg (2007) is useful. Though choice experiments analyzed with the multinomial model are valuable for examination of multiple credence attributes, they are not fully compatible with a standard consumer test whose first priority is sensory evaluation. The approach developed here fits well into a multiple product test though, as with a choice experiment, fewer credence attributes can be examined unless more consumers are tested. 1.1. Background In the last decade research programs have been developing colored flesh potatoes at least partly in the interest of making their greater nutritional properties available. To encourage the adoption of these varieties by producers, and the use of them by consumers, it is important to examine consumer’s willingness to purchase these varieties and to examine whether providing information about the nutritional properties will assist in marketing those potatoes. It is also critical that a premium price can be obtained to produce and distribute these potatoes when costs to produce and distribute them are higher than for conventional varieties. This study examines these factors using data collected during a consumer test including both highly colored and more conventional yellow fleshed and skinned specialty potato varieties. Surveys conducted by the United States Potato Board (2002) indicated that 57.2% of consumers ranked quality, appearance, or color to be more important in their potato buying decision than price, with only 18.2% of consumers considering price the most important factor. Despite price not ranking as the most important by many it is still a critical or determining factor for nearly all consumers and helps to measure the importance of all other factors. Assuming that varieties introduced to the market meet basic consumer standards, the focus shifts to other factors that may influence purchase, and these factors can be intrinsic or extrinsic in nature (Di Monaco, Cavella, Torrieri, & Masi, 2007). For potatoes, intrinsic factors are those which are associated with their sensory properties (i.e. appearance, flavor, texture). Extrinsic factors lie outside of these basic characteristics, and can be in the form of information about cultivar name or origin, suggested preparations or recipes, price, packaging, nutritional properties, or potential health benefits. Out of these extrinsic factors, the impact of health benefits on purchase intent for fresh market potatoes has not been explored. Exploring the impact of health benefits on purchase intent is particularly relevant for colorful potato varieties, as they exhibit unique health properties associated with their pigment. Colorful potatoes have high levels of antioxidants, including anthocyanins, carotenoids, phenolics, and vitamin C (Brown, 2005; Woolfe, 1987). Red and purple (skin and flesh) potatoes contain the highest levels of these compounds (Lachman, Hamouz, & Orsak, 2005). Purple fleshed potatoes have ten times the anthocyanin content of red fleshed potatoes (Lewis, Walker, Lancaster, & Sutton, 1998). Purple skinned potatoes also have high levels of phenolic acids and purple fleshed potatoes have been reported to have twice the level of flavonoids as white fleshed potatoes (Lewis et al., 1998). Yellow (skin and flesh) potatoes have higher levels of carotenoids than white fleshed potatoes (Brown, Culley, Bonierbale, & Amoros, 2007; Brown, Culley, Yang, Durst, & Wrolstad, 2005; Tevini & Schonecker, 1986), and the deeper the color, the greater the antioxidant value (Iwanzik, Tevini, Stute, & Hilbert, 1983). Brown et al. (2005) studied red and purple potatoes with anthocyanin levels from 17 to 38 lg per 100 g. of potato, which they

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compare to strawberry varieties ranging from 15 to 25 reported by Clifford (2000) and ORAC level in percent compared to white flesh potatoes of 183–330 for red fleshed potatoes which they compare to red bell pepper, broccoli, and brussel sprouts at 229–316 (Cao, Sofic, & Prior, 1996). Several studies have examined the impact of health information on consumer choice using other analytical models. Ginon, Lohéac, Martin, Combris, and Issanchou (2009) assessed the impact of label information about fiber content and general information about the long-term health benefits of fiber on the price consumers were willing-to-pay for baguettes. The study revealed that label information had a positive effect on price, though this effect was only observed when the baguette received high hedonic scores. Baixauli, Salvador, Hough, and Fiszman (2008) explored the effect of information about fiber on consumer acceptance and purchase intent measured on 9-point scales using an advanced ANOVA technique for plain, whole meal, and fiber-enriched muffins. Fiber information did not have a significant effect on purchase intent for plain and fiber-enriched muffins, but did have a significant effect on whole meal muffins. A purchase intent scale for a new fat spread with a proven health benefit was compared to an established spread in a study by Bower, Saadat, and Whitten (2003). Information about the health benefits of the new fat spread had a significant effect on purchase intent, especially when combined with high hedonic scores. Each of these studies produces useful information about factors which have significant effects on purchase intent, but they do not provide the marginal impacts of each explanatory factor on the probability of purchase.

2. Materials and methods 2.1. Materials, participants, and test procedure Data for this analysis was collected as part of a consumer test to evaluate new varieties of specialty potatoes. A standard multiple-sample approach was used. All participants were recruited from a list of consumers living in the greater Portland metropolitan area provided by the Oregon State University Food Innovation Center where the consumer test was conducted. Participants were contacted by e-mail to take the online screener. Screener questions included usage questions about three vegetables to reduce focus on the potatoes, and included demographic and scheduling information. The screener asked potential participants a variety of questions regarding their liking, usage, and purchase of three vegetables, as well as four Likert scale questions to assess their attitudes on health and food. Questions regarding the consumption and use of squash and greens as well as of potatoes were asked in order to distract the potential participants from realizing the intent of the test and therefore falsifying their answers in order to qualify for the test. Participants were compensated $35 for their involvement in the study. Further details on the screener process are available in (Wechsler, 2010); participant selection is discussed with their related variables in Section 2.4. Participants tested samples in one of 10 partitioned taste test booths equipped with computers and touch screen monitors. Participant data was collected using Compusense Five (Version 5.0, Guelph, Ontario). Each consumer tested four potatoe varieties (two yellow fleshed, one red fleshed, and one purple fleshed) drawn from six new varieties and one commonly available variety. The groupings are shown in Table 1 which also provides details on the raw appearance of the varieties tested as well as the clone number and market name if known. One of the four tested by a consumer was always the commonly available yellow fleshed and skinned variety Yukon Gold, which provided a baseline for the sensory testing. Thus, though seven different varieties were

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Table 1 Potato varieties by presentation group. Variety #, Market Name (Current or Proposed) Group 1 POR02PG26-5, Smilin’ Eyes POR00068-11 POR01PG22-1, Amarosa Yukon Gold Group 2 POR02PG37-2, Yukon Nugget POR01PG161, Purple Fiesta POR01PG20-12, TerraRosa Yukon Gold

Skin/flesh color

Overall likingappearance score

Yellow, Red Eyes/ Yellow Purple/Purple white streaks Red/Red Yellow/ Yellow

2.16 ± 1.36a

Yellow, Red Eyes/ Yellow Purple/Purple Red/Red Yellow/ Yellow

1.75 ± 1.38b

0.93 ± 2.17b 1.25 ± 1.89b 2.38 ± 1.23a

0.50 ± 2.28c 2.22 ± 1.24ab 2.49 ± 1.27a

a, b, ab, c

different superscript letters in each column indicate significantly different results, p < 0.05.

