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Using item response theory to examine gambling attitudes and beliefs
Personality and Individual Differences 36 (2004) 1515–1529 www.elsevier.com/locate/paid
Using item response theory to examine gambling attitudes and beliefs David R. Strong a
a,*
, Robert B. Breen b, C.W. Lejuez
c
Brown University and Butler Hospital, 345 Blackstone Boulevard, Providence, RI 02906, USA b Brown University and Rhode Island Hospital, USA c University of Maryland, College Park, USA Received 23 August 2002; received in revised form 8 April 2003; accepted 8 June 2003
Abstract The gambling attitudes and beliefs scale (GABS: Breen & Zuckerman, 1999) was designed to assess a latent affinity for gambling. Using methods based in item response theory we demonstrated how a reduced set of GABS items maintained their relative severity and discriminated similarly when used among nonproblem gambling students selected to represent low levels of gambling behavior (n ¼ 487) and when used clinically among treatment seeking pathological gamblers (n ¼ 234). This stability increases confidence both in the construct measured by the GABS and in the ability to assess levels of gambling affinity across disparate ranges of gambling-problem severity. The GABS also demonstrated incremental validity in predicting increases in the frequency of gambling behavior among non-problem gambling students beyond that explained by an index of gambling-problem severity. Implications for assessment of gambling affinity across pathological and nonpathological gamblers are discussed. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Gambling; Gambling attitudes; Gambling beliefs; Item response theory; Gambling affinity
1. Introduction The United States is currently in the midst of a period of widespread expansion in the availability of legal gambling. The prevalence of pathological gambling (PG) has increased along with this expansion (Shaffer, Hall, & Bilt, 1997; Volberg, 1996; Wallish, 1996; Welte, Barnes, Wieczorek,
*
Corresponding author. Tel.: +1-401-455-6479; fax: +1-401-455-6424. E-mail address: [email protected] (D.R. Strong).
0191-8869/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.paid.2003.06.001
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Tidwell, & Parker, 2002). Effective measurement of positive interest and attitudes towards gambling is needed before we can better understand clinically how attitudinal shifts may be related to the maintenance of gambling behavior, particularly as the frequency of gambling increases and gambling related consequences accrue. One perspective on the psychology of gambling suggests that certain gambling-related cognitive biases facilitate involvement in gambling at levels associated with gambling-related problems (Ladoucer & Walker, 1996). In contrast to many current gambling assessment tools that focus exclusively on experienced consequences to index gambling involvement (e.g., South Oaks Gambling Screen; SOGS; Lesieur & Blume, 1987), the gambling attitudes and beliefs scale (GABS; Breen & Zuckerman, 1999) was designed to tap a wide range of beliefs, attitudes, values and biases thought to accompany progressive increases in gambling involvement. The utility of the GABS lies in its potential for tapping cognitions that may potentiate gambling frequency, yet precede significant gambling-related consequences. Therefore, the GABS may tap an underlying vulnerability to gambling problems. The GABS utilizes items reflecting positive social self-presentation through gambling (Holtgraves, 1988), cognitive biases regarding gambling (e.g., illusions of control, belief in luck), and the instrumental use of gambling to increase positive and relieve negative affect (Breen & Zuckerman, 1999). GABS scores are thought to reflect the degree to which one is engaged in gamblingrelated cognitions that contribute to continued gambling and gambling problems. This construct was labeled ‘‘affinity for gambling’’. The GABS is positively associated with sensation seeking, impulsivity, and gambling problems in both pathological and nonpathological gamblers (Breen, 2000; Lejuez, Strong, Breen, & Read, 2003) and has been shown to be sensitive to attitudinal changes in PGs following treatment (Breen, Kruedelbach, & Walker, 2001). In its current form, the GABS total score is derived by summing the score on each item in the scale. The use of summed items as a measure of gambling affinity assumes that the content of each item is equally informative at all levels of affinity and that the interpretation or manner of endorsement of items is similar across populations of non-problem and pathological gamblers. Although traditional psychometric evaluation using item-total correlations and reliability coefficients can estimate the GABS internal consistency and test–retest reliability, these group-level estimates can not inform how item performance varies across different levels of gambling affinity. Instead, using an approach rooted in item response theory (IRT), the ability of individual GABS items to discriminate among individuals across a wide range of gambling affinity can be examined. Additionally, the relative severity of items also can be evaluated by identifying the point on the continuum where individuals begin to agree with each item. For example, individuals at low levels of gambling affinity may believe in luck, but only individuals at high levels may agree that it is important to bet larger amounts when feeling lucky. Item response models also provide a visual and statistical approach for investigating whether items may be biased towards either infrequent or pathological gamblers. Assuring uniform responses to these items is essential before making comparisons across individuals with different levels of gambling because a summation of a scale that includes biased items may result in infrequent and pathological gamblers with different levels of gambling affinity obtaining the same total score (Drasgow, 1984; Reise, Widaman, & Pugh, 1993). In the current study, we evaluate the psychometric properties and external correlates of the GABS. Using a large sample of students to represent the lower range of gambling affinity and
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a large sample of pathological gamblers in treatment to represent the upper range of gambling affinity, we used methods based in IRT to examine the GABS. We evaluated GABS items ability to discriminate among individuals similarly in both samples and whether GABS items maintained their relative severity across these disparate ranges of gambling involvement and problems. Sample invariance in item performance across heterogeneous populations selected by high and low levels of affinity will increase confidence in the ability to compare obtained GABS scores across populations and improve understanding of the construct measured by the GABS.
2. Method 2.1. Participants This study utilizes data collected from two samples of gamblers representing upper and lower ends of a continuum of gambling behavior and includes: (a) pathological gamblers seeking treatment and (b) college students with a range of social/recreational gambling behavior (individuals who reported no gambling behavior in the past six months were not included). The pathological gambler (PG) sample consisted of 138 men and 96 women who filled out the GABS and SOGS as part of their enrollment in treatment for pathological gambling. The sample was known to be predominantly Caucasian and the mean age was 42.39 (SD ¼ 11:34). Additional demographic data were unavailable in this archival data set. The student sample included 487 students (42.5% women) who attended a large university in the mid-atlantic region of the United States and volunteered to fill out questionnaires during undergraduate coursework. All subjects provided informed consent and procedures were approved by the university institutional review board. The sample consisted of young adults and is expected to be similar to the general population of the university, with the majority of students Caucasian (87%) and between the ages of 18 and 22. 2.2. Measures 2.2.1. Gambling Attitudes and Beliefs Survey (GABS) The GABS is a 35-item measure that rates affinity for gambling on a 4-point Likert scale (GABS; Breen & Zuckerman, 1999). Total scores can range between 35 and 140, with higher scores indicating higher levels of gambling affinity. Principal components analysis supports the unidimensionality of the GABS (Breen & Zuckerman, 1999). Item means and standard deviations are reported in Table 1. The coefficient alpha was 0.93 and 0.89 in students and pathological gamblers respectively. Mean scores on the GABS were 79.50 (SD ¼ 15:23, skewness ¼ )0.18, kurtosis ¼ 0.81) and 91.94 (SD ¼ 12:76, skewness ¼ 0.13, kurtosis ¼ 0.21) respectively. 2.2.2. South Oaks Gambling Screen (SOGS) The SOGS is a 20 item self-report instrument that is scored by summing across dichotomously scaled questions. The SOGS is one of the most widely used screens for problem and pathological
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Table 1 Item means, standard deviations and estimated level of DIF Gambling Attitudes and Beliefs Survey
Students (n ¼ 487)
Pathological gamblers ðn ¼ 234Þ
v
SD
v
SD
