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Journal Information Journal ID (publisherid): jgi ISSN: 19107595 Publisher: Centre for Addiction and Mental Health 
Article Information Article Categories: JGI Scholar's Award Publication date: December 2016 Publisher Id: jgi.2016.34.11 DOI: 10.4309/jgi.2016.34.11 
A Method for Classifying Pathological Gamblers According to ‘‘Enhancement,’’ ‘‘Coping,’’ and ‘‘Low Emotion Regulation’’ Subtypes
Special Issue: JGI Scholar’s Award, Category B
Marcus Juodis  Psychology and Neuroscience, Dalhousie University, Halifax, Nova Scotia 
Sherry Stewart  Psychology and Neuroscience, Dalhousie University, Halifax, Nova Scotia 
Abstract
Pathological gamblers vary in their personality traits, psychopathological characteristics, and motivations for gambling. Methods for classifying them according to disseminated subtyping schemes, however, are not readily available, which may hinder further research on subtypes or efforts to incorporate subtyping schemes into clinical practice. With regard to affective motivations for gambling, we describe and evaluate a method for classifying pathological gamblers according to ‘‘enhancement,’’ ‘‘coping,’’ and ‘‘low emotion regulation’’ subtypes. Generalized squared distance was used to determine the best proﬁle ﬁt for 158 pathological gamblers on the basis of their Inventory of Gambling Situations (IGS) scores and in relation to reﬁned IGS subtype proﬁles obtained through cluster analysis, these reﬁned subtypes also having been validated via Gambling Motives Questionnaire scores. No gamblers were misclassiﬁed, suggesting that this method may perform well on crossvalidation. For interested researchers and practitioners, an easytouse tool is available that automates this proﬁlematching approach to classiﬁcation. Additional research is needed on how this method fares in independent samples of regular gamblers and of individuals with gambling disorder.
Keywords: gambling disorder, gambling motives, subtyping, classiﬁcation, assessment
Résumé
Les joueurs pathologiques varient quant à leurs traits de personnalitè, leurs caractèristiques psychopathologiques et leurs motivations à jouer. Il n’existe cependant pas de mèthodes facilement utilisables pour les classès selon des schèmas de soustypes dissèminès, ce qui risque de ralentir la recherche sur les soustypes ou les efforts dèployès pour intègrer des schèmas de soustypes à la pratique clinique. En ce qui concerne les motivations affectives au jeu, la prèsente ètude dècrit et analyse une mèthode de classement des joueurs pathologiques reposant les soustypes suivants : la << stimulation >>, l’<< adaptation >> et la << faible règulation des èmotions >>. La distance gènèralisèe au carrè a ètè utilisèe pour dèterminer la << meilleure correspondance de proﬁl >> pour 158 joueurs pathologiques en fonction de leur score au questionnaire de la liste des occasions de jeu (LOJ) et relativement à des proﬁls plus prècis de soustypes de la LOJ obtenus au moyen d’une analyse typologique et validès à partir des rèsultats du questionnaire sur les motivations à jouer. Aucun joueur n’a ètè classè de manière erronèe à l’aide de la mèthode analysèe, ce qui laisse entendre qu’elle peut être efﬁcace dans le cadre d’une validation croisèe. Un outil << facile d’emploi >> permettant d’automatiser une telle approche de classiﬁcation par association avec des proﬁls se trouve ainsi accessible aux chercheurs et aux praticiens intèressès. Des recherches supplèmentaires sont nècessaires pour dèterminer l’efﬁcacitè de cette mèthode avec des èchantillons indèpendants de joueurs ordinaires et de joueurs prèsentant un problème de jeu.
Introduction
Individuals with gambling disorder vary in their personality traits, psychopathological characteristics, and motivations for gambling. In fact, a comprehensive review of the literature revealed 18 articles that described subtypes of gambling disordered individuals according to these variables (Milosevic & Ledgerwood, 2010). Some of these subtypes included ‘‘recurringly depressed’’ and ‘‘chronically understimulated’’ gamblers (McCormick, 1987); ‘‘escape seekers’’ and ‘‘action seekers’’ (Lesieur & Blume, 1991); ‘‘simple,’’ ‘‘demoralized,’’ and ‘‘hedonic’’ gamblers (Vachon & Bagby, 2009); and ‘‘behaviorally conditioned,’’ ‘‘emotionally vulnerable,’’ and ‘‘antisocial impulsivist’’ gamblers (Blaszczynski & Nower, 2002; Ledgerwood & Petry, 2010). Subtyping pathological gamblers in such ways may lead to a better understanding of the potentially distinct etiologies of problem gambling for each subtype, which could have implications for tailoring treatment strategies to best meet the needs of each group and improve their respective treatment outcomes. However, despite dissemination of potentially useful subtyping schemes, we are unaware of any empirically supported methods for classifying pathological gamblers according to these proposed schemes, which may hinder further research on subtypes themselves or efforts to incorporate subtyping schemes into clinical practice.
