The Dimensional Structure of the Gambling Attitudes and Beliefs Survey: Challenging the Assumption of the Unidimensionality of Gambling-Specific Cognitive Distortions

The aim of the present study was to examine the dimensional structure of the Gambling Attitudes and Beliefs Survey (GABS). The GABS was administered to a sample of 415 individuals with self-reported problem or pathological gambling who were taking part in two different treatment studies preregistered with the German Clinical Trials Register (DRKS00013888) and ClinicalTrials.gov (NCT03372226). Exploratory factor analyses revealed a three-factor structure. We labeled the factors sensation seeking/illusion of control, luck/gambler’s fallacy, and attitude/emotions. Subsequent confirmatory factor analyses proved the three-factor model superior to the one-factor model proposed by the developers of the GABS. All dimensions were significantly correlated with symptom severity scores. Group comparisons showed significantly higher factor scores on the first factor (sensation seeking/illusion of control) for individuals reporting both skill-based and chance-based gambling compared to those reporting only chance-based gambling. The present study questions the unidimensionality of the GABS. A multidimensional assessment of gambling-related cognitive biases, beliefs, and positively valued attitudes may be useful in determining treatment outcomes and goals and in the development of novel interventions.


Introduction
Pathological gambling is classified as a behavioral addiction (American Psychiatric Association, 2013) that entails severe psychosocial, financial, and legal impairments (Cowlishaw et al., 2016) as well as high psychiatric comorbidity, further increasing the distress of those affected (Kessler et al., 2008;Lorains et al., 2011). Even subclinical gambling results in a lower quality of life and an increased number of stressful live events compared to non-gambling individuals (Weinstock et al., 2017).
Gambling-related cognitive biases and irrational beliefs are considered important mechanisms in the formation and maintenance of problem and pathological gambling (Ciccarelli et al., 2017;Cocker & Winstanley, 2015;Fortune & Goodie, 2012). The presence of these biases and beliefs has been found to increase the chance of relapse (Oei & Gordon, 2008;Smith et al., 2015), whereas a reduction has been found to predict recovery (Rossini-Dib et al., 2015). Therefore, the assessment and monitoring of gamblingrelated cognitive distortions is deemed important for treatment (Bodor et al., 2021).
Gambling-related cognitive distortions are frequently assessed with the Gambling Attitudes and Beliefs Survey (GABS; Breen & Zuckerman, 1994). The GABS is a 35-item self-report questionnaire capturing "a wide range of cognitive biases, irrational beliefs, and positively valued attitudes to gambling" (Breen & Zuckerman, 1999, p. 1102. Items are responded to on a 4-point Likert scale ranging from 1 = "strongly disagree" to 4 = "strongly agree." Higher scores on the GABS indicate positive attitudes towards gambling (e.g., exciting, socially meaningful) and proneness to cognitive distortions regarding luck and strategies (e.g., illusion of control, gambler's fallacy; Breen & Zuckerman, 1999). The GABS shows good internal consistency (Cronbach's α = 0.90) and significant correlation with gambling severity and frequency (Breen & Zuckerman, 1999;Breen et al., 2001;. The developers of the GABS, Breen and Zuckerman (1999), were surprised to find a unidimensional structure of the GABS capturing an overall gambling affinity. Unfortunately, in their original study they did not describe the results of their factor analyses in detail, and there has been disagreement in the literature on the dimensionality of the GABS ever since. For example, Strong and colleagues initially found that it had a two-factor structure but evaluated the second factor as uninterpretable and concluded that their findings lent further support to the unidimensionality of the measure . Moreover, they proposed a 15-item short form of the GABS with comparable quality to the original 35-item version. In another study, they investigated the unidimensionality of their 15-item version with a confirmatory analysis and found a predominant first dimension plus two additional factors (Strong, Daughters, et al., 2004). However, they excluded five items, leaving a unidimensional 10-item version of the GABS, which they recommended for use with male college student gamblers, and did not further investigate or discuss the two additional factors that initially emerged in their analyses. Further questioning the unidimensionality of the GABS, Bouju and colleagues' confirmatory factor analyses revealed a bad fit for the one-factor structure of the GABS in their data (Bouju et al., 2014). They proposed a 23-item version of the GABS with a five-factor structure (strategies, chasing, attitudes, luck, and emotions) with a significantly better fit.
In view of these inconsistent findings and the aforementioned limitations of previous studies, the aim of the present study was to reexamine the dimensional structure of the GABS in a sample of individuals with self-reported gambling problems. As the GABS-15 was found to be of equal psychometric quality to the original form  and might be of greater use in gambling research due to its lower number of items, we focused on this short form of the GABS. As the presence of different cognitive distortions has been found to differ between individuals preferring different forms of gambling (e.g., the higher presence of illusion of control in skill-based vs. chance-based gambling; Kalke et al., 2018;Mallorquí-Bagué et al., 2019), we assumed that gambling-related cognitive distortions would be best represented by more than one latent construct and therefore expected a multidimensional structure of the GABS-15 to emerge.