1. Gambling makes me feel really alive 2. If I have not won any of my bets for a while, I am probably due for a big win 3. ThereÕs no way I can know if I will have good or bad lucka 4. I respect a person who makes very large bets and remains calm and coolb 5. Sometimes I forget about the time when IÕm gamblingb 6. I know when I’m on a streak 7. When I gamble it is important to act as if I am calm, even if I am not 8. Some people are unluckya 9. I feel great when I win a betb 10. It is important to feel confident when I gamble 11. Gambling is boringa 12. Some people are lucky to have around when IÕm gamblingb 13. People who gamble are more daring and adventurous than those who never gamble 14. I donÕt like to quit when IÕm losingb 15. It takes some skill to be successful at crapsa 16. Sometimes I just know Im going to have good luck 17. People who make big bets can be very sexya 18. If you have never experienced the excitement of making a big bet, you have never really lived 19. No matter what the game is, there are betting strategies that can help you win 20. I have carried a lucky charm when I gambleda 21. If I lose at gambling, it is important to stay calm 22. I usually donÕt get very excited when I gamblea 23. Roulette takes more skill than playing the lotterya 24. Casinos are glamorous, exciting placesa 25. If I have been lucky lately, I should press my bets 26. I feel angry when I lose at gamblinga 27. If I were feeling down, gambling would probably pick me upb 28. I must be familiar with a gambling game if I am going to win 29. Some people can bring bad luck to other people 30. ItÕs important to act a certain way when I winb 31. If I lose, it is important to stick with it until I get evenb 32. To be successful at gambling, I must be able to identify streaks 33. If I have lost my bets recently, my luck is bound to change 34. ItÕs important to be a gracious winnera 35. I like gambling because it helps me forget my everyday problemsb
2.09 2.06
0.87 0.82
2.95 2.74
1.74 2.21
0.78 0.89
1.92 2.31 2.63
DIF
SE
0.84 0.89
0.15 0.12
0.12 0.12
1.79 2.28
0.71 0.88
0.11 0.22
0.11 0.11
0.91 0.90 0.90
3.43 2.81 2.85
0.72 0.85 0.81
0.43 0.08 0.09
0.12 0.13 0.12
2.82 3.38 2.96 3.02 1.98 2.13
0.82 0.69 0.76 0.74 0.77 0.87
2.86 3.34 2.97 3.34 1.91 2.31
0.82 0.63 0.76 0.73 0.68 0.81
0.12 0.26 0.14 0.06 0.23 0.15
0.13 0.10 0.12 0.12 0.11 0.13
2.07 2.23 2.25 1.72 1.72
0.83 0.82 0.81 0.75 0.72
3.26 2.32 2.60 1.70 2.04
0.68 0.79 0.80 0.59 0.76
0.32 0.07 0.02 0.13 0.01
0.11 0.13 0.12 0.11 0.12
2.46
0.83
2.37
0.84
0.14
0.12
1.97 2.54 2.65 2.08 2.71 2.04 2.58 1.81 2.48 2.01 2.42 1.75 2.13 2.00 2.87 1.71
0.82 0.76 0.80 0.79 0.78 0.66 0.84 0.74 0.82 0.81 0.85 0.67 0.76 0.70 0.82 0.78
1.98 2.70 2.69 2.02 2.95 2.58 3.09 2.81 2.61 2.16 2.42 2.68 2.44 2.61 2.75 3.00
0.84 0.69 0.79 0.74 0.82 0.75 0.78 0.77 0.82 0.79 0.75 0.82 0.77 0.77 0.72 0.89
0.11 0.06 0.07 0.09 0.13 0.15 0.13 0.29 0.05 0.14 0.22 0.32 0.11 0.15 0.17 0.29
0.13 0.12 0.13 0.12 0.12 0.11 0.12 0.12 0.13 0.12 0.11 0.12 0.11 0.12 0.12 0.13
Note: Bold identifies the 15 items that were effective across student and PG samples. a Items with poor discrimination. b Items with estimated differential item functioning (DIF) greater than or equal to twice the standard error.
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gambling. Both student and PG participants were asked to respond to SOGS questions about their gambling in the last six months. Mean scores on the SOGS was 1.40 (SD ¼ 2:39) for students and 12.68 (SD ¼ 3:48) for PGs. Relative to other student populations (Winters, Bengston, Dorr, & Stinchfield, 1998), there was an elevated rate of problem gambling among this student sample with 11% scoring in the problem gambler range (3–4) and 7% scoring in the probable pathological range ( P 5). Among pathological gamblers, 97.4% scored in the pathological range. 2.2.3. Frequency of gambling All participants across groups reported some form of gambling over the previous six months. Gambling was defined as the act of wagering actual money on the outcomes of games of chance such as cards, dice, slot machines, lottery games, sporting events, or horse or dog racing. Frequency of gambling behavior was assessed by asking students to report whether in the past six months they gambled once a week, once a month, or less than once a month. In the general student sample, a broad range of gambling was endorsed. Specifically, 15% gambled at least once a week, 16.4% gambled at least once a month, and 68.6% gambled less than once per month. In the PG sample 92.6% gambled weekly, 5.4% gambled monthly, and 2% gambled less than monthly. 2.3. Analyses 2.3.1. Analysis of the unidimensionality of the GABS Given our interest in describing item response probabilities as a function of a latent affinity for gambling, we wanted assurance that only one primary construct was being measured by the GABS. We employed principal axes factor analysis of polychoric correlations using squared multiple correlations as initial estimates of communalities. We used the scree test, the ratio of first to second eigenvalues, and the interpretability of additional factors (Floyd & Widaman, 1995) to examine whether items essentially measured a unidimensional construct and retained items with final estimates of communalities >0.30 (cf. Roberts, Donoghue, & Laughlin, 2000). 2.3.2. Concurrent and incremental validity of the GABS In order to examine the relative strength of association of GABS and SOGS to gambling frequency we used ordered logistic regression to predict increases in gambling frequency. In order to make parameters more comparable we standardized the GABS and SOGS scores before entering them into the models. 2.3.3. GABS item analyses To examine the utility of the GABS in providing information across varying levels of gambling affinity, we conducted item-level analyses using methods based in IRT. IRT methods allow examination of how the probability of choosing each option for each GABS item varies in relation to individual levels of affinity for gambling. These response probabilities are examined by constructing option characteristic curves (OCC) for each item. OCC allow for both the inspection of item performance and examination of how particular item contents are endorsed differentially across the continuum of gambling affinity.
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To conduct the IRT analyses, we used a non-parametric kernel smoothing method and software (TESTGRAF) developed by Ramsay (2000). These methods have been used previously in several papers on the performance of scales measuring depression (Santor & Coyne, 1997, 2001; Santor, Zuroff, Ramsay, Cervantes, & Palacios, 1995), assessment of standard measures of nicotine dependence (Strong, Brown, Ramsay, & Myers, in press), and assessment of alcohol dependence (Kahler, Strong, Hayaki, Ramsey, & Brown, 2003). Individuals are ranked according to total scores on the GABS and these ranks are then converted to standard normal scores. OCC are then constructed across a specified number of evaluation points within these standard normal scores by using a non-parametric smoothing kernel (Ramsay, 1991). This approach estimates OCC at each evaluation point by using a local average, a method that gives observations increased influence in determining the estimated OCC values if they fall closer to the specific evaluation point. This method is particularly useful when OCC change rapidly across the range of gambling affinity and/or if the relationship between response probabilities and level of gambling affinity operate asymmetrically. We chose not to use parametric models for the OCC as we had no a priori reasons to expect a particular form for response distributions and wanted to allow for OCC with nonmonotonic functions to be revealed. 2.3.4. Comparing item analysis across samples Before assuming the GABS measures the affinity construct similarly among students and PGs, we wanted to explore whether there were qualitative differences in the response to particular GABS items. Differential item functioning (DIF) was deemed present when students and PGs with the same level of estimated gambling affinity do not have the same probability of endorsing an item option or options. We assumed quantitative differences in levels of gambling affinity (e.g. students have lower affinity), but we did not want item responses to be influenced by factors other than differences in gambling affinity. DIF was deemed present when OCC diverged significantly and/or if estimated average discrepancies were greater than or equal to two times their standard error (Ramsay, 2000). It is useful to look at the overall effects of DIF on each item by constructing item characteristic curves (ICC). Rather than looking at the likelihood of a particular option, (e.g. ‘‘agree’’), ICC provide a summary of which option is most likely (e.g. ‘‘strongly disagree’’, ‘‘disagree’’, ‘‘agree’’, or ‘‘strongly agree’’) at a particular level of gambling affinity. ICC are constructed by plotting estimates of the expected score on each item across levels of affinity (expected total score). If DIF was present, offending items would be removed before computing maximum likelihood estimates of individualsÕ level of affinity for gambling. This allows inspection of all item OCC with the effect of DIF removed. 2.3.5. Assessing levels of discrimination among students Effective items are identified by their ability to show increasing response options as a function of increasing levels of gambling affinity. For items that satisfied this assumption, we estimated the level of gambling affinity where each response category becomes more likely than the previous category. Using 95% confidence intervals we then estimated a range of affinity where GABS items were performing. Understanding the degree of overlap among items can inform selection of reduced item sets that map unique levels of affinity and identify underrepresented areas where new items may be needed. Any reduced sets of items were evaluated against the full scale for changes in correlation with SOGS and frequency of gambling behavior.