Table 2 Information presented in three cards. Antioxidant Information

Content of Card*

None

Sample Sample Sample Sample

Simple (SINFO)

Colored flesh potatoes are high in antioxidants Sample 127 has yellow flesh Sample 913 has purple flesh Sample 485 has yellow flesh Sample 648 has red flesh

Detailed (DINFO)

Recent studies show that potatoes with darker yellow, red, and purple flesh have high antioxidant levels similar to other colored vegetables and fruits like red peppers, broccoli, and strawberries Sample 127 has yellow flesh Sample 913 has purple flesh Sample 485 has yellow flesh Sample 648 has red flesh

127 913 485 648

has has has has

yellow flesh purple flesh yellow flesh red flesh

* The sample numbers listed in this table are for the first set of potatoes; the second set used the same cards, with only the sample numbers changed.

used in the consumer test each consumer tasted only four of the seven. Since the Yukon Gold potato was used in both groups of consumers, it had 222 sensory observations and the six new varieties each had 111 sensory observations. Though this study focuses on the participants examination in a raw whole state, later questions in the consumer test were based on cooked samples so to facilitate preparation consumers were tested over four days. Consumers first rated each variety on a 9-point liking scale for overall appearance, followed by color, size, and shape in raw whole form. The purchase intent questions followed the standard sensory questions in a design intended to approximate a shopping situation, in which a consumer sees fresh market specialty potatoes side-by-side in their raw uncut state, makes an assessment of

how much they like the potatoes based on appearance, reads the information that may be presented to them at the point of purchase (possibly in the form of a display sign or on packaging) and then makes a decision to buy based on that information and price. This was simulated in the consumer test by providing them with one of three sets of product information on a laminated card, and then asking them to rate their willingness to purchase each potato on a 5-point willingness to buy category scale (‘Would definitely not buy’, ‘Would probably not buy’, ‘Might not buy/might buy’, ‘Would probably buy’, ‘Would definitely buy’) at a high price, a moderate price, and a low price while still viewing the four potatoes. The product information given to the consumers is a key part of the analysis because we are interested in examining whether the higher antioxidant of the newer colored flesh potatoes could be used to increase purchase intent for fresh market potatoes. The material on antioxidants varied across three versions of product information cards. As shown in the right-hand column of Table 2 all three cards included information about the flesh color of the potatoes along with its sample number. One information card had no additional information about antioxidants, one had the color information plus the simple statement about being high in antioxidants, the third had the color information and an antioxidant statement that included details associating the antioxidant levels with that of other colored vegetables and fruits like red peppers, broccoli, and strawberries. Table 3 reports the percentage of individuals that received each information card and the set of potatoes the individuals in the group tested. Participants were asked to rate purchase intent at three prices to better assess how much they valued each sample and to develop more information about how the probability of buying changed as price changed. To approximate a buying situation, in which they see products available at various prices, they were given a range of current prices from which to compare the product. Due to the multiple sample presentation they were asked about all four potatoes on a single screen, this also increased the efficiency of presentation. The top of the screen statement was ‘‘Currently, specialty potatoes are selling for $0.79–$2.79/lb locally. Would you BUY each of these potatoes if their price was $2.99/lb?’’ No further detail on the type of potato in local markets was provided to the participants. For the question at one price the sample numbers and then a five point category scale (category text in Table 4) of purchase intent were viewed for each of the four varieties on one screen. The Yukon Gold potato, though unlabeled, would have been familiar to most. By stating that these were specialty potatoes we expected participants to infer that the potatoes they viewed fell in that category. The specialty potato designation includes any potato that is not a standard baking or frying potatoes exemplified by larger, darker, thicker skinned russet potatoes. On the next screen/question the price was changed to $1.89/lb, and in the last the price was $0.79/lb. Note that the first price, $2.99, they saw was higher than the $2.79 end of the range in the statement on current market prices. The price range statement was valid for the range of specialty potatoes observed in the local the market at the time of test. These include prices for Yukon Gold (mostly $0.89–0.99/lb), red-skinned potatoes ($0.79–0.89/lb for standard size and

Table 3 Percentage of observations of individuals receiving each of the two combinations of potato varieties tested and information level received. Antioxidant level in information sets Varieties sampled by sub-group (Y = Yellow, P = Purple, R = Red) Purple Fiesta(P), Terra Rosa(R), Yukon Nugget (Y), Yukon Gold(Y) POR00068-11(P), Amarosa(R), Smilin’ Eyes(Y), Yukon Gold(Y)

No antioxidant information 17.6% 16.7%

Single sentence SINFO 14.9% 16.7%

Two sentence DINFO 17.6% 16.7%

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Table 4 Variables (descriptions, names and statistics) used in purchase intent model, n = 2664 (consumer characteristics from 222 participants, testing 4 samples each, at each of 3 prices). Dependent variables

Choice

Purchase intent Ordinal category name

Would definitely not buy DNB Proportions

Would probably not buy PNB

Might not buy/might buy MNMB

Would probably buy PB

Would definitely buy DB

Overall Yellow Red/purple

0.130 0.137 0.125 Name

0.156 0.155 0.158 Mean

0.227 0.230 0.224 Std. Dev.

0.223 0.230 0.217 Min.

0.264 0.248 0.276 Max.

Fractional purchase intent Explanatory variables Potato is yellow fleshed Purchase price Liking of appearance, overall Food interest PC score Health interest PC score Antioxidant information, simple Health interestsimple info Antioxidant information, detailed Health interestdetailed info Age in 10ths High school (degree or less) Some college Advanced degree Income midpoints in $100,000 Potatoes used at least once a week

PINTENT

0.582

0.340

0

1

NOTCOLOR PRICE LIKING FOODI HLTHI SINFO HLTHISINFO DINFO HLTHIDINFO AGE EDUHS EDU2YR EDUADV INCOME USAGE

0.500 1.890 1.709 0.000 0.000 0.315 0.167 0.342 0.041 4.091 0.135 0.275 0.189 0.456 0.518

0.500 0.898 1.786 0.998 0.998 0.465 0.571 0.475 0.639 1.387 0.342 0.446 0.392 0.289 0.500

0.000 0.790 4.000 2.957 3.263 0.000 3.186 0.000 3.263 1.900 0.000 0.000 0.000 0.095 0.000

1.000 2.990 4.000 1.811 2.032 1.000 2.032 1.000 1.898 7.500 1.000 1.000 1.000 1.100 1.000

$1.99/lb for baby, the smallest size), and ($1.33–1.59/lb) for fingerlings, observed at conventional supermarkets. These were all sold loose rather than in bags2, and all had yellow or white flesh. Red, purple, and blue fleshed potatoes were rare at that time, and available at few stores at that time of year, and the high price used in the range, $2.79, was based on an organic blue fleshed potato at a specialty grocer. Prices have changed little since that period for yellow and white fleshed potatoes. Yukon Golds can be found selling at $0.99/ pound and fingerlings at 1.79/ pound. Red-skinned potatoes can be found at $0.69/ pound, baby red-skinned at $3.79/1.5 lb and small sized Yukon Gold at $1.69/pound. At a specialty store non-organic purple potatoes were observed at $1.49. Organic Amarosa (one of the red fleshed varieties used in this consumer test, now commercial), as well as Ruby Crescent, and Russian Banana which are fingerling varieties were available in 1.5 lb bags for 3.99 per bag.3 Of course our concern in developing the top end of the range was not to provide a perfect limit to the possible prices, but to give individuals a good idea of what the alternatives might be. The prices we select to ask the consumers for purchase intent are chosen to help us evaluate what the consumer thinks these attributes are worth, and how that changes across individuals. We want low and high prices to be able to examine premiums, and also to evaluate whether the new varieties can be successful if the production and distribution costs result in higher prices for those varieties. An advantage to using results from a purchase intent scale rather than binary yes–no is that participants can respond with greater subtlety. For example a consumer’s purchase intent could change, presumably rise, as prices decline, even if it doesn’t change whether they would have selected yes or no in a binary question. Since a consumer’s individual characteristics also affect their purchase decisions, usage frequency (how often they cook potatoes 2 In US supermarkets it is common for potatoes to be sold loose, though usually bags are available for some varieties. Traditionally, these are bags of 3–10 lb of potatoes at lower prices. In recent years some producers have made smaller bags of unique (typically colored flesh and/or fingerling types) specialty potatoes available from 1 to 1.5 lb in size, generally at higher prices. 3 The bag format seems to have become quite common for unique potato sales, presumably in aid of identity preservation. It also is common to see a mix of different flesh colors sold in a bag.