In clinical practice, establishing why a client gambles (i.e., functional analysis) may facilitate a focused intervention that could enhance the therapeutic outcome (Stewart & Zack, 2008). The purpose of this article is to describe and evaluate a method for classifying individuals with gambling disorder according to their affective motivations for gambling, more speciﬁcally, for classifying those with gambling disorders according to the ‘‘enhancement,’’ ‘‘coping,’’ and ‘‘low emotion regulation’’ subtypes ﬁrst described by Stewart, Zack, Collins, Klein, and Fragopoulos (2008). In their original study, Stewart et al. (2008) had pathological gamblers complete the Inventory of Gambling Situations (IGS; LittmanSharp, Turner, & Toneatto, 2009)—a measure of the relative frequency of heavy gambling in various highrisk situations. Principal components analysis (PCA) was performed on the IGS subscale scores and revealed two higher order factors that were inferred from the observed pattern of factor loadings of the IGS subscale scores. These higher order factors included Unpleasant Emotions (i.e., a Negative Gambling Situations factor) and Pleasant Emotions (i.e., a Positive Gambling Situations factor). The factor scores were subjected to cluster analysis, which revealed three clusters: (a) enhancement gamblers, who were characterized by low negative and high positive highrisk gambling situation factor scores; (b) coping gamblers, who were characterized by very high negative and high positive highrisk gambling situation factor scores; and (c) low emotion regulation gamblers, who were characterized by low negative and low positive highrisk gambling situation factor scores. Factors were labelled according to the primary motives suggested by the main situations in which the participants reported heavy gambling. From these observed patterns of situationspeciﬁc gambling, it was inferred that enhancement gamblers gambled purely for positive reinforcement reasons; coping gamblers gambled for both positive and negative reinforcement, but mainly for negative reinforcement reasons; and low emotion regulation gamblers gambled for reasons other than to directly alter their mood (Stewart et al., 2008). Given that these subtypes were obtained by using a single, relatively brief, selfreport measure of situationspeciﬁc gambling, it was argued that this subtyping scheme had the advantage of being readily applicable in the clinical setting. However, without an easytouse method for classifying pathological gamblers that approximates the subtyping scheme obtained through cluster analysis, practitioners may not be able to classify new clients according to the scheme, which could hamper its possible clinical utility and which further underscores the need for an empirically based method of classiﬁcation.
The method for classiﬁcation described here was borrowed from the pain literature (see McKillop & Nielson, 2011; Turk & Rudy, 1988) and has been used successfully to match chronic pain patients, from their responses to a multiitem pain inventory known as the Multidimensional Pain Inventory (MPI; Kerns, Turk, & Rudy, 1985), to ‘‘dysfunctional,’’ ‘‘interpersonally distressed,’’ or ‘‘adaptive coper’’ subtype proﬁles. More precisely, generalized squared distance (D^{2}), also referred to as Mahalanobis distance, was used in the present study to determine the best proﬁle ﬁt for pathological gamblers on the basis of their IGS factor scores and in relation to IGS enhancement, coping, and low emotion regulation subtype proﬁles obtained through cluster analysis. From some of the favourable results observed in the pain literature showing misclassiﬁcation rates as low as 1.6% and 3% with kappa reliability coefﬁcients as high as .96 and .975 (McKillop & Nielson, 2011; Turk & Rudy, 1988), we hypothesized that D^{2} would approximate the assignment of gamblers to subtypes via cluster analysis with good precision.
Another equally important purpose of the present study was to ﬁrst determine the extent to which the original subtypes derived by Stewart et al. (2008) could be reﬁned by using an alternative, and perhaps more appropriate, clustering algorithm. It has been demonstrated that collinearity among variables can be problematic when conducting Kmeans cluster analysis with Euclidean distance speciﬁed as the distance metric because it assumes independence of the clustering variables and may produce distorted results (Sambandam, 2003). In the original study by Stewart et al. (2008), Kmeans cluster analysis was conducted by using the moderately correlated IGS Negative Gambling Situations and Positive Gambling Situations factor scores with Euclidean distance used as the distance measure. The present article describes the results obtained from a cluster analysis by using these original IGS factor scores with Mahalanobis distance speciﬁed as the distance metric, as it has been deemed an effective solution to the problem of collinearity (Sambandam, 2003). Moreover, given that Mahalanobis distance takes the correlated nature of variables into account, both as a clustering algorithm and as a method of determining individuals’ best proﬁle ﬁt, it made sense to reﬁne the original IGS subtype proﬁles for enhancement, coping, and low emotion regulation gamblers. In keeping with this study purpose, and consistent with the original study conducted by Stewart et al. (2008), it was also necessary to determine the extent to which a reﬁned cluster solution could be validated via scores on a measure of explicitly deﬁned, directly assessed gambling motives, separate from the IGS and its focus on antecedents/highrisk situations and inferred motives.