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3. Results 3.1. Assessment of latent dimensionality of the GABS Analyses were conducted separately in the student and PG samples. Results from the scree test and examination of relative size of eigenvalues revealed a single dominant unrotated factor that accounted for 61.1% and 47% of the common variance in student and PG samples respectively. In the student sample, 32 of 35 items loaded >0.30 on the first factor and items 3, 22, and 34 had loadings of 0.20, 0.25, 0.24, respectively. In the PG sample, 32 of 35 items had first-factor loadings >0.30, with the items 3, 22, and 23 loading 0.04, 0.29, and 0.29, respectively. The second factor extracted was significantly smaller in both samples and added an additional 9.7% and 14% of variance in the student and PG samples respectively. We retained all items for additional analyses as no item had a communality <0.40 or a factor loading <0.30 on the first factor in both student and PG samples and the items that loaded on the second factor were inconsistent across samples making a second factor uninterpretable. Mean inter-item correlations of 0.25 (SD ¼ 0:11) among students and 0.19 (SD ¼ 0:12) among PGs also were consistent with a predominantly unidimensional construct (Clark & Watson, 1995). 3.2. Concurrent validity The GABS was related significantly to the SOGS among the student (r ¼ 0:50, p < 0:001) and PG (r ¼ 0:41, p < 0:001) samples. As expected, the GABS and SOGS were not related significantly to the restricted range of gambling frequency among PG with r ¼ 0:10 and 0.07 respectively. Both the GABS and SOGS were related significantly (p < 0:001) to the frequency of gambling behavior among students with r ¼ 0:44 and 0.49 respectively. While controlling for the effect of gender (B ¼ 1:45, SE ¼ 0:27, p ¼ 0:0001) in the student sample, the GABS (B ¼ 0:69, SE ¼ 0:15, p ¼ 0:0001) and SOGS (B ¼ 0:83, SE ¼ 0:15, p ¼ 0:0001) total scores predicted independently an increase in the odds of being in a category of more frequent gamblers. The proportional odds assumption was met indicating that the predicted increase in odds of moving from less than monthly to monthly gambling, and the odds of moving from monthly to weekly gambling were equal (v2 ¼ 3:40, df ¼ 3, p ¼ 0:33). These results suggest that: (a) increasing GABS scores are related to increasing reports of gambling related problems in both student and PG samples; (b) both the GABS and SOGS scales are associated with an underlying continuum of gambling frequency, and (c) the GABS provides unique information about gambling frequency beyond that explained by the SOGS. 3.3. Differential item functioning Nine items exhibited DIF as evidenced by average OCC discrepancies greater than or equal to twice their standard error (see Table 1). At similar levels of gambling affinity, PGs were more likely than students to agree to items reflecting forgetting about time gambling (item 5), not wanting to quit when losing (item 14), using gambling to relieve negative affect (item 27 and item 35) and wanting to continue gambling until getting even (item 31). PGs were less likely across all levels of affinity for gambling to agree that it is important to act a certain way when winning (item
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30), that others are lucky to have around (item 12), and that they respect people who calmly make large bets (item 4). PGs were more likely to agree that winning a bet made them feel great (item 9). However, PGs were less likely than students to strongly agree, particularly for PGs at higher levels of affinity for gambling. Fig. 1 illustrates examples of ICC with 95% confidence intervals for biased items. Inspection of these curves reveals how for a biased item, students and PGs with the same level of affinity are expected to choose different options. Fig. 1 presents an example of four items where PG were more likely than students to report increased agreement and two items (12, 30), where students were more likely than PG to agree with items. 3.4. Assessing items’ ability to discriminate among levels of affinity Before comparing student and PG item-level characteristics, we removed GABS items with significant DIF and reanalyzed individual levels of affinity for gambling. Using the adjusted estimates of gambling affinity, we examined item characteristic curves (ICC) for students and PGs to assess each itemÕs overall ability to discriminate among the levels of gambling affinity. We plotted ICC according to an estimated total score and expected effective items to display ascending sloped curves. For example, Fig. 2 contrasts item discrimination differences for item 3 (a poorly performing item) and item 16 (a well performing item) in student and PG samples. Items 3, 8, 9, 11, 22, 23, and 34 showed poor ability to discriminate among either students or gamblers relative to other GABS items across levels of gambling affinity. Among PGs, additional items (12, 15, 17, 20) performed poorly because few PGs agreed with these items or because few PGs disagreed with these items (5, 14, 24, 26). 3.5. Comparing option characteristic curves for students and pathological gamblers OCC for all the 35 items were examined and compared across student and PG samples using the DIF adjusted index of level of affinity. We examined all 35 items OCC, including items with poor discrimination, as we were interested in whether particular options may be causing the poor discrimination and whether we could collapse responses to salvage items. Items effective in discriminating among levels of affinity for gambling in both student and PGs are described first, followed by examples of items that did not discriminate well. Fig. 3 illustrates examples of OCC from a discriminating item (item 6) and an item (item 3) that did not discriminate well in either sample. 3.6. Effective items Fifteen of the items without DIF (1, 2, 6, 7, 10, 13, 16, 18, 19, 21, 25, 28, 29, 32, 33) and five of the items with DIF (4, 27, 30, 31, 35) were effective in making discriminations in both samples. The belief that gambling makes one feel really alive (item 1) performed best among students. In PGs, item 1 was less discriminating because most PGs agreed but the top 25% of the PG sample were distinguished by the ‘‘strongly agree’’ option. Therefore, this item was retained as it discriminated well across the lower ranges and also provided additional discrimination in the highest regions of gambling affinity, a region populated primarily by PGs. We saw a similar pattern among item 7 (acting calm while gambling) and item 13 (viewing gamblers as more daring and
D.R. Strong et al. / Personality and Individual Differences 36 (2004) 1515–1529 4
4
PG
PG
3
Item 5
Item 14
3
2
Students
Students
2
1
1 40
60
80
100
40
120
4
4
3
3
Item 31
Item 27
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PG
60
80
100
120
PG
2
2 Students
Students
1
1 60
80
100
40
120
4
4
3
3
Item 30
Item 12
40
Students
2
60
80
100
120
100
120
Students
2 PG
PG
1
1 40
60
80
100
Expected Score
120
40
60
80
Expected Score
Fig. 1. Item characteristic curves (ICC) for six of the ten items with differential item functioning (DIF).
adventurous). Among students, the probability of endorsing increasing options on these items varied directly with increasing levels of affinity for gambling. However, among PGs more than two-thirds were more likely to agree with item 7 and to disagree with item 13 than to endorse any
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Expected Item Score
4
3
Item 16 PG Item 16 Students Item 3 Students 2
Item 3 PG 1 40
60
80
100
120
Expected Total Score
Fig. 2. Expected item scores as a function of expected total score show that item 3 does not discriminate well in either student or PG samples while item 16 performs consistently well in both samples.
of the other options. Therefore, these items perform well, but operate primarily at lower levels of gambling affinity. There were several items that performed well in both samples. Items included feeling due for a big win following a losing streak (item 2), the ability to identify winning and losing streaks (items 6 and 32), believing that there are strategies for winning no matter what the game (item 19), believing it is important to stay calm if losing (item 21), and believing that others can bring bad luck (item 29). Items describing the feeling of knowing when good luck is imminent (item 16), the belief that one should press their luck if they have been lucky (item 25), and the belief that bad luck is bound to change (item 33) also performed well in both the student and PG samples. Three items, item 10 (importance of feeling confident when gambling), item 18 (unparalleled excitement of making big bets), and item 28 (familiarity with games leads to success) performed best at the highest levels of gambling affinity. Only students and PGs at the highest levels of affinity agreed or strongly agreed to these items. While few students or PGs disagreed with these items, the strongly disagree option on item 18 did provide discrimination among those students and PGs at the lowest 20% of the distribution. 3.7. Ineffective items In contrast to the above items that effectively discriminated between students and PGs, several items exhibited significant floor effects across both samples. Few people agreed that making bets
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Item 6 1.0
1.0 PG
Students
4 3
2
4
Probability
Probability
1
0.5
0.0
2
0.5
3
1
0.0 40
60
80
100
120
60
Expected Total Score
70
80
90 100 110 120
Expected Total Score
Item 3 1.0
1.0 Students
PG
2
Probability
Probability
1 3
0.5 1
2
0.5
4
3 4
0.0
0.0 40
60
80
100
Expected Total Score
120
60
70
80
90 100 110 120
Expected Total Score
Fig. 3. Example option characteristic curves for items 6 and 3 demonstrating item 6 options ability to discriminate along expected total score while item 3 options are less discriminating.
was sexy (item 17) regardless of levels of gambling affinity. Similarly, the belief that one is unable to know when luck is good or bad (item 3), belief in carrying a lucky charm while gambling (item 20), the belief that skills increase the probability of winning (item 15), the belief that others are lucky to have around (item 12), the belief that roulette takes more skill than playing the lottery (item 23), believing that gambling is boring (item 11), and the expectation that one will not get excited when gambling (item 22) all discriminated poorly in both samples with few people agreeing with these items. Additional items demonstrated significant ceiling effects across samples. Across all levels of gambling affinity, both students and PGs were more likely to agree or strongly agree than disagree or strongly disagree that some people are unlucky (item 8), that it feels great to win a bet (item 9), that casinos are glamorous and exciting places (item 24), that it is important to be a gracious winner (item 34), and that they get angry when losing at gambling (item 26). Additionally, items reflecting lost time while gambling (item 5) and disliking quitting when losing (item 14) were able to make discriminations among students, however, the same items performed poorly among PG
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Fig. 4. Map of the levels of discrimination provided by the 15 effective GABS items. Shaded areas reflect level of gambling affinity and 95%CI where each option from each of the 15 effective items becomes more likely than the previous option.