at home), level of interest in health and food, and demographics (age, gender, income, and education level) were included in the model as variables explaining purchase intent. Consumer information was collected from both the screener and questions from the final stage of the consumer test ballot. Questions on demographics and personal attitudes (health, food, nutrition) included on the consumer test were asked at the end of the ballot to ensure that they did not influence participants’ assessment of the antioxidant information or other sensory factors. 2.2. Method of analysis A single model of purchase intent was estimated with different parameters for the two color groups. Fourteen explanatory variables were of interest for their impact on consumer purchase intent. The impact of these variables on the dependent variable – purchase intent – was evaluated using a non-linear model based on a cumulative distribution function (CDF). While many analysts are familiar with this approach for binary choices using a probit or logit model, it has surprisingly not been adopted for categorical purchase intent, and in fact many analysts still take a 5-point purchase intent scale turn it into binary responses and then analyze the result. However, if the buying response categories are assigned as a probability (in a proportion form for the CDF) the dependent variable can be treated as continuous, and a fractional model (Papke & Wooldridge, 1996) estimated. If the categories do not lend themselves to such treatment the logical choice is an ordinal model which treats the dependent variable as ordered and does not assume a particular distance between ordered responses. Finally, we could consider the data as non-ordered and that the probability of choosing one level is only related in the sense that the probabilities add up to one, and the parameter estimates for each are associated only in that sense, and not in a clear direction. In this instance the dependent variable is clearly ordered and related to a probability of buying, thus a non-ordered choice model is inappropriate (Greene & Hensher, 2010; Williams, 2006). Thus, the two models that will be compared are an ordered model and a fractional model. An example of what these two models produce can be seen in Fig. 1. The solid black line shows the fractional models prediction of the probability of purchasing

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non-linear CDFs. Fractional models are typically estimated in these packages using Papke and Wooldridge’s (1996) quasi-likelihood form which maximizes the Bernoulli log-likelihood function:

Max ln L ¼

N X fyi  ln½Gðzi Þ þ ð1  yi Þ  ln½1  Gðzi Þg

ð1Þ

i¼1

where yi is the fractional dependent variable for a single observation and G() is the cumulative distribution function utilized. In Eqs. (1) and (2) the subscript ‘i’ denotes a single observation and zi will be a linear function of variables such xi’b with xi and b the vectors of explanatory variables for individual i and the parameters to be estimated. Ordinal models maximize the log-likelihood function in (2).

Max ln L ¼

J N X X mij ln½Gðlj  zi Þ  Gðlj1  zi Þ

ð2Þ

i¼1 j¼0

Fig. 1. Five category selection probabilities for ordinal compared to fractional model single probability as purchase intent changes with respect to liking.

versus liking. The five broken lines show the predictions for selecting each of the 5 ordered categories against liking. This graphic difference introduces the advantages of a fractional model over an ordinal model which are parsimony and ease of interpretation. Though it only requires the estimation of j-2 (with j as the number of categories) more parameters than the fractional model, the ordinal model predicts a probability for each response level separately. In evaluating results one must consider which responses are of most interest, in a buying context this is likely to be ‘Would definitely buy’ with some interest in ‘Would probably buy’. A key question is whether the ordinal model can provide additional information. The advantage of the ordinal model is that one does not assign a particular value or relationship between categories other than the ordinal nature, the model allows the data to determine the threshold over which the respondents are shifting from one category to the next. An ordinal approach is necessary when the categories bear no clear interval relationship such as ‘‘__terrible __ horrible __ awful __fair __slightly good __all right __reasonably good’’ (Friedman & Amoo, 1999). While the fractional model would not require that they be the same distance, it does require an assumption regarding that distance, and in this case the assumption of equal distances is reasonable and the assignment of definitely would not buy to a 0.0 proportion, might buy/might not buy to a 0.5 proportion, and definitely would buy to 1.0 proportion is natural. A cumulative normal distribution (CDF) has the principal property of a probability based dependent variable: when appropriately scaled, predictions are limited to the range between 0 and 1. The functional form underlying the CDF is usually based on the normal (probit model) or logistic distribution (logit model). The choice between probit and logit should be based on goodness of fit. These CDFs are frequently used to analyze dichotomous (0–1) binary data and in the context of consumer purchasing evaluation, where the consumer is making a choice between two food products or buying and not buying (Johnston, Wessells, Donath, & Asche, 2001; Nayga, Aiew, & Nichols, 2005), but they are also suitable for examining purchase intent on a scale or as a proportion. 2.3. Analytical model Most econometric packages can estimate models for ordinal and fractional dependent variables. Nlogit 5.0 (Greene, 2012) software, used in this analysis of both the fractional and ordinal models, allows for fractional dependent variables using a number of

where mij = 1 if yi = j, i.e. if that choice occurred, and 0 otherwise, yi is the dependent variable represented numerically from 0 to J, and lj is an estimated threshold parameter. If zi is less than l0 then yi = 0, if l0 < zi < l1 yi = 1, and so on until the highest category J is predicted if zi > lJ1. G() is again the cumulative distribution function utilized. As previously discussed the two most commonly used distribution functions are the normal and logistic, the cumulative logistic and cumulative normal distribution functions are:

logistic :Gðzi Þ ¼ 1=ð1 þ ezi Þ normal :Gðzi Þ ¼

1 2p

Z

zi

et

2 =2

ð3Þ dt

ð4Þ

1

in which ‘e’ represents the base of natural logarithms and zi will be an index or function of variables. The relationship between z and the probability as defined by these CDFs can be seen in Fig. 2. From these CDFs, if z represents a function such as x’b the marginal effect, or change in purchase intent, PI, for a one unit change in an explanatory variable, xh, or the oPI/oxh is calculated as bhg(x’b) where g is the PDF (probability density function) associated with the CDF utilized. Marginal effects are generally reported at the mean values of the variables in x, or by averaging the calculation over the entire set of observations. For the ordinal model there are marginal affects for each purchase intent category. 2.4. Model variables Table 4 provides statistics on the ordinal and fractional versions of the dependent variables and explanatory variables. There are 2664 purchase intent observations based on 222 participants, examining 4 potatoes each, with purchase intent queried at 3 prices. For the analytical model 63 of the 2664 observations on purchase intent are removed because they displayed higher purchase intent at a higher price for the same potato by the same individual. This reduction had no appreciable impact on parameter estimates and marginal effect estimates, though it improved the percentage of correct predictions. Of the 63 purchase intent observations showing higher purchase intent at a higher price for the same potato by the same individual, 52 occurred between the first presented highest price and the second price level. Twenty of these occurrences were from five people on all four potatoes. These five got all four intent relationships correct in terms of not having higher purchase intent when moving from the middle to the lowest price, from which it might be inferred that the second question made them pay more attention to price. In Table 4 the ordinal dependent variable is presented overall and by color category, and overall in its fractional version. Beyond the intercept and NOCOLOR shifter there are fourteen

C.A. Durham et al. / Food Quality and Preference 46 (2015) 66–78

Fig. 2. Relationship between Z and fractional probability for logistic and normal distributions.

explanatory variables including two additional interactive variables in the model. With each of these applied separately to yellow and colored flesh varieties in the purchase intent models and additional intercept shifter for color group, there are thirty parameters to be estimated. In this analysis, for both the ordinal and fractional models the zi as used in Eqs. (1) and (2) is composed as follows with explanatory variables in capitals and parameters in Greek letters: zijk ¼ a þ x y  NOCOLOR þ