Study Design
The present study used data from the baseline assessments of two randomized controlled trials (RCTs) on the effectiveness of unguided Internet-based interventions in problem and pathological gambling (Bücker et al., 2018Wittekind et al., 2019). The first RCT examined the effectiveness of the depression-focused program Deprexis in 140 slot-machine gamblers with self-reported gambling and mood problems compared to a wait-list control group (Bücker et al., 2018). The second RCT examined the effectiveness of the gambling-specific program Restart  compared to a wait-list control group and an Internet-based approach-avoidance task (AAT; Wittekind et al., 2019) compared to sham training in 265 participants with self-reported gambling problems. Deprexis and Restart are both based on cognitive-behavioral therapy and provide psychoeducational texts, videos, audios, and interactive exercises. Both RCTs incorporated two times of measurement (baseline and post intervention), which were enrolled online using the software Questback ® .
On the first page of the baseline assessment, participants were informed about the aims and design of the particular trial. After providing informed consent for study participation, sociodemographic data and several questionnaires on symptom severity were applied. Finally, participants were asked to provide a pseudonymous e-mail address and create a personal code. Next, participants were randomly allocated to one of the intervention groups (direct access to either Deprexis, Restart, or AAT), or control groups (access to the intervention after completion of the post assessment) of the particular trial. Randomization was conducted using parallel assignment (ratio 1:1 or 1:1:1:1, respectively) and a computer-generated randomization sequence (block randomization). Participants were informed about group allocation via e-mail. For the intervention group, the e-mail included information on how to access Deprexis, Restart, or the AAT/sham training. After an intervention period of 8 weeks, participants were invited to the post assessment via e-mail. As an incentive, participants received a self-help manual about progressive muscle relaxation and mindfulness (Bücker et al., 2018;Wittekind et al., 2019) or an Amazon ® voucher of 20€ and access to an online approach bias modification training for gambling .

Participants
Participants were recruited online via gambling-and addiction-related Internet forums, Facebook ® groups, and information websites. Moreover, a Google AdWords ® campaign was run in German-speaking countries that displayed the webpage of the studies to individuals entering keywords such as "treatment + gambling disorder" or "self-help + gambling" into the search engine Google ® . The webpage of the studies contained information on study participation and the link to the baseline assessment. In addition, study flyers were sent to several institutions, including counseling centers and gambling halls.
Inclusion criteria for both studies were age between 18 and 65 (75 in the Restart-RCT), self-reported problem with pathological gambling and emotional distress (no formal diagnosis needed), Internet access, sufficient command of the German language, and informed consent. Exclusion criteria were acute suicidality (assessed with one item of the Patient Health Questionnaire-9 depression module) or a lifetime diagnosis of a psychotic disorder (assessed by self-report). Treatment as usual (TAU) was allowed for all participants in both studies.

Questionnaires
Only the measures of the two RCTs that were used for data analysis in the present study are described here. In addition to the instruments described in this section, we assessed sociodemographic variables (e.g., age, gender) and gambling-related characteristics (e.g., age at first gambling, average monthly loss).

Gambling Attitudes and Beliefs Survey-15 (GABS-15)
Similar to its original form, the 15-item short version of the GABS  measures irrational beliefs and attitudes towards gambling on a 4-point Likert scale (1 = "strongly disagree" to 4 = "strongly agree"). Higher scores indicate higher gambling affinity. The GABS-15 differentiates between non-problem, problem, and pathological gambling and demonstrates high incremental validity .

South Oaks Gambling Screen (SOGS)
The SOGS (Lesieur & Blume, 1987) uses 20 items to assess gambling severity over the previous 6 months. The total score can range from zero to 20 and differentiates between subclinical gambling (0-2), at-risk gambling (3-4). and pathological gambling (5-20). Internal consistency of the SOGS was found to be moderate (Cronbach's α = 0.69), and convergent validity was found to be good (Goodie et al., 2013).