as almost all PG strongly agreed. Thus these items provided little information about differences among either students or PGs and should be eliminated in a reduced scale. 3.7.1. Assessing levels of discrimination Finally, we evaluated the ability of the set of 15 effective items to cover a wide enough range of severity to be useful in maximally separating individuals across a wide range of gambling affinity. We first estimated the severity of gambling affinity reflected by each item option and then examined options across items to determine if items reflected similar or non-overlapping levels of affinity (see Fig. 4). Each band represents the region and 95% confidence interval where each response becomes more likely (>50% chance) than the previous option. The width of the bands reflect the precision with which each item option places an individual below or above a particular level of affinity and narrower bands reflecting increased precision. With a four-option item, three discriminations are possible. Visual inspection of Fig. 1 suggests that several items are covering overlapping levels of affinity and that the 15 items also cover a considerable range of gambling affinity. For example, item 2 and item 6 appear to cover similar ground yet item 16 and item 18 appear to map non-overlapping regions. The 15-item set of GABS items retained significant correlations with SOGS and frequency of gambling, r ¼ 0:48 and 0.43, respectively in the student sample and r ¼ 0:36 and 0.09, respectively in the PG sample.
4. Discussion Current gambling assessment instruments are useful for the identification of gambling consequences and the characterization of individuals as pathological or nonpathological. However,
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these measures do not assess the attitudes and beliefs thought to accompany gambling activity. Assessing positive attitudes and beliefs about gambling may help to identify individuals at the lower end of the gambling continuum who may engage in frequent gambling and possess cognitive risk factors for gambling related problems. Item and content analyses support the GABS as a measure that taps a unidimensional construct we refer to as gambling affinity. The GABS has been shown to have good internal consistency and is related to the frequency of gambling behavior and indexes of gambling pathology (Breen et al., 2001; Breen & Zuckerman, 1999). In the current study, we provided additional support for the unidimesionality of the construct, internal consistency of the GABS, and the GABS relationship to gambling frequency and gambling problems (e.g. SOGS). We then used item-response theory to examine the construct of gambling affinity and whether the GABS indexed this latent construct similarly across samples selected by their low and high levels of gambling behavior (e.g. student and PG samples). As an initial analysis, we established the relationship of the GABS with a standard measure of gambling problems and the unique contribution of the GABS in predicting the frequency of gambling behavior among students. We then examined DIF to identify items that performed differently among students and PGs. Nine GABS items were endorsed in qualitatively different ways by student and PG samples even after equating both groups on levels of gambling affinity. Most notably, the content of these items reflected more extreme symptoms such as loss of time when gambling, loss of control, use of gambling to reduce negative affect and chasing lost bets. Indeed, items endorsed differentially by PGs potentially support a discontinuity in the continuum of gambling that is consistent with DSM-IV conceptualizations of pathological gambling typified by compulsivity or loss of control over gambling, gambling to escape problems, and chasing losses. Although our limited information about the demographic characteristics of these samples precluded follow-up analyses to examine whether differences were related to alternative sources such as age, education level or socioeconomic status, we were able to identify 26 items for which DIF was not found despite likely dramatic demographic differences across these samples. Following the identification of 9 items with a high degree of DIF, we examined the option characteristic curves of the items, which revealed an additional 11 items that did not discriminate well along the underlying continuum of gambling affinity. The remaining 15 GABS items (bolded items in Table 1) demonstrated the ability to effectively discriminate individual levels of gambling affinity across both student and PG samples. These effective items primarily fell in content domains related to cognitive biases including the misunderstanding of randomness, the belief in luck, and gambling-related illusions of control. Despite the promise of the current results, additional evaluation of the remaining itemÕs discriminate validity and stability of estimates across time is needed before we can be confident that affinity for gambling is a stable latent trait. Additional work also is needed to evaluate the statedependence of the GABS using more online behavioral measures of gambling involvement (cf. Lejuez et al., 2002; Lejuez et al., 2003). Further, a primary limitation of this study is the lack of detailed demographic information and therefore our inability to explore potential sources of differential item functioning limits immediate generalizability of obtained item characteristics. These groups are expected to differ on a number of characteristics that could include age, gender, education, socioeconomic status, levels of psychopathology, and levels of substance use disorders. Additionally, the differences in item responses of students may be specific to the developmental stage of college age gamblers or the kinds of gambling activities that are available to students and
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therefore discarded items may not show DIF among non-college age gamblers. Conversely, the differences in item responses among PG may be due to comorbid psychopathology among PGs and therefore discarded items may not show DIF when compared across student and nonpathological gamblers from the community. The degree to which we are justified in dropping items due to differences found in the current samples will need exploration in more representative samples of adults with more frequent and non-problem levels of gambling behavior. Lack of representation of regular non-problem gamblers in these samples prevents immediate generalization. Given the GABS stability within high and low levels of gambling behavior, an important next step will be to evaluate the GABS utility among gamblers who represent middle regions of the continuum and engage in more moderate levels of gambling behavior. 4.1. Future directions Cognitive biases are not unique to gambling behavior, but systematic variability in gamblingrelated cognitions across a range of gambling involvement supports the important theoretical contribution of cognitive biases to the development and maintenance of gambling behavior (e.g., Ladoucer & Walker, 1996). For example, people commonly demonstrate a self-serving bias when they attribute their gambling losses to situational factors such as a fumble or other ‘‘fluke’’ plays in a football game, or a ‘‘hot’’ dealer at a blackjack table. Winning at gambling is conversely explained as evidence of internal, stable traits such as competitiveness and intelligence. The potential net effect is that cognitive biases (and gambling affinity) are strengthened with cumulative experience and may contribute to increased gambling behavior. Interventions that target biases and misunderstanding of randomness by exposing individuals to information about actual contingencies have shown clinical effectiveness in treating PGs (e.g., Blaszczynski & McConaghy, 1989; Sylvain, Ladouceur, & Boisvert, 1997) and GABS scores have been shown to be sensitive to intervention as evidenced by decreased scores after treatment (Breen et al., 2001). In conclusion, whereas most assessment measures of gambling focus primarily on the categorization of pathological and nonpathological gamblers, the assessment of gambling affinity using the GABS provides the opportunity to examine the attitudes and beliefs of individuals across various levels of gambling activity. Such an assessment may be especially useful when looking to identify individuals with an underlying vulnerability to become pathological gamblers, but who currently do not meet the criteria. Future studies can evaluate prospectively, how levels of affinity predict progression towards pathological gambling, how levels of affinity upon entry into treatment predict outcomes, and how specific cognitive treatment components affect this potential riskfactor.
References Blaszczynski, A. P., & Mcconaghy, N. (1989). The medical model of pathological gambling: Current shortcomings. Journal of Gambling Behavior, 5, 42–52. Breen, R. B. (2000). Affinity for gambling and impulsivity: Effects on participation and perseverance. Unpublished doctoral dissertation, University of Delaware. Breen, R. B., Kruedelbach, N., & Walker, H. (2001). Cognitive changes in pathological gamblers following a 28-day inpatient program. Psychology of Addictive Behaviors, 3, 246–248.