X

Dc  ðqc PRICEijk þ cc RAWLIKij þ gc HLTHIi þ kc SINFOi

c¼r;y

þ pc HLTHIi  SINFOi þ sc DINFOi þ uc HLTHIi  DINFOi þ dc ri Þ þ uijk

ð5Þ

The subscripts are expanded up to ijk. Though some explanatory variables are constant by individual so the subscript is only an i, RAWLIK varies for each potato variety for each individual so the subscript is ij, but PRICE has subscript ijk because there are k = 3 observations by price for each individual for each variety. The superscripts on parameters in Eq. (5) represent red/purple (‘r’) or yellow (‘y’) varieties, respectively. The Dc are binary (0, 1) terms with c = r for red and purple and c = y for yellow potatoes. Capitalized terms are explanatory variables described in Section 2.4. The Greek letters represent unknown parameters that need to be estimated with d a vector of parameters and r a vector of levels for seven model variables representing participant characteristics other than health interest and uijk is an error term. Seven variables are binary (NOCOLOR, SINFO, DINFO, EDUHS, EDU2YR, EDUADV, and USAGE), having a value of 0 or 1. NOCOLOR, in (5), is an intercept shifter for the yellow varieties. SINFO (simple antioxidant information) and DINFO (detailed antioxidant information) were 0 if the participant did not receive this information and 1 if the participant did. USAGE was 1 if the frequency of cooking potatoes at home was equal to or greater than once a week, and 0 if a few times a month, consumers with lower usage were screened out. EDUHS was 1 if the highest level of education attended by a participant was high school (combining categories of high school degree or less). EDU2YR was 1 if the highest level of education achieved was some college (combining categories for current student in a 2-year/4-year college or 2-year college degree). EDUADV was 1 if the highest level of

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education achieved was an advanced degree (combining current student in an advanced degree program or an advanced degree earned). A 4-year college degree was chosen as the baseline case because it was the most frequently observed level of education for participants. Usage and education categories were combined to eliminate small categories and reduce parameters. The rest of the explanatory variables had a range of values. Overall liking for raw potato appearance (LIKING) had nine possible values, depending on the category selected on the 9-point hedonic scale, with the lowest being ‘dislike extremely’ and highest being ‘like extremely’. A statistical comparison of liking by color is included in Table 4. For the model these values were transformed to range from 4 (lowest) to 4 (highest). This transformation results in a zero value for the central ‘neither like nor dislike’ response. Purchase intent was queried at three PRICE levels ($2.99, $1.89, and $0.79) by each consumer for each potato. This triples the number of observations on purchase intent and allows price impact to be examined. The range given was based on conventional and specialty grocery store prices for fresh market potatoes sold in Portland, Oregon at the time the research was conducted. Values for AGE were entered by participants in the screener. These values were transformed by dividing AGE by 10. For INCOME, participants selected a range which contained their total household income. The midpoints of these ranges, divided by 100,000, were used in estimating the model. Level of interest in health and food issues were captured by attitude scores developed from the questions in Table 5. These were answered on a five point agreement or likelihood scale, ranging from ‘strongly agree’ to ‘strongly disagree’ and ‘never true’ to ‘always true’. Four of the questions in Table 5 (superscripted with a d) came from the screener: these were first used to ensure a good distribution of response in the attitude scores that were to be developed. In the screener response population those with high food or nutrition interest (Hf and Hn) were identified based on whether the two food or the two nutrition related questions respectively were both answered often true or always true. If they answered in the bottom three categories they were designated as moderate/low interest (Mf and Mn). Eight groups are created when these are interacted with the USAGE variable. Participants were randomly recruited from each group for the consumer test in a stratified sample. The resulting participants sample was 33.7% in HnHf and 33.3% in MnMf, and 32.9% in HnMf or MnHf. For the analysis these interests are assessed more comprehensively using all of the questions in Table 5 as variables4 in a principal components analysis (PCA). Individuals responses to the questions listed in the first column were analyzed using the Varimax rotation method with Kaiser normalization. The rotation converged in seven iterations with two components extracted that together explained 97.2% of the variance. PCA was performed using the factor procedure in Statistical Analysis Software (SAS, Version 9.2, Cary, NC). The first component, labeled FOODI, suggested by the rotated matrix results of the PCA could be interpreted as measuring where an individual falls on a cooking and ‘‘foodie’’ scale from questions with a higher number in the FOODI column than the HLTHI column. The second component, HLTHI, can be interpreted as representing health and nutrition attitudes. Questions that contributed most to HLTHI or to FOODI are noted with ‘H’ and ‘F’ respectively in the Score Category column. Individual placement is calculated as a principal component score which has mean of 0 and standard

4 PCA terminology usually describes these variables as the ‘columns’ and the individuals as the ‘rows’ of the matrix for the analysis. There are 222 rows and 18 columns for this PCA. As an aid to interpreting the components the rotated component matrix as shown in Table 4 is produced in which the ‘variables’ are displayed in rows and the extracted components are in columns.

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Table 5 Variables used in principal components analysis to develop scores of participant interest in food and health and resulting Rotated Component Matrix. Type of Likert scale used in the question is T for ‘very true’, often true’, ‘sometimes true’, ‘rarely true’, and ‘never true’ questions and A for ’strongly agree’, ’agree’, ’neither agree nor disagree’, ’disagree’, and ’strongly disagree’ questions. For score category, F indicates questions contributing most strongly to the FOODI and H to the HLTHI score, respectively. Variables for PCA (Likert questions)

Type

Score category

Rotated Component Matrix

I seek out new recipes to try at home. I read articles or watch shows about food and/or cookingd I read magazines about food (e.g. Gourmet, Saveur, Bon Appetit)a I look for new types of foods to try.a,d I enjoy cooking. I enjoy watching cooking shows. I value new experiences and exotic flavors in food. I seek out seasonal and local ingredients.c I place great value on the quality and flavor of food. I like to eat out in restaurants that feature local and seasonal food.c I am interested in information about my health.b I am concerned about my health all the time.b I worry that there are harmful chemicals in my food.b Before buying a new food item, I read the ingredient listing and/or nutritional information.d I try to avoid high levels of cholesterol in my diet. I eat five servings of fruits and vegetables a day.d Good health takes active participation on my part.b I read more health related articles than I did 3 years ago.b

T T

F F

0.817 0.813

0.154 0.070

T

F

0.746

0.146

T A A A

F F F F

0.739 0.730 0.687 0.652

0.210 0.007 0.121 0.158

T

F

0.573

0.378

A

F

0.560

0.235

T

F

0.531

0.312

T

H

0.041

0.725

A

H

0.023

0.689

A

H

0.207

0.664

T

H

0.066

0.663

A

H

0.006

0.589

T

H

0.276

0.563

A

H

0.126

0.525

A

H

0.152

0.395

FOODI

a b c d

HLTHI

From McCluskey, Durham, and Horn (2009). From the Wellness Scale, Kraft and Goodell (1993). From Gwin, Durham, Miller, and Colonna (2012). Used for sample stratification.

deviation of 1 for the sample. Despite a fairly small consumer sample, the composition of both component scores was substantiated by Cronbach’s alpha values, 0.741 for the HLTHI and 0.835 for the FOODI set which were greater than the generally recommended minimum of 0.7 (Cronbach, 1951). Two additional variables are created to examine how or whether differences in health interest and antioxidant information interact in their effect on purchase intent. These variables are created by multiplying the health score with the two antioxidant information variables (HLTHISINFO, HLTHIDINFO). 3. Results