Statistical Analyses
All analyses were performed using IBM SPSS Statistics 27. We conducted varimax-rotated exploratory factor analyses with all items of the GABS-15. We used both the Kaiser-Guttman criterion and scree plot inspection for interpretation. Factor scores were saved to the dataset and correlated with scores on gambling-related and depressive symptom severity. To compare our factor solution to the unidimensional factor structure proposed by Breen and Zuckerman (1999), subsequent confirmatory factor analyses were conducted using the SPSS extension SPSS2LAVAAN. Chi-square test, comparative fit index (CFI), Tucker-Lewis index (TLI), root mean square error of approximation (RMSEA), and standardized root mean square residual (SRMR) were used for interpretation. Finally, we compared factor scores of individuals reporting both skill-based and chance-based gambling to those reporting only chance-based gambling by means of unpaired t tests.

Baseline Characteristics
Sociodemographic characteristics, severity of gambling, and depressive symptoms as well as gambling-related characteristics of the sample (N = 415) are presented in Table 1. Almost three quarters of the sample were male. Participants on average reported moderate gambling severity and moderate depressive symptoms at baseline.

Factor Analysis
The matrix of intercorrelations of GABS items is displayed in Table 2. Criteria for conducting an exploratory factor analysis were met with a Kaiser-Meyer-Olkin index of 0.87, which confirmed sampling adequacy, and a significant Bartlett test (χ 2 (105) = 1972.43, p < 0.001), which confirmed the assumption of sphericity. According to the Kaiser-Guttmann criterion (eigenvalue > 1), three factors were extracted, which explained 53% of the total variance. Taking into account prior findings on the dimensionality of gambling-specific attitudes and beliefs (e.g., Bouju et al., 2014;Moritz et al., 2021;Steenbergh et al., 2002), we labeled the first dimension sensation seeking/illusion of control (explained variance after rotation: 20%), the second dimension luck/gambler's fallacy (explained variance after rotation: 19%), and the third dimension attitude/emotions (explained variance after rotation: 14%). Factor loadings for all 15 items are presented in Table 3.
Six items loaded on the first dimension (all loadings > 0.5), four items loaded on the second dimension (all loadings > 0.6), and three items loaded on the third dimension (all loadings > 0.7). Two items showed ambiguous loadings (item 1: Gambling makes me feel really alive; item 7: Sometimes I just know I am going to have good luck). All factors showed small correlations with SOGS scores and PHQ-9 (see Table 4). Whereas attitude/emotions was not correlated with the PG-YBOCS total as well as subscale scores (all p > 0.05), sensation seeking/illusion of control was significantly correlated with the total score as well as the subscales thoughts and behavior at small effect sizes. For luck/gambler's fallacy, moderate correlations were observed with the PG-YBOCS total score and the subscale thoughts, whereas small correlations were observed for the subscale behavior. None of the three factors correlated significantly with amount of monthly loss or debts (all p > 0.05). Only sensation seeking/illusion of control but not luck/gambler's fallacy and attitude/emotions significantly correlated with age at first gambling, age at frequent gambling, and number of forms of gambling played.
Interestingly, scree plot inspection indicated that the data could also be represented by only one factor, which is in line with the assumption of the unidimensionality of the GABS and had previously been proposed for the GABS and the GABS-15 (Breen & Zuckerman, 1999;. We compared our three-factor solution to a one-factor solution in confirmatory factor analyses. Items 1 and 7 were excluded from these analyses due to ambiguous loadings (see above). Confirmatory factor analyses proved the three-factor model (χ 2 (62) = 178.40, p < 0.001, CFI = 0.93, TLI = 0.91, RMSEA = 0.07, SRMR = 0.05) superior compared to the conventional one-factor model (χ 2 (65) = 434.70, p < 0.001, CFI = 0.76,   344 .302 .247 .305 .262 .315 .341 .183 .174 .249 .257 .201 .251 .277 2. If I have not won any of my bets for a while, I am probably due for a big win 1 .427 .203 .236 .245 .419 .299 .290 .165 .413 .239 .268 .355 .671 3. I know when I am on a streak 1 .144 .328 .214 .413 .224 .344 .215 .376 .243 .216 .388 .386 4. When I gamble, it is important to act as if I am calm even if I am not 1 .490 .171 .249 .160 .142 .415 .203 .258 .111 .216 .188 5. It is important to feel confident when I gamble 1 .241 .312 .213 .227 .396 .200 .343 .186 .297 .235 6. People who gamble are more daring and adventurous than those who never gamble .337 TLI = 0.71, RMSEA = 0.12, SRMR = 0.08). However, the statistically significant chi square test of both models, which indicates that the observed and expected covariance matrices differ significantly, implies that none of the compared models provides an ideal fit for the present data. On the other hand, it should be noted that the chi square test in confirmatory factor analysis is affected by sample size, with p values considerably decreasing in larger samples (Alavi et al., 2020;Babyak & Green, 2010).