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Breen, R. B., & Zuckerman, M. (1999). Chasing in gambling behavior: Personality and cognitive determinants. Personality and Individual Differences, 27, 1097–1111. Clark, L. A., & Watson, D. (1995). Constructing validity: Basic issues in objective scale development. Psychological Assessment, 7, 309–319. Drasgow, F. (1984). Scrutinizing psychological tests: Measurement equivalence and equivalent relations with external variables are central issues. Psychological Bulletin, 95, 134–135. Floyd, F. J., & Widaman, K. F. (1995). Factor analysis in the development and refinement of clinical assessment instruments. Psychological Assessment, 7, 286–299. Holtgraves, T. (1988). Gambling as self-presentation. Journal of Gambling Behavior, 4, 78–91. Kahler, C. W., Strong, D. R., Hayaki, J., Ramsey, S. E., & Brown, R. A. (2003). An item response analysis of the alcohol dependence scale in treatment-seeking alcoholics. Journal of Studies on Alcohol, 64, 127–136. Ladoucer, R., & Walker, M. (1996). A cognitive perspective on gambling. In P. M. Salkovskis (Ed.), Trends in cognitive and behavioural therapies (pp. 89–120). John Wiley & Sons Ltd. Lejuez, C. W., Read, J. P., Kahler, C. W., Richards, J. B., Ramsey, S. E., Stuart, G. L., Strong, D. R., & Brown, R. A. (2002). Evaluation of a behavioral measure of risk-taking: The balloon analogue risk task (BART). Journal of Experimental Psychology: Applied, 8, 75–84. Lejuez, C. W., Strong, D. R., Breen, R. B., & Read, J. P. (2003). A tool for assessing the continuum of gambling in college students: The gambling attitudes and beliefs scale (GABS). Unpublished manuscript. Lesieur, H. R., & Blume, S. B. (1987). The South Oaks Gambling Screen (SOGS): A new instrument for the identification of pathological gamblers. American Journal of Psychiatry, 144, 1184–1188. Ramsay, J. O. (1991). Kernel-smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611–630. Ramsay, J. O. (2000). TestGraf: A program for the graphical analysis of multiple choice test and questionnaire data. Unpublished Manuscript. Reise, S. P., Widaman, K. F., & Pugh, R. H. (1993). Confirmatory factor analysis and item response theory: Two approaches for exploring measurement invariance. Psychological Bulletin, 114, 552–566. Roberts, J. S., Donoghue, J. R., & Laughlin, J. E. (2000). A general item response theory model for unfolding unidimensional polytomous responses. Applied Psychological Measurement, 24, 3–32. Santor, D. A., & Coyne, J. C. (1997). Shortening the CES-D to improve its ability to detect cases of depression. Psychological Assessment, 9, 233–243. Santor, D. A., & Coyne, J. C. (2001). Examining symptom expression as a function of symptom severity: Item performance on the Hamilton rating scale for depression. Psychological Assessment, 13, 127–139. Santor, D. A., Zuroff, D. C., Ramsay, J. O., Cervantes, P., & Palacios, J. (1995). Examining scale discriminibility in the BDI and the CES-D as a function of depression severity. Psychological Assessment, 7, 131–139. Shaffer, H. J., Hall, M. N., & Bilt, J. V. (1997). Estimating the prevalence of disordered gambling in the United States and Canada: A meta-analysis. Boston: Harvard Medical School, Division on Addictions. Strong, D. R., Brown, R. A., Ramsay, S. E., & Myers, M. (in press). Nicotine dependence measures among adolescents with psychiatric disorders: Evaluating symptom expression as a function of dependence severity. Nicotine and Tobacco Research. Sylvain, C., Ladouceur, R., & Boisvert, J. M. (1997). Cognitive and behavioral treatment for pathological gambling: A controlled study. Journal of Consulting and Clinical Psychology, 65, 727–732. Volberg, R. A. (1996). Prevalence studies of problem gambling in the United States. Journal of Gambling Studies, 12, 111–128. Wallish, L. S. (1996). Gambling in Texas: 1995 surveys of adult and adolescent gambling behavior. Austin: Texas Commision on Drug and Alcohol Abuse. Welte, J. W., Barnes, G. M., Wieczorek, W. F., Tidwell, M. C., & Parker, J. (2002). Gambling participation in the USresults from a national survey. Journal of Gambling Studies, 18, 313–337. Winters, K. C., Bengston, P., Dorr, D., & Stinchfield, R. (1998). Prevalence and risk factors of problem gambling among college students. Psychology of Addictive Behaviors, 12, 127–135.
Using item response theory to examine gambling attitudes and beliefs David R. Strong a
a,*
, Robert B. Breen b, C.W. Lejuez
c
Brown University and Butler Hospital, 345 Blackstone Boulevard, Providence, RI 02906, USA b Brown University and Rhode Island Hospital, USA c University of Maryland, College Park, USA Received 23 August 2002; received in revised form 8 April 2003; accepted 8 June 2003
Abstract The gambling attitudes and beliefs scale (GABS: Breen & Zuckerman, 1999) was designed to assess a latent affinity for gambling. Using methods based in item response theory we demonstrated how a reduced set of GABS items maintained their relative severity and discriminated similarly when used among nonproblem gambling students selected to represent low levels of gambling behavior (n ¼ 487) and when used clinically among treatment seeking pathological gamblers (n ¼ 234). This stability increases confidence both in the construct measured by the GABS and in the ability to assess levels of gambling affinity across disparate ranges of gambling-problem severity. The GABS also demonstrated incremental validity in predicting increases in the frequency of gambling behavior among non-problem gambling students beyond that explained by an index of gambling-problem severity. Implications for assessment of gambling affinity across pathological and nonpathological gamblers are discussed. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Gambling; Gambling attitudes; Gambling beliefs; Item response theory; Gambling affinity
1. Introduction The United States is currently in the midst of a period of widespread expansion in the availability of legal gambling. The prevalence of pathological gambling (PG) has increased along with this expansion (Shaffer, Hall, & Bilt, 1997; Volberg, 1996; Wallish, 1996; Welte, Barnes, Wieczorek,
*
Corresponding author. Tel.: +1-401-455-6479; fax: +1-401-455-6424. E-mail address: [email protected] (D.R. Strong).
0191-8869/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.paid.2003.06.001
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Tidwell, & Parker, 2002). Effective measurement of positive interest and attitudes towards gambling is needed before we can better understand clinically how attitudinal shifts may be related to the maintenance of gambling behavior, particularly as the frequency of gambling increases and gambling related consequences accrue. One perspective on the psychology of gambling suggests that certain gambling-related cognitive biases facilitate involvement in gambling at levels associated with gambling-related problems (Ladoucer & Walker, 1996). In contrast to many current gambling assessment tools that focus exclusively on experienced consequences to index gambling involvement (e.g., South Oaks Gambling Screen; SOGS; Lesieur & Blume, 1987), the gambling attitudes and beliefs scale (GABS; Breen & Zuckerman, 1999) was designed to tap a wide range of beliefs, attitudes, values and biases thought to accompany progressive increases in gambling involvement. The utility of the GABS lies in its potential for tapping cognitions that may potentiate gambling frequency, yet precede significant gambling-related consequences. Therefore, the GABS may tap an underlying vulnerability to gambling problems. The GABS utilizes items reflecting positive social self-presentation through gambling (Holtgraves, 1988), cognitive biases regarding gambling (e.g., illusions of control, belief in luck), and the instrumental use of gambling to increase positive and relieve negative affect (Breen & Zuckerman, 1999). GABS scores are thought to reflect the degree to which one is engaged in gamblingrelated cognitions that contribute to continued gambling and gambling problems. This construct was labeled ‘‘affinity for gambling’’. The GABS is positively associated with sensation seeking, impulsivity, and gambling problems in both pathological and nonpathological gamblers (Breen, 2000; Lejuez, Strong, Breen, & Read, 2003) and has been shown to be sensitive to attitudinal changes in PGs following treatment (Breen, Kruedelbach, & Walker, 2001). In its current form, the GABS total score is derived by summing the score on each item in the scale. The use of summed items as a measure of gambling affinity assumes that the content of each item is equally informative at all levels of affinity and that the interpretation or manner of endorsement of items is similar across populations of non-problem and pathological gamblers. Although traditional psychometric evaluation using item-total correlations and reliability coefficients can estimate the GABS internal consistency and test–retest reliability, these group-level estimates can not inform how item performance varies across different levels of gambling affinity. Instead, using an approach rooted in item response theory (IRT), the ability of individual GABS items to discriminate among individuals across a wide range of gambling affinity can be examined. Additionally, the relative severity of items also can be evaluated by identifying the point on the continuum where individuals begin to agree with each item. For example, individuals at low levels of gambling affinity may believe in luck, but only individuals at high levels may agree that it is important to bet larger amounts when feeling lucky. Item response models also provide a visual and statistical approach for investigating whether items may be biased towards either infrequent or pathological gamblers. Assuring uniform responses to these items is essential before making comparisons across individuals with different levels of gambling because a summation of a scale that includes biased items may result in infrequent and pathological gamblers with different levels of gambling affinity obtaining the same total score (Drasgow, 1984; Reise, Widaman, & Pugh, 1993). In the current study, we evaluate the psychometric properties and external correlates of the GABS. Using a large sample of students to represent the lower range of gambling affinity and
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a large sample of pathological gamblers in treatment to represent the upper range of gambling affinity, we used methods based in IRT to examine the GABS. We evaluated GABS items ability to discriminate among individuals similarly in both samples and whether GABS items maintained their relative severity across these disparate ranges of gambling involvement and problems. Sample invariance in item performance across heterogeneous populations selected by high and low levels of affinity will increase confidence in the ability to compare obtained GABS scores across populations and improve understanding of the construct measured by the GABS.