3.2. Fractional and Ordinal Model Goodness of Fit Normal and logistic CDFs were tested for both the ordinal and fractional models. Likelihood based measures favor the normal distribution for both the fractional and ordinal models, but the difference was negligible, with log-likelihoods of 1461.0 and 1459.4 for the logistic and normal CDF for the fractional model and 3339.0 and 3334.7 for the ordinal model. However, direct comparison of the fractional and ordinal models is not possible using likelihood measures, so several measures to evaluate how well the models predict purchase intent category are examined. Because the fractional model predicts a probability value of purchase rather than one of 5 categories of purchase intent it is necessary to assign each probability value to one of the 5 categories. Two range assignments are used for the comparison. The simplest default is to assign each of the 5 categories to a range of 20%. A prediction between 0 and less than 0.2 would be associated with would definitely not buy category, 0.2–0.4 would be assigned to ‘would probably not buy’ and so on. When we use these values to allocate predictions to 5 categories the fractional logistic predicts 42.2% correctly and the fractional normal with predicts 42.3% correctly. We also examine whether predicted intent is best allocated by the midpoints between the probability assignments of 0, 0.25, 0.5, 0.75, and 1 using 0.125, 0.375, 0.625, and 0.875 as the cutoffs, with these assignments the fractional logistic predicts 37.1% correctly and the fractional normal predicts 37.5% correctly. The 20% allocations seem to make more sense with these combinations of CDF as an assessment of individual’s intent. In both allocations the normal distribution was superior for the fractional model. The ordinal model could be expected to do somewhat better in these assignments, because of the three additional threshold parameters included which in essence allows the model to improve fit using these as shifters. The ordinal model does best using the logistic CDF making 43.2% correct predictions and the normal CDF getting 42.9%. To better examine the two approaches a repeated random sampling cross-validation procedure is also undertaken. For the sample in this population the strongest test seemed to be to randomly remove individuals5 from the sample rather than observations. To accomplish this random uniform numbers on the 0,1 interval were generated for each individual. All individuals with a random number less than 0.1 became the hold-out sample, removing approximately 10% in each run of the model.6 Both the fractional and ordinal models were then estimated using the logistic (superior in OPSI fit measure discussed below) CDF with the remaining individuals. The parameters from those models were used to predict choice for the held-out individuals. This process was replicated 1000 times with new draws from the uniform distribution to determine the individuals held out.7 Correct out of sample predictions were remarkably close to the original full sample correct predictions with the fractional model averaging 40.2% correct and the ordinal model 41.2%, with standard deviations of 3.9 and 4.0, respectively. In 33.4% of the replications the fractional model actually had a greater number of correct predictions than the ordinal model from the same subsample, with an equal number of predictions in 4.8%. However, it is important to look at how well the fractional versus ordinal models predict by purchase intent category rather than

3.1. Participant demographics Table 4 includes the statistics for the variables included in the model. Demographic variables other than age were collected in categorical questions. Most of the participants had a combined income that fell within the range of $20,000 to $39,999 per year (32%) or $40,000 to $59,999 per year (24%). The omitted (base) education category, a four year college degree, was 40.1% of the sample. In addition, of the 222 participants, 59% were female.

5 This approach ensures that that individuals used to generate the parameters aren’t among those individuals whose purchase intent is being predicted out-of-sample. 6 Note that the number of observations removed was not identical in each run, both because a random generated number was used to select those held-out and because some individuals had some observations dropped as discussed at the beginning of Section 2.4. 7 This procedure will not ensure that all individuals are held out at least once, because it is random selection with replacement.

C.A. Durham et al. / Food Quality and Preference 46 (2015) 66–78

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rect. More convincingly, with the hold-out sample cross-validations the ordinal model was only better than the fractional model at predicting the C3D sum in one of the thousand subsamples (0.1%). The C3D average in the cross validation replications for the ordinal models is 78.3%, compared to 82.5% correct or next to correct for the fractional replications. In other words, from this data set the ordinal model predicted 21.7% of observations more than one purchase intent category away from the actual purchase intent, compared to the fractional model with only 17.5%. 3.3. Parameter estimates and marginal effects

Fig. 3. Percentage correctly predicted by purchase intent selection, fractional and ordinal models.

overall. Fig. 3 charts how well the fractional and ordinal models predict the purchase intent categories for both normal and logistic distributions. From this we see that the distribution of correct predictions is higher at the ends and middle for the ordinal, but quite a bit lower in the two off center categories. As many analysts of choice models have pointed out, a model’s ability should really be measured by how much more often it predicts correctly than would be predicted by chance. This is the idea behind the overall prediction success index (OPSI) based on McFadden (1977). OPSI is the sum of the differences between percentage correctly predicted in a category Njj and the percentage that N:: 2

Þ where N.. is the would be predicted in that category by chance ðN:j N:: total number in the estimation, N.j is the actual number that selected category j, and Njj is the number correctly predicted in category j. Thus each difference represents the amount of improvement for that category.8

r¼

"  2 # Njj N:j  j¼1 N:: N::

XJ

ð6Þ

In Eq. (6) the first part of the difference in brackets is the proportion shown as correctly predicted in Fig. 3, the second is the actual share in that category squared. The fractional by 20% ranges allocation results in an OPSI of 0.1907 using the normal CDF and 0.1912 for the logistic. For the ordinal model the OPSI is 0.1539 using a normal CDF and 0.1830 using the logistic CDF. Thus by the OPSI measure the fractional model (20% range assignments) using the logistic CDF performs best overall and the logistic CDF performs better for both fractional and ordinal. While the OPSI does a better job of considering predictions, some important information is still overlooked. Because this data is ordered, there is an additional goodness of fit implication for getting it nearly right, that is, if not a perfect prediction, by predicting the next nearest purchase intent category rather than one further away. This can be calculated as the sum of the center three-diagonals (C3D) from a cross-tabulation of prediction versus correct outcomes divided by the sample size. As a final comparison then, the fractional model (logistic CDF) gets a total 84.3% of predictions correct or nearly correct and the more accurate of the ordinal models (also using the logistic CDF) has 80.2% correct or next to cor8

It may be helpful to note that the squaring creates a measure of correct by chance predictions so if a category is 30% of the sample, randomly assigning 30% of all the predictions to that category would be expected to predict 0.3⁄0.3 = 0.09 or 9% correct in the model from that category. The OPSI rises as predictions improve versus chance.

As described above, a single model for purchase intent was estimated for all potatoes but separate parameters were included for the red/purple potatoes and for the yellow potatoes. This allowed for direct testing for significant differences in parameters for the two groups. The results are reported in Table 6 with parameter estimates for the two color groups in columns to facilitate comparison. Wald tests (Engle, 1983) were used to examine which parameter estimates are significantly different for the two color groups. The examination of differences is of interest when at least one is significant. In this model of purchase intent nearly all of the differences are significant between color groups. As noted earlier, when using a non-linear CDF, partial effects to assess the impact of explanatory variables on the probability of the choice must be calculated as a function of the PDF and the parameter. However, if the explanatory variable is a dummy (binary) variable, the partial effect is calculated as the difference between predicted choice when the value of the binary variable is 1 and when the value of the binary variable is 0. For the ordinal model the partial effect measures the proportional increase or decrease in probability of each choice category rather than overall probability of purchase as in the fractional model. Thus unlike the fractional or binary model which both produce one set of partial effects, the ordinal model produces probabilities, and thus partial effects as well, for each of the ordered choices, in this case five. Because they are the most relevant, only the partial effects of the explanatory variables on the choices of ‘would probably buy’ and ‘would definitely buy’ are reported. A key issue in examining the partial effects is whether the ordinal model tells us anything more than the fractional model, a simple comparison of the PINTENT and ‘Would Definitely Buy’ marginal effects gives nearly the same answer, and all of the significant ‘Would Definitely Buy’ marginal effects from the ordinal model are within the confidence interval of the fractional marginal effects. The continuous explanatory variables in the model that are significant at p < 0.05 are also all within 5% of the value of the ‘Would Definitely Buy’ marginal effects. Thus both models are providing similar information about the impact of the various explanatory variables on purchase intent. The following sections will be based on the fractional model results. 3.3.1. Color Color itself was included as a shifter of purchase intent and the parameter estimate is shown in the INTERCEPT row in the yellow columns for Table 6 and its effect on purchase intent shown as NOTCOLOR in Table 7. The marginal effect indicates an 11.1% decrease in PINTENT when the potato was not one of the colored varieties. The color attribute was quite significant, indicating that the uniqueness of the potatoes led to a higher willingness to purchase the colored potatoes, separate from liking or price. 3.3.2. Price and liking For both red/purple and yellow potatoes, PRICE and LIKING had significant (p < 0.01) effects on PINTENT. For a one unit ($1) increase in PRICE, there was an 18.6% lower probability of purchase