Group Differences in Factor Loadings
Based on the first item of the SOGS, we categorized the forms of gambling played by participants as skill-based (i.e., card games, sports betting, horse betting, stock games, and skill games) and chance-based (i.e., dice games, casino games, lotteries, bingo, slot machines, and scratch lotteries). The majority of participants reported playing only chance-based games (n = 217); only nine participants reported playing only skill-based games. Playing both skillbased and chance-based forms of gambling was indicated by 183 participants. We then compared factor scores of individuals reporting chance-based gambling to those reporting skillbased gambling or both gambling forms. Unpaired t tests showed significantly higher scores on the first factor (sensation seeking/illusion of control) for the latter group (t (407) = 3.96, p < 0.001, d = 0.39). No group differences emerged regarding luck/gambler's fallacy (t (407) = 1.47, p = 0.143, d = 0.15) or attitude/emotions (t (407) = 1.24, p = 0.216, d = 0.12).

Discussion
The aim of the present study was to examine the dimensional structure of the GABS-15 in a sample of individuals with problem and pathological gambling. As hypothesized, a multidimensional structure emerged in the exploratory factor analysis, which is in line with a prior factor analysis challenging the unidimensional construct of the GABS (Bouju et al., 2014) and supports the statement of the scale's developers, Breen and Zuckerman: "the fact that only one factor emerged was surprising" (Breen & Zuckerman, 1999, p. 1102. Three factors emerged, which we labeled sensation seeking/illusion of control, luck/gambler's fallacy, and attitude/emotions. Subsequent confirmatory factor analyses found our threefactor model superior to the one-factor model. In a follow-up step, we aimed to assess convergent external correlates for these factors in order to validate the multidimensional model. All factor scores were significantly positively correlated with symptom severity scores, with strongest effect sizes found for the second factor (luck/gambler's fallacy). Moreover, significantly higher scores on the first factor (sensation seeking/illusion of control) were found for individuals playing both skillbased and chance-based games compared to those playing only chance-based games. These findings are in line with recent studies reporting greater illusion of control in individuals preferring skill-based forms of gambling such as poker or sports betting (Kalke et al., 2018;Mallorquí-Bagué et al., 2019) and further bring into question the relevance of illusion of control in chance-based forms of gambling such as slot machines .
Our findings imply that cognitive distortions are represented by more than one latent construct. As proposed by Bouju and colleagues (2014), a multidimensional approach of assessing cognitive biases, irrational beliefs, and positively valued attitudes to gambling might be helpful as it would allow treatment to be tailored to the specific beliefs and biases experienced by specific patients. Moreover, a multidimensional assessment might also help to further investigate differences in cognitive distortions experienced by different subgroups of individuals with gambling problems and contribute to more tailored treatment approaches.
Importantly, it has to be noted that the sample of the present study was comprised of help-seeking individuals with subclinical and clinical gambling problems. Therefore, our findings are limited to individuals seeking help; they might be more aware of dysfunctional thoughts compared to individuals not seeking help. Moreover, it remains to be tested whether our factor structure can be replicated in a sample of individuals with pathological gambling with a verified diagnosis and in a sample of healthy individuals. Finally, as described in the results section of this paper, the model fit was not fully satisfactory for either the three-factor or the unidimensional model.
To conclude, our findings further question the unidimensionality of the GABS. A multidimensional assessment of gambling-related cognitive biases, beliefs, and positively valued attitudes may be informative, especially for planning treatment targets. Psychotherapy research should take into account the multidimensionality of biases when devising new interventions as not all individuals and not all games are prone to the same fallacies/biases. Funding Open Access funding enabled and organized by Projekt DEAL.

Data availability
The data that support the findings of this study are available from the corresponding author upon request.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.