2. Method 2.1. Participants This study utilizes data collected from two samples of gamblers representing upper and lower ends of a continuum of gambling behavior and includes: (a) pathological gamblers seeking treatment and (b) college students with a range of social/recreational gambling behavior (individuals who reported no gambling behavior in the past six months were not included). The pathological gambler (PG) sample consisted of 138 men and 96 women who filled out the GABS and SOGS as part of their enrollment in treatment for pathological gambling. The sample was known to be predominantly Caucasian and the mean age was 42.39 (SD ¼ 11:34). Additional demographic data were unavailable in this archival data set. The student sample included 487 students (42.5% women) who attended a large university in the mid-atlantic region of the United States and volunteered to fill out questionnaires during undergraduate coursework. All subjects provided informed consent and procedures were approved by the university institutional review board. The sample consisted of young adults and is expected to be similar to the general population of the university, with the majority of students Caucasian (87%) and between the ages of 18 and 22. 2.2. Measures 2.2.1. Gambling Attitudes and Beliefs Survey (GABS) The GABS is a 35-item measure that rates affinity for gambling on a 4-point Likert scale (GABS; Breen & Zuckerman, 1999). Total scores can range between 35 and 140, with higher scores indicating higher levels of gambling affinity. Principal components analysis supports the unidimensionality of the GABS (Breen & Zuckerman, 1999). Item means and standard deviations are reported in Table 1. The coefficient alpha was 0.93 and 0.89 in students and pathological gamblers respectively. Mean scores on the GABS were 79.50 (SD ¼ 15:23, skewness ¼ )0.18, kurtosis ¼ 0.81) and 91.94 (SD ¼ 12:76, skewness ¼ 0.13, kurtosis ¼ 0.21) respectively. 2.2.2. South Oaks Gambling Screen (SOGS) The SOGS is a 20 item self-report instrument that is scored by summing across dichotomously scaled questions. The SOGS is one of the most widely used screens for problem and pathological
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Table 1 Item means, standard deviations and estimated level of DIF Gambling Attitudes and Beliefs Survey
Students (n ¼ 487)
Pathological gamblers ðn ¼ 234Þ
v
SD
v
SD
1. Gambling makes me feel really alive 2. If I have not won any of my bets for a while, I am probably due for a big win 3. ThereÕs no way I can know if I will have good or bad lucka 4. I respect a person who makes very large bets and remains calm and coolb 5. Sometimes I forget about the time when IÕm gamblingb 6. I know when I’m on a streak 7. When I gamble it is important to act as if I am calm, even if I am not 8. Some people are unluckya 9. I feel great when I win a betb 10. It is important to feel confident when I gamble 11. Gambling is boringa 12. Some people are lucky to have around when IÕm gamblingb 13. People who gamble are more daring and adventurous than those who never gamble 14. I donÕt like to quit when IÕm losingb 15. It takes some skill to be successful at crapsa 16. Sometimes I just know Im going to have good luck 17. People who make big bets can be very sexya 18. If you have never experienced the excitement of making a big bet, you have never really lived 19. No matter what the game is, there are betting strategies that can help you win 20. I have carried a lucky charm when I gambleda 21. If I lose at gambling, it is important to stay calm 22. I usually donÕt get very excited when I gamblea 23. Roulette takes more skill than playing the lotterya 24. Casinos are glamorous, exciting placesa 25. If I have been lucky lately, I should press my bets 26. I feel angry when I lose at gamblinga 27. If I were feeling down, gambling would probably pick me upb 28. I must be familiar with a gambling game if I am going to win 29. Some people can bring bad luck to other people 30. ItÕs important to act a certain way when I winb 31. If I lose, it is important to stick with it until I get evenb 32. To be successful at gambling, I must be able to identify streaks 33. If I have lost my bets recently, my luck is bound to change 34. ItÕs important to be a gracious winnera 35. I like gambling because it helps me forget my everyday problemsb
2.09 2.06
0.87 0.82
2.95 2.74
1.74 2.21
0.78 0.89
1.92 2.31 2.63
DIF
SE
0.84 0.89
0.15 0.12
0.12 0.12
1.79 2.28
0.71 0.88
0.11 0.22
0.11 0.11
0.91 0.90 0.90
3.43 2.81 2.85
0.72 0.85 0.81
0.43 0.08 0.09
0.12 0.13 0.12
2.82 3.38 2.96 3.02 1.98 2.13
0.82 0.69 0.76 0.74 0.77 0.87
2.86 3.34 2.97 3.34 1.91 2.31
0.82 0.63 0.76 0.73 0.68 0.81
0.12 0.26 0.14 0.06 0.23 0.15
0.13 0.10 0.12 0.12 0.11 0.13
2.07 2.23 2.25 1.72 1.72
0.83 0.82 0.81 0.75 0.72
3.26 2.32 2.60 1.70 2.04
0.68 0.79 0.80 0.59 0.76
0.32 0.07 0.02 0.13 0.01
0.11 0.13 0.12 0.11 0.12
2.46
0.83
2.37
0.84
0.14
0.12
1.97 2.54 2.65 2.08 2.71 2.04 2.58 1.81 2.48 2.01 2.42 1.75 2.13 2.00 2.87 1.71
0.82 0.76 0.80 0.79 0.78 0.66 0.84 0.74 0.82 0.81 0.85 0.67 0.76 0.70 0.82 0.78
1.98 2.70 2.69 2.02 2.95 2.58 3.09 2.81 2.61 2.16 2.42 2.68 2.44 2.61 2.75 3.00
0.84 0.69 0.79 0.74 0.82 0.75 0.78 0.77 0.82 0.79 0.75 0.82 0.77 0.77 0.72 0.89
0.11 0.06 0.07 0.09 0.13 0.15 0.13 0.29 0.05 0.14 0.22 0.32 0.11 0.15 0.17 0.29
0.13 0.12 0.13 0.12 0.12 0.11 0.12 0.12 0.13 0.12 0.11 0.12 0.11 0.12 0.12 0.13
Note: Bold identifies the 15 items that were effective across student and PG samples. a Items with poor discrimination. b Items with estimated differential item functioning (DIF) greater than or equal to twice the standard error.
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gambling. Both student and PG participants were asked to respond to SOGS questions about their gambling in the last six months. Mean scores on the SOGS was 1.40 (SD ¼ 2:39) for students and 12.68 (SD ¼ 3:48) for PGs. Relative to other student populations (Winters, Bengston, Dorr, & Stinchfield, 1998), there was an elevated rate of problem gambling among this student sample with 11% scoring in the problem gambler range (3–4) and 7% scoring in the probable pathological range ( P 5). Among pathological gamblers, 97.4% scored in the pathological range. 2.2.3. Frequency of gambling All participants across groups reported some form of gambling over the previous six months. Gambling was defined as the act of wagering actual money on the outcomes of games of chance such as cards, dice, slot machines, lottery games, sporting events, or horse or dog racing. Frequency of gambling behavior was assessed by asking students to report whether in the past six months they gambled once a week, once a month, or less than once a month. In the general student sample, a broad range of gambling was endorsed. Specifically, 15% gambled at least once a week, 16.4% gambled at least once a month, and 68.6% gambled less than once per month. In the PG sample 92.6% gambled weekly, 5.4% gambled monthly, and 2% gambled less than monthly. 2.3. Analyses 2.3.1. Analysis of the unidimensionality of the GABS Given our interest in describing item response probabilities as a function of a latent affinity for gambling, we wanted assurance that only one primary construct was being measured by the GABS. We employed principal axes factor analysis of polychoric correlations using squared multiple correlations as initial estimates of communalities. We used the scree test, the ratio of first to second eigenvalues, and the interpretability of additional factors (Floyd & Widaman, 1995) to examine whether items essentially measured a unidimensional construct and retained items with final estimates of communalities >0.30 (cf. Roberts, Donoghue, & Laughlin, 2000). 2.3.2. Concurrent and incremental validity of the GABS In order to examine the relative strength of association of GABS and SOGS to gambling frequency we used ordered logistic regression to predict increases in gambling frequency. In order to make parameters more comparable we standardized the GABS and SOGS scores before entering them into the models. 2.3.3. GABS item analyses To examine the utility of the GABS in providing information across varying levels of gambling affinity, we conducted item-level analyses using methods based in IRT. IRT methods allow examination of how the probability of choosing each option for each GABS item varies in relation to individual levels of affinity for gambling. These response probabilities are examined by constructing option characteristic curves (OCC) for each item. OCC allow for both the inspection of item performance and examination of how particular item contents are endorsed differentially across the continuum of gambling affinity.