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Table 6 Fractional and ordinal logistic parameter estimates (n = 2601). Variable

Red and purple Fractional

INTERCEPTa PRICE RAWLIKE FOODI HLTHI SINFOb HLTHISINFO DINFOb HLTHIDINFO AGE EDUHSb EDU2YRb EDUADVb INCOMEb USEAGEb

Fractional

Ordinal

Parameter (br)

Std. Error

Parameter (br)

Std. Error

Parameter (by)

Std. Error

Parameter (by)

Std. Error

(br)(by)

(br)(by)

1.959⁄⁄⁄ 0.851⁄⁄⁄ 0.363⁄⁄⁄ 0.257⁄⁄⁄ 0.144⁄ 0.426⁄⁄⁄ 0.591⁄⁄⁄ 0.694⁄⁄⁄ 0.236⁄⁄⁄ 0.160⁄⁄⁄ 0.025 0.018 0.094 0.066 0.105

0.161 0.043 0.021 0.039 0.076 0.093 0.100 0.090 0.089 0.030 0.120 0.096 0.104 0.145 0.075 1.323⁄⁄⁄ 2.780⁄⁄⁄ 4.243⁄⁄⁄

4.845⁄⁄⁄ 1.217⁄⁄⁄ 0.520⁄⁄⁄ 0.354⁄⁄⁄ 0.195⁄ 0.632⁄⁄⁄ 0.866⁄⁄⁄ 0.931⁄⁄⁄ 0.349⁄⁄⁄ 0.214⁄⁄⁄ 0.025 0.030 0.155 0.112 0.182⁄ 0.063 0.076 0.087

0.236 0.062 0.030 0.056 0.109 0.133 0.146 0.132 0.125 0.043 0.168 0.138 0.148 0.209 0.106

0.703⁄⁄⁄ 0.971⁄⁄⁄ 0.301⁄⁄⁄ 0.127⁄⁄⁄ 0.059 0.059 0.008 0.242⁄⁄⁄ 0.035 0.048 0.094 0.303⁄⁄⁄ 0.372⁄⁄⁄ 0.174 0.143⁄

0.233 0.042 0.031 0.043 0.072 0.094 0.100 0.093 0.099 0.032 0.121 0.099 0.111 0.146 0.078

0.894⁄⁄⁄ 1.438⁄⁄⁄ 0.435⁄⁄⁄ 0.179⁄⁄⁄ 0.078 0.109 0.009 0.359⁄⁄⁄ 0.006 0.070 0.119 0.414⁄⁄⁄ 0.538⁄⁄⁄ 0.236 0.234⁄⁄

0.344 0.063 0.046 0.066 0.102 0.137 0.143 0.136 0.1449 0.047 0.180 0.145 0.162 0.215 0.114

0.120⁄⁄ 0.062⁄ 0.131⁄⁄ 0.203⁄ 0.367⁄⁄⁄ 0.599⁄⁄⁄ 0.452⁄⁄⁄ 0.271⁄⁄ 0.209⁄⁄⁄ 0.119 0.284⁄⁄ 0.466⁄⁄⁄ 0.240 0.248⁄⁄

0.221⁄⁄⁄ 0.085 0.175⁄⁄ 0.273⁄ 0.523⁄⁄⁄ 0.857⁄⁄⁄ 0.573⁄⁄⁄ 0.355⁄ 0.284⁄⁄⁄ 0.145 0.385⁄ 0.693⁄⁄⁄ 0.348 0.416⁄⁄⁄

l0 l1 l3 Log-L Function Log-L(r) ⁄ ⁄⁄

,

a b c

Wald testsc

Yellow Ordinal

1461.0 1763.0

Fractional

Ordinal

3339.0 4097.5

, and ⁄⁄⁄ indicate significance at p < 0.10, 0.05, and 0.01, respectively. INTERCEPT row parameter estimate in yellow potato columns is for NOTCOLOR. Variable is a binary (0–1) variable. Significant Wald tests indicate difference in response from explanatory variable for red/purple versus yellow fleshed potatoes.

Table 7 Marginal effects are change in probability of buying for fractional model and change in probability of selecting each of the two highest purchase intent categories for ordinal model: PB = ‘Would probably buy’ and DB = ‘Would definitely buy’. Partials are calculated for each observation and then averaged. Variable

Red/purple Fractional PINTENT

NOTCOLOR PRICE RAWLIKE FOODI HLTHI SINFOb HLTHISINFO DINFOb HLTHIDINFO AGE EDUHSb EDU2YRb EDUADVb INCOMEb USEAGEb

Yellow Ordinal PB

a

a

DB

Fractional

Ordinal

PINTENT

PBa

⁄⁄⁄

0.160⁄⁄⁄ 0.070⁄⁄⁄ 0.047⁄⁄⁄ 0.028⁄ 0.078⁄⁄⁄ 0.111⁄⁄⁄ 0.120⁄⁄⁄ 0.047⁄⁄⁄ 0.034⁄⁄⁄ 0.007 0.001 0.022 0.021 0.024

0.025⁄⁄⁄ 0.011⁄⁄⁄ 0.007⁄⁄⁄ 0.004⁄ 0.012⁄ 0.017⁄⁄⁄ 0.015⁄⁄⁄ 0.007⁄⁄⁄ 0.004⁄⁄⁄ 0.001 0.001 0.004 0.002 0.005

0.158⁄⁄⁄ 0.068⁄⁄⁄ 0.046⁄⁄⁄ 0.025⁄ 0.091⁄⁄⁄ 0.113⁄⁄⁄ 0.137⁄⁄⁄ 0.045⁄⁄⁄ 0.028⁄⁄⁄ 0.003 0.004 0.022 0.015 0.025⁄

0.111 0.186⁄⁄⁄ 0.056⁄⁄⁄ 0.024⁄⁄⁄ 0.012 0.009 0.002 0.040⁄⁄ 0.006 0.005 0.017 0.047⁄⁄ 0.069⁄⁄⁄ 0.034 0.024

DBa ⁄⁄⁄

0.022 0.043⁄⁄⁄ 0.013⁄⁄⁄ 0.005⁄⁄⁄ 0.002 0.003 0.000 0.008⁄⁄⁄ 0.000 0.002 0.004 0.008⁄⁄ 0.018⁄⁄⁄ 0.007 0.006⁄

0.122⁄⁄ 0.188⁄⁄⁄ 0.057⁄⁄⁄ 0.023⁄⁄⁄ 0.010 0.015 0.001 0.050⁄⁄ 0.001 0.009 0.016 0.059⁄⁄⁄ 0.070⁄⁄⁄ 0.031 0.032⁄⁄

⁄ ⁄⁄

, and ⁄⁄⁄ indicate significance at p < 0.10, 0.05, and 0.01, respectively. Partial Effects for the fractional model are change in purchase intent as a fraction of when the explanatory variable increases by 1 unit. For the ordinal choices it is the change in probability of the specific category being chosen. These are displayed for ‘Would probably buy’, PB, and ‘Would definitely buy’, DB. b Partial effect for dummy variables for the fractional model the E[PINTENT|d = 1]  E[PINTENT|d = 0]; for the ordinal model PINTENT is replaced by probability of choosing PB or DB. ,

a

for yellow potatoes and a 16.0% lower probability of purchase for red/purple potatoes. Participant liking ratings for the overall appearance of the raw whole potatoes had a significant positive effect on the probability of purchase for both yellow and red/purple potatoes. This was not surprising, as sensory affective qualities such as appearance, taste, or smell are basic motivators for consumer willingness to try a food (Fallon & Rozin, 1983; Martins, Pelchat, & Pliner, 1997). For a one unit increase in LIKING, there was a 7.0% higher probability of purchase for red and for yellow 5.6%. The effect of liking on PINTENT for the fractional model is shown in Fig. 2 as a solid line. While this study emphasizes other factors it should not be overlooked that price and liking across their range of value are without doubt the most important.