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To conduct the IRT analyses, we used a non-parametric kernel smoothing method and software (TESTGRAF) developed by Ramsay (2000). These methods have been used previously in several papers on the performance of scales measuring depression (Santor & Coyne, 1997, 2001; Santor, Zuroff, Ramsay, Cervantes, & Palacios, 1995), assessment of standard measures of nicotine dependence (Strong, Brown, Ramsay, & Myers, in press), and assessment of alcohol dependence (Kahler, Strong, Hayaki, Ramsey, & Brown, 2003). Individuals are ranked according to total scores on the GABS and these ranks are then converted to standard normal scores. OCC are then constructed across a specified number of evaluation points within these standard normal scores by using a non-parametric smoothing kernel (Ramsay, 1991). This approach estimates OCC at each evaluation point by using a local average, a method that gives observations increased influence in determining the estimated OCC values if they fall closer to the specific evaluation point. This method is particularly useful when OCC change rapidly across the range of gambling affinity and/or if the relationship between response probabilities and level of gambling affinity operate asymmetrically. We chose not to use parametric models for the OCC as we had no a priori reasons to expect a particular form for response distributions and wanted to allow for OCC with nonmonotonic functions to be revealed. 2.3.4. Comparing item analysis across samples Before assuming the GABS measures the affinity construct similarly among students and PGs, we wanted to explore whether there were qualitative differences in the response to particular GABS items. Differential item functioning (DIF) was deemed present when students and PGs with the same level of estimated gambling affinity do not have the same probability of endorsing an item option or options. We assumed quantitative differences in levels of gambling affinity (e.g. students have lower affinity), but we did not want item responses to be influenced by factors other than differences in gambling affinity. DIF was deemed present when OCC diverged significantly and/or if estimated average discrepancies were greater than or equal to two times their standard error (Ramsay, 2000). It is useful to look at the overall effects of DIF on each item by constructing item characteristic curves (ICC). Rather than looking at the likelihood of a particular option, (e.g. ‘‘agree’’), ICC provide a summary of which option is most likely (e.g. ‘‘strongly disagree’’, ‘‘disagree’’, ‘‘agree’’, or ‘‘strongly agree’’) at a particular level of gambling affinity. ICC are constructed by plotting estimates of the expected score on each item across levels of affinity (expected total score). If DIF was present, offending items would be removed before computing maximum likelihood estimates of individualsÕ level of affinity for gambling. This allows inspection of all item OCC with the effect of DIF removed. 2.3.5. Assessing levels of discrimination among students Effective items are identified by their ability to show increasing response options as a function of increasing levels of gambling affinity. For items that satisfied this assumption, we estimated the level of gambling affinity where each response category becomes more likely than the previous category. Using 95% confidence intervals we then estimated a range of affinity where GABS items were performing. Understanding the degree of overlap among items can inform selection of reduced item sets that map unique levels of affinity and identify underrepresented areas where new items may be needed. Any reduced sets of items were evaluated against the full scale for changes in correlation with SOGS and frequency of gambling behavior.
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3. Results 3.1. Assessment of latent dimensionality of the GABS Analyses were conducted separately in the student and PG samples. Results from the scree test and examination of relative size of eigenvalues revealed a single dominant unrotated factor that accounted for 61.1% and 47% of the common variance in student and PG samples respectively. In the student sample, 32 of 35 items loaded >0.30 on the first factor and items 3, 22, and 34 had loadings of 0.20, 0.25, 0.24, respectively. In the PG sample, 32 of 35 items had first-factor loadings >0.30, with the items 3, 22, and 23 loading 0.04, 0.29, and 0.29, respectively. The second factor extracted was significantly smaller in both samples and added an additional 9.7% and 14% of variance in the student and PG samples respectively. We retained all items for additional analyses as no item had a communality <0.40 or a factor loading <0.30 on the first factor in both student and PG samples and the items that loaded on the second factor were inconsistent across samples making a second factor uninterpretable. Mean inter-item correlations of 0.25 (SD ¼ 0:11) among students and 0.19 (SD ¼ 0:12) among PGs also were consistent with a predominantly unidimensional construct (Clark & Watson, 1995). 3.2. Concurrent validity The GABS was related significantly to the SOGS among the student (r ¼ 0:50, p < 0:001) and PG (r ¼ 0:41, p < 0:001) samples. As expected, the GABS and SOGS were not related significantly to the restricted range of gambling frequency among PG with r ¼ 0:10 and 0.07 respectively. Both the GABS and SOGS were related significantly (p < 0:001) to the frequency of gambling behavior among students with r ¼ 0:44 and 0.49 respectively. While controlling for the effect of gender (B ¼ 1:45, SE ¼ 0:27, p ¼ 0:0001) in the student sample, the GABS (B ¼ 0:69, SE ¼ 0:15, p ¼ 0:0001) and SOGS (B ¼ 0:83, SE ¼ 0:15, p ¼ 0:0001) total scores predicted independently an increase in the odds of being in a category of more frequent gamblers. The proportional odds assumption was met indicating that the predicted increase in odds of moving from less than monthly to monthly gambling, and the odds of moving from monthly to weekly gambling were equal (v2 ¼ 3:40, df ¼ 3, p ¼ 0:33). These results suggest that: (a) increasing GABS scores are related to increasing reports of gambling related problems in both student and PG samples; (b) both the GABS and SOGS scales are associated with an underlying continuum of gambling frequency, and (c) the GABS provides unique information about gambling frequency beyond that explained by the SOGS. 3.3. Differential item functioning Nine items exhibited DIF as evidenced by average OCC discrepancies greater than or equal to twice their standard error (see Table 1). At similar levels of gambling affinity, PGs were more likely than students to agree to items reflecting forgetting about time gambling (item 5), not wanting to quit when losing (item 14), using gambling to relieve negative affect (item 27 and item 35) and wanting to continue gambling until getting even (item 31). PGs were less likely across all levels of affinity for gambling to agree that it is important to act a certain way when winning (item
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30), that others are lucky to have around (item 12), and that they respect people who calmly make large bets (item 4). PGs were more likely to agree that winning a bet made them feel great (item 9). However, PGs were less likely than students to strongly agree, particularly for PGs at higher levels of affinity for gambling. Fig. 1 illustrates examples of ICC with 95% confidence intervals for biased items. Inspection of these curves reveals how for a biased item, students and PGs with the same level of affinity are expected to choose different options. Fig. 1 presents an example of four items where PG were more likely than students to report increased agreement and two items (12, 30), where students were more likely than PG to agree with items. 3.4. Assessing items’ ability to discriminate among levels of affinity Before comparing student and PG item-level characteristics, we removed GABS items with significant DIF and reanalyzed individual levels of affinity for gambling. Using the adjusted estimates of gambling affinity, we examined item characteristic curves (ICC) for students and PGs to assess each itemÕs overall ability to discriminate among the levels of gambling affinity. We plotted ICC according to an estimated total score and expected effective items to display ascending sloped curves. For example, Fig. 2 contrasts item discrimination differences for item 3 (a poorly performing item) and item 16 (a well performing item) in student and PG samples. Items 3, 8, 9, 11, 22, 23, and 34 showed poor ability to discriminate among either students or gamblers relative to other GABS items across levels of gambling affinity. Among PGs, additional items (12, 15, 17, 20) performed poorly because few PGs agreed with these items or because few PGs disagreed with these items (5, 14, 24, 26). 3.5. Comparing option characteristic curves for students and pathological gamblers OCC for all the 35 items were examined and compared across student and PG samples using the DIF adjusted index of level of affinity. We examined all 35 items OCC, including items with poor discrimination, as we were interested in whether particular options may be causing the poor discrimination and whether we could collapse responses to salvage items. Items effective in discriminating among levels of affinity for gambling in both student and PGs are described first, followed by examples of items that did not discriminate well. Fig. 3 illustrates examples of OCC from a discriminating item (item 6) and an item (item 3) that did not discriminate well in either sample. 3.6. Effective items Fifteen of the items without DIF (1, 2, 6, 7, 10, 13, 16, 18, 19, 21, 25, 28, 29, 32, 33) and five of the items with DIF (4, 27, 30, 31, 35) were effective in making discriminations in both samples. The belief that gambling makes one feel really alive (item 1) performed best among students. In PGs, item 1 was less discriminating because most PGs agreed but the top 25% of the PG sample were distinguished by the ‘‘strongly agree’’ option. Therefore, this item was retained as it discriminated well across the lower ranges and also provided additional discrimination in the highest regions of gambling affinity, a region populated primarily by PGs. We saw a similar pattern among item 7 (acting calm while gambling) and item 13 (viewing gamblers as more daring and
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adventurous). Among students, the probability of endorsing increasing options on these items varied directly with increasing levels of affinity for gambling. However, among PGs more than two-thirds were more likely to agree with item 7 and to disagree with item 13 than to endorse any
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of the other options. Therefore, these items perform well, but operate primarily at lower levels of gambling affinity. There were several items that performed well in both samples. Items included feeling due for a big win following a losing streak (item 2), the ability to identify winning and losing streaks (items 6 and 32), believing that there are strategies for winning no matter what the game (item 19), believing it is important to stay calm if losing (item 21), and believing that others can bring bad luck (item 29). Items describing the feeling of knowing when good luck is imminent (item 16), the belief that one should press their luck if they have been lucky (item 25), and the belief that bad luck is bound to change (item 33) also performed well in both the student and PG samples. Three items, item 10 (importance of feeling confident when gambling), item 18 (unparalleled excitement of making big bets), and item 28 (familiarity with games leads to success) performed best at the highest levels of gambling affinity. Only students and PGs at the highest levels of affinity agreed or strongly agreed to these items. While few students or PGs disagreed with these items, the strongly disagree option on item 18 did provide discrimination among those students and PGs at the lowest 20% of the distribution. 3.7. Ineffective items In contrast to the above items that effectively discriminated between students and PGs, several items exhibited significant floor effects across both samples. Few people agreed that making bets
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was sexy (item 17) regardless of levels of gambling affinity. Similarly, the belief that one is unable to know when luck is good or bad (item 3), belief in carrying a lucky charm while gambling (item 20), the belief that skills increase the probability of winning (item 15), the belief that others are lucky to have around (item 12), the belief that roulette takes more skill than playing the lottery (item 23), believing that gambling is boring (item 11), and the expectation that one will not get excited when gambling (item 22) all discriminated poorly in both samples with few people agreeing with these items. Additional items demonstrated significant ceiling effects across samples. Across all levels of gambling affinity, both students and PGs were more likely to agree or strongly agree than disagree or strongly disagree that some people are unlucky (item 8), that it feels great to win a bet (item 9), that casinos are glamorous and exciting places (item 24), that it is important to be a gracious winner (item 34), and that they get angry when losing at gambling (item 26). Additionally, items reflecting lost time while gambling (item 5) and disliking quitting when losing (item 14) were able to make discriminations among students, however, the same items performed poorly among PG
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Fig. 4. Map of the levels of discrimination provided by the 15 effective GABS items. Shaded areas reflect level of gambling affinity and 95%CI where each option from each of the 15 effective items becomes more likely than the previous option.