3.3.3. Food interest FOODI had a significant effect on PINTENT for red and purple potatoes at the p < 0.01 levels, but was not significant for the yellow potatoes. For a one standard deviation increase in FOODI, there was a 4.7% higher probability of purchase for red/purple potatoes. 3.3.4. Health interest and antioxidant information Among this set of explanatory variables HLTHI, SINFO, DINFO, HLTHISINFO, and HLTHIDINFO only DINFO had a significant impact on yellow potatoes. For the yellow potatoes, DINFO had a smaller positive significant effect on purchase intent than it did for the colored potatoes (4% v. a 12% increase). The detailed information states ’darker yellow, red, and purple flesh potatoes have

C.A. Durham et al. / Food Quality and Preference 46 (2015) 66–78

high antioxidant levels’. The significant positive result for the yellow potatoes may indicate that some participants associated the potatoes described as yellow fleshed with higher antioxidants. The results for red/purple potatoes are interesting and complex. When participants did not receive any antioxidant information those with a 1 unit (1 standard deviation) higher than average value on HLTHI would have a 2.8% lower probability of purchase (p = 0.052), indicating that there is a slight negative response to the colored potatoes by individuals of this type. However, there is a significant positive effect when interacted with antioxidant information which offsets the negative. Independently, both SINFO and DINFO had a significant effect on PINTENT for the red/purple potatoes at the p < 0.01 levels. When the value for the binary variable changed from 0 to 1 for SINFO, there was a 7.8% higher probability of purchase for red/purple potatoes. For an individual that is one standard deviation higher on the health score, the sum effect of the simple information and HLTHI would increase purchase intent level by 18.9%. When the value for the binary variable changed from 0 to 1 for DINFO, the probability of purchase for red/purple potatoes was 12.0% higher.

3.3.5. Demographic variables The demographic variables that had a significant effect on purchase intent were AGE on red/purple potatoes at p < 0.01, EDU2YR and EDUADV on yellow potatoes at p < 0.01. For a 10 year increase in age, purchase intent is predicted to be 3.4% lower for red/purple potatoes. Those with an advanced degree (EDUADV) a 6.9% lower purchase intent is predicted for the yellow potatoes. EDU2YR is in the opposite direction with a 4.7% higher purchase intent for yellow potatoes than the baseline four year college degree group. While positive, the 1.7% impact estimated for yellow potatoes for EDUHS is not significant. This finding is somewhat surprising given the significant value for EDU2YR. Though USAGE was only marginally significant for yellow it was significantly different between the two color categories, those with high USAGE having their purchase intent slightly reduced for colored potatoes and slightly higher for yellow potatoes than those with low USAGE. Differences in gender were also tested, but the variable was dropped due to extremely low, insignificant parameter estimates.

4. Discussion 4.1. Fractional and ordinal models The ordinal and fractional models were identical with respect to signs of the variables and only one parameter with a different significance level. Despite the three extra parameters ability to predict categories correctly was only slightly better for the ordinal model, predicting 43.2% correctly compared to the fractional at 42.2% with the full sample, and 41.2% v. 40.2% of the time in the 1000 out of sample predictions. Furthermore, the three-diagonal (C3D) statistic introduced here demonstrates that the fractional model keeps predictions closer to the actual overall. The unevenness of correct allocation to categories demonstrated by the ordinal model is a common finding. Ordinal models often miss categories all together in favor of predicting a large category more often. The OPSI, which measures how much more often the model is predicting correctly compared to predicting the average, produces a higher value for the fractional model supporting the idea that the ordinal model is in essence getting more predictions right by a sort of guessing. Verbeke (2015), in a footnote, discusses such an outcome regarding the use of an ordinal model in modeling a 5-point category purchase intent scale when more than 65% of responses were in the two bottom categories. A fractional

75

model offers a reasonable alternative without requiring a collapse of the data into fewer categories. 4.2. Price, health interest, and information relationships In Fig. 4 the effect of price on PINTENT and in Fig. 5 the effect of HLTHI is compared across antioxidant information. Each line plots the fractional probability given by the logistic CDF (Eq. (3)) as the specified variables change. All variables not specified in the figures are held at their average value in creating the plot. The basic higher PINTENT at each price for the red/purple potatoes is shown by the dotted dark lines compared to the light dotted line, and the way in which that willingness changes when receiving health information (SINFO dark dashed line, DINFO dark solid line). In Fig. 4 the price impact on purchase intent is predicted from $0.79 to $2.99, the range used in the survey questions. Considering the price effect, rather than the probability changes it can be observed that to have at least a 75% probability of purchase the price for yellow potatoes would need to be less than a $1.00, but a price of a $1.65 achieves the same 75% probability for the red/purple potatoes without information as $2.15 and $2.45 do with the simple and detailed antioxidant information. Thus, a major jump was observed simply because the potatoes were unique and an additional $0.40–0.70 is added from the antioxidant information. As shown in the graph the average person only has about a 65% possibility of buying the colored potatoes even with the detailed information at the 2.99 price. While this may or may not be the market price for the colored flesh potatoes, consider that all of these graphical comparisons are made at average LIKING, which was like slightly, and with the FOODI scale at its average of zero, and an age of about 41 years. There are combinations of these significant consumer characteristics such as younger, with higher FOODI and/or HLTHI, and or greater liking for the appearance that lead to predicted purchase intent in the highest category even at the highest price examined. In Fig. 5 we see the same overall shifts for antioxidant information for the average participant but there are differences as HLTHI changes. Model results show that the simple and detailed antioxidant information had a significant positive effect on the probability of purchase for the red/purple potatoes, and DINFO has smaller though significant effect for the yellow potatoes. Based on the information given to them, the participants would have associated increased levels of antioxidants with color. Additionally, for the simple information, the meaning of the word ‘colorful’ was not explained, but for the detailed statement, colors indicating high antioxidant levels were stated explicitly (‘darker yellow, red, and purple’). This is one reason why purchase intent for the red/purple potatoes may have been more affected by detailed than simple information, by solidifying the association between increased color and high antioxidant levels. Stating that ‘research studies’ were involved in the ‘high antioxidant levels’ claim for colorful potatoes may also have increased the credibility of the detailed statement for participants. This is in contrast to the simple information, which did not provide participants with any source or background for the claim. Comparing colorful potatoes to other colorful fruits and vegetables (‘broccoli’ and ‘strawberries’) may have been more or as important, associating the ‘high antioxidant levels’ claim by referencing foods familiar to consumers that are frequently noted as particularly healthful. Either or both of these types of extra information may be critical to consumer purchase intent. We would also note that a question in the survey, ‘‘Do you consider yourself well informed about the possible benefits of eating foods high in antioxidants?’’ with possible responses ‘‘Very well informed’’ (3.6%),’’ Somewhat informed’’ (62.2%), and ‘‘Not at all