as almost all PG strongly agreed. Thus these items provided little information about differences among either students or PGs and should be eliminated in a reduced scale. 3.7.1. Assessing levels of discrimination Finally, we evaluated the ability of the set of 15 effective items to cover a wide enough range of severity to be useful in maximally separating individuals across a wide range of gambling affinity. We first estimated the severity of gambling affinity reflected by each item option and then examined options across items to determine if items reflected similar or non-overlapping levels of affinity (see Fig. 4). Each band represents the region and 95% confidence interval where each response becomes more likely (>50% chance) than the previous option. The width of the bands reflect the precision with which each item option places an individual below or above a particular level of affinity and narrower bands reflecting increased precision. With a four-option item, three discriminations are possible. Visual inspection of Fig. 1 suggests that several items are covering overlapping levels of affinity and that the 15 items also cover a considerable range of gambling affinity. For example, item 2 and item 6 appear to cover similar ground yet item 16 and item 18 appear to map non-overlapping regions. The 15-item set of GABS items retained significant correlations with SOGS and frequency of gambling, r ¼ 0:48 and 0.43, respectively in the student sample and r ¼ 0:36 and 0.09, respectively in the PG sample.
4. Discussion Current gambling assessment instruments are useful for the identification of gambling consequences and the characterization of individuals as pathological or nonpathological. However,
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these measures do not assess the attitudes and beliefs thought to accompany gambling activity. Assessing positive attitudes and beliefs about gambling may help to identify individuals at the lower end of the gambling continuum who may engage in frequent gambling and possess cognitive risk factors for gambling related problems. Item and content analyses support the GABS as a measure that taps a unidimensional construct we refer to as gambling affinity. The GABS has been shown to have good internal consistency and is related to the frequency of gambling behavior and indexes of gambling pathology (Breen et al., 2001; Breen & Zuckerman, 1999). In the current study, we provided additional support for the unidimesionality of the construct, internal consistency of the GABS, and the GABS relationship to gambling frequency and gambling problems (e.g. SOGS). We then used item-response theory to examine the construct of gambling affinity and whether the GABS indexed this latent construct similarly across samples selected by their low and high levels of gambling behavior (e.g. student and PG samples). As an initial analysis, we established the relationship of the GABS with a standard measure of gambling problems and the unique contribution of the GABS in predicting the frequency of gambling behavior among students. We then examined DIF to identify items that performed differently among students and PGs. Nine GABS items were endorsed in qualitatively different ways by student and PG samples even after equating both groups on levels of gambling affinity. Most notably, the content of these items reflected more extreme symptoms such as loss of time when gambling, loss of control, use of gambling to reduce negative affect and chasing lost bets. Indeed, items endorsed differentially by PGs potentially support a discontinuity in the continuum of gambling that is consistent with DSM-IV conceptualizations of pathological gambling typified by compulsivity or loss of control over gambling, gambling to escape problems, and chasing losses. Although our limited information about the demographic characteristics of these samples precluded follow-up analyses to examine whether differences were related to alternative sources such as age, education level or socioeconomic status, we were able to identify 26 items for which DIF was not found despite likely dramatic demographic differences across these samples. Following the identification of 9 items with a high degree of DIF, we examined the option characteristic curves of the items, which revealed an additional 11 items that did not discriminate well along the underlying continuum of gambling affinity. The remaining 15 GABS items (bolded items in Table 1) demonstrated the ability to effectively discriminate individual levels of gambling affinity across both student and PG samples. These effective items primarily fell in content domains related to cognitive biases including the misunderstanding of randomness, the belief in luck, and gambling-related illusions of control. Despite the promise of the current results, additional evaluation of the remaining itemÕs discriminate validity and stability of estimates across time is needed before we can be confident that affinity for gambling is a stable latent trait. Additional work also is needed to evaluate the statedependence of the GABS using more online behavioral measures of gambling involvement (cf. Lejuez et al., 2002; Lejuez et al., 2003). Further, a primary limitation of this study is the lack of detailed demographic information and therefore our inability to explore potential sources of differential item functioning limits immediate generalizability of obtained item characteristics. These groups are expected to differ on a number of characteristics that could include age, gender, education, socioeconomic status, levels of psychopathology, and levels of substance use disorders. Additionally, the differences in item responses of students may be specific to the developmental stage of college age gamblers or the kinds of gambling activities that are available to students and
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therefore discarded items may not show DIF among non-college age gamblers. Conversely, the differences in item responses among PG may be due to comorbid psychopathology among PGs and therefore discarded items may not show DIF when compared across student and nonpathological gamblers from the community. The degree to which we are justified in dropping items due to differences found in the current samples will need exploration in more representative samples of adults with more frequent and non-problem levels of gambling behavior. Lack of representation of regular non-problem gamblers in these samples prevents immediate generalization. Given the GABS stability within high and low levels of gambling behavior, an important next step will be to evaluate the GABS utility among gamblers who represent middle regions of the continuum and engage in more moderate levels of gambling behavior. 4.1. Future directions Cognitive biases are not unique to gambling behavior, but systematic variability in gamblingrelated cognitions across a range of gambling involvement supports the important theoretical contribution of cognitive biases to the development and maintenance of gambling behavior (e.g., Ladoucer & Walker, 1996). For example, people commonly demonstrate a self-serving bias when they attribute their gambling losses to situational factors such as a fumble or other ‘‘fluke’’ plays in a football game, or a ‘‘hot’’ dealer at a blackjack table. Winning at gambling is conversely explained as evidence of internal, stable traits such as competitiveness and intelligence. The potential net effect is that cognitive biases (and gambling affinity) are strengthened with cumulative experience and may contribute to increased gambling behavior. Interventions that target biases and misunderstanding of randomness by exposing individuals to information about actual contingencies have shown clinical effectiveness in treating PGs (e.g., Blaszczynski & McConaghy, 1989; Sylvain, Ladouceur, & Boisvert, 1997) and GABS scores have been shown to be sensitive to intervention as evidenced by decreased scores after treatment (Breen et al., 2001). In conclusion, whereas most assessment measures of gambling focus primarily on the categorization of pathological and nonpathological gamblers, the assessment of gambling affinity using the GABS provides the opportunity to examine the attitudes and beliefs of individuals across various levels of gambling activity. Such an assessment may be especially useful when looking to identify individuals with an underlying vulnerability to become pathological gamblers, but who currently do not meet the criteria. Future studies can evaluate prospectively, how levels of affinity predict progression towards pathological gambling, how levels of affinity upon entry into treatment predict outcomes, and how specific cognitive treatment components affect this potential riskfactor.
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