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Fig. 4. Fractional model predicted purchase intent as price rises for different levels of antioxidant information for the average participant with average liking rating.

informed (34.2%)’’ was examined for inclusion as a binary variable, ‘Very well’/’Somewhat’ versus ‘Not at all’, and a levels variable (0, .5, 1) and was not significant, suggesting that prior knowledge of antioxidants was not impacting purchase intent toward these potatoes. Focus groups indicated that consumers did not associate antioxidants with potatoes (Wechsler, 2010). However, those answering ‘‘Not at all informed’’ had an average HLTHI score of 0.538, compared to 0.233 for the ‘Somewhat’ group and 1.081 for the ‘Very Well’ group. Thus the predicted purchase intent for the low HLTHI level on the left of Fig. 5 represents this group fairly well. The linkage of the two information sets to health interest is particularly informative. As seen in Fig. 5, when those who receive no antioxidant statement were high on the health interest scale their

purchase intent was considerably lower than if they expressed less health interest. This result seems to indicate that at least some of those (the effect, though large was only significant at p = .0611) with strong health interests were somewhat worried about the dark colored potatoes. However, for those who got antioxidant information as their score on the health scale increased, their purchase intent does as well. As can be seen by the crossing of the Red-Detailed Info and Red-Simple Info lines the effect of the two levels of information have about the same effect for those with high-levels of HLTHI. We interpret this as due to those with higher HLTHI having greater knowledge regarding antioxidants thus requiring less explanation. Alternatively, a person with low HLTHI = 1 that got only simple information were no more likely to purchase the colored potatoes than those receiving no information, indicating lack of knowledge about antioxidants. In fact the predicted impact of the SINFO antioxidant message is reduced even further as HLTHI becomes more negative. The figure also shows that DINFO information was necessary to get the more average individual (HLTHI = 0) to the same level of purchase intent as SINFO for an individual high on the health interest scale. Beyond health interest, the variables linked to individual participants that had a significant effect on probability of purchase included food interest, age, and an advanced degree of education. If a participant had a strong interest in food (scoring higher, on average, in response to the ‘food’ category of the Likert scale questions in Table 5), this had a significant (p < 0.01) positive effect on probability of purchase for red/purple potatoes. For consumers with a high food interest, sensitivity to price can be superseded by a higher utility from novelty, which in this case was the novel color of the potatoes. Note however that willingness to pay for the colored potatoes was higher for all individuals as denoted by the significantly higher intercept term, versus the yellow potatoes. This reflects that the average consumer was willing to pay more for the red and purple varieties given equal liking. This may be due to the novelty or a recognition that one may need to pay more for a less widely available type of potato. The older the participant, the less likely they would be to buy the red/purple potatoes. Since age only had a significant (p < 0.01) effect on red/purple potatoes and not on yellow potatoes, it is not greater price sensitivity on the part of older participants that causes the shift, because the age parameter should have been significant for both potato types if that was the case. Instead, the observed effect was linked to specific characteristics of the purple and red potatoes. Since the purple and red potatoes were novel in appearance, the observed effect may have been due to food neophobia, which has been found to increase with age (Meiselman, King, & Gillette, 2010). Older participants may have been less willing to purchase the red and purple varieties due to their unfamiliar coloration. Having an advanced degree or being a student in an advanced degree program lowered the probability of purchase for yellow potatoes. The cause of this is unknown; it may be due to greater reluctance to eat potatoes due to health perceptions. Finally, more frequent consumers (USEAGE) raises purchase intent slightly for yellow potatoes. However, the participant population was limited to individuals that consumed potatoes at home at least once a month. It would be useful to see a response from less frequent potato users.

5. Conclusions 5.1. Purchase intent in consumer tests Fig. 5. Fractional model predicted purchase intent as health concern score rises for different levels of antioxidant information for the average participant with average liking rating and price.

With respect to analysis, these approaches have the potential to effectively utilize information from, without interfering with, standard consumer tests. Purchase intent could be measured either

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after visual hedonic ratings are completed or after hedonic ratings for taste, or both. Using hedonic ratings after tasting would allow for better consideration of potential repeat buyers. A simple adjustment in methods would be to assign range percentages to the purchase intent categories; this change would provide guidance to the test participant and enable a better analysis of the prediction categories for the fractional model versus the ordinal model. However, the range ends are a fairly arbitrary decision on the researcher’s part at present, and it would be better if the range offered was similar to consumer’s typical perception of ranges. A long-term approach might be to survey consumers about what ranges they would assign to each of the categories commonly in use; this would be useful in examining existing data and provide guidance for what ranges ought to be added to future purchase intent categories. In this context, finally note that when considered from the other direction the interpretation of the ordinal categories is no better than the assignment of probabilities in the fractional. Consumers have different ideas about what the category means to them in likelihood of purchase and thus the prediction of purchase category is also problematic. 5.2. Fractional, ordinal, and multinomial analysis This study investigated the use of fractional and ordinal models for analysis of expanded purchase intent questions included in consumer tests. In terms of parsimony and ease of interpretation, the fractional model is an improvement on the alternative ordinal model. In terms of identifying significant parameter and the important marginal effects of the explanatory variables the findings are essentially the same for the fractional model and the meaningful ordinal definitely buy category. To improve testing of the goodness of fit of models from the fractional approach we make one suggestion for immediate use but feel that further research could make the ordinal and fractional model easier to compare. A choice-based model in which consumers choose between two or more products with different attributes, as mentioned in the introduction, could also be used to examine the impact of antioxidant information and consumer characteristics. Choice based models have the main benefit of being able to examine several credence attributes for a product. They are particularly useful for looking at products like computers and mobile phones, or examining the relative value of organic and local foods simultaneously. To collect information on these multiple attributes does require larger populations and/or longer surveys. The approach developed in this analysis, using purchase intent as the dependent variable, fits more readily into a consumer test, and has advantages in ease of interpretation and graphical representation for appropriate attributes and consumer characteristics. Both approaches are based on a utility model of consumer choice, and both can be used to look at price premiums for attributes and how those vary by consumer characteristics. 5.3. Purchase intent for colored fresh potatoes and antioxidant information This study investigated the effect of information about antioxidants on consumer purchase intent for colorful potato varieties. The study found that information about antioxidants affects purchase intent for red and purple colored varieties, thus providing a potential tool for differentiation and promotion of varieties that are similar in appearance. This finding is especially relevant since red and purple potatoes receive mixed responses from consumers when evaluated on the basis of appearance alone (Jemison, Sexton, & Camire, 2008). This study also confirms that hedonic assessment and price are important factors affecting purchase intent of colorful

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potatoes, and these should be carefully considered when introducing new varieties to the fresh market. Consumer variables, such as age, advanced levels of education, interest in food, and interest in health also affected purchase intent for potatoes, and this information can be used to identify target markets. The level of interest in food and in health may be higher in this study because the sample is limited to consumers living in the Portland metropolitan area. However, the recruitment of individuals lower on these scales and their inclusion as explanatory variables will assist in looking at other types of consumers. As noted earlier, the representation of high school or less education group in particular is fairly small which may have something to do with its lack of significance in the models.

Acknowledgements This work was partly supported by the Oregon Potato Commission through a grant to the Oregon State University Agricultural Research Foundation for ‘‘Identification of Potato Characteristics for Culinary Uses.’’ The authors thank Bill Brewer, director of the Oregon Potato Commission, and Steve James of the Oregon State University Potato Breeding and Genetics Program whose program supplied the potatoes used in the consumer test. We also thank the two anonymous reviewers whose comments/suggestions helped improve and clarify this manuscript.

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