Method
Participants
The sample comprised the same 158 gamblers (mean age = 36.0 years, SD = 10.7 years; 77% men) who were recruited from the community by Stewart et al. (2008) through advertisements, and the data analyzed here are the same data obtained from that sample. Gamblers had to meet probable pathological gambler status by obtaining a score of 5 or greater on the South Oaks Gambling Screen (SOGS; Lesieur & Blume, 1987; mean score at screening = 11.8, SD = 4.0). They also had to disclose consuming alcohol at least 50% of the time when they gambled, as they were originally recruited for a study that examined the parallels between drinking and gambling motives (see Stewart & Zack, 2008). The minimum age to be eligible to participate was 19 years, and gamblers also had to be alcohol, drug, and medicationfree during their testing session. Exclusionary criteria included a history of chronic and serious mental illness (e.g., bipolar disorder, schizophrenia).
Materials
Participants completed a variety of selfreport measures. The measures of relevance to the present study included the IGS (LittmanSharp et al., 2009), the Gambling Motives Questionnaire (GMQ; Stewart & Zack, 2008), and the SOGS (Lesieur & Blume, 1987). Sample items for these measures can be seen in Table 1, along with the number of items for each of the subscales and internal consistencies (alphas) for the subscales in the present sample.
Inventory of Gambling Situations
The IGS (LittmanSharp et al., 2009) is a selfreport questionnaire made up of 63 items that measure the relative frequency of heavy gambling in various highrisk situations. It is used to proﬁle possible relapse situations for problem gamblers in both research and treatment settings (LittmanSharp et al., 2009). The IGS was modelled after the reliable and valid Inventory of Drinking Situations (IDS; Annis, Graham, & Davis, 1987; Carrigan, Samoluk, & Stewart, 1998; Stewart, Samoluk, Conrod, Pihl, & Dongier, 2000). That is, items from the IDS Unpleasant Emotions, Pleasant Emotions, Social Pressure, Urges and Temptations, Testing Personal Control, and Conﬂict with Others scales were reworded to ﬁt the context of gambling. Furthermore, new items were added that were speciﬁc to the context of gambling: items from the Winning and Chasing Losses, Conﬁdence in Skills, Need For Excitement, and Worried Over Debts scales. The initial pool of items was reviewed by experts, and items were selected on the basis of psychometric analyses, including factor analysis (LittmanSharp et al., 2009). When completing the IGS, gamblers indicate their frequency of heavy gambling over the past year (with responses ranging from 1 = almost never/never gambled heavily in that situation to 4 = almost always gambled heavily in that situation) in 10 separate categories of situations. The IGS has demonstrated strong psychometric properties (LittmanSharp et al., 2009). It was used as the primary measure of gambling motives in the present study, where motives were inferred by virtue of the primary situations in which gamblers reported gambling heavily.
Gambling Motives Questionnaire
Participants completed Stewart and Zack’s (2008) GMQ, a measure modelled after the reliable and valid Drinking Motives Questionnaire (DMQ; Cooper, Russell, Skinner, & Windle, 1992). The GMQ captures the relative frequency of gambling for 15 speciﬁc reasons. GMQ items were adapted directly from the DMQ, except for one item. More speciﬁcally, this one item was rephrased from ‘‘to get high’’ on the DMQ to ‘‘to get a high feeling’’ on the GMQ, so that it was more appropriate to the context of gambling. Consistent with the DMQ, there are three subscales: Social, Coping, and Enhancement gambling motives. Participants rated the relative frequency of their gambling on the same 4point scale used for the DMQ (i.e., 1 = almost never/never; 2 = sometimes; 3 = often; 4 = almost always). Stewart and Zack (2008) demonstrated that the GMQ has strong psychometric properties.
South Oaks Gambling Screen
The SOGS (Lesieur & Blume, 1987) is a 20item selfreport measure that taps respondents’ lifetime gambling habits. The 20 items used to obtain the SOGS total score were derived from problem gambling counsellors, Gamblers Anonymous 20 questions, and the Diagnostic and Statistical Manual of Mental Disorders (3rd ed., American Psychiatric Association, 1980). Those with a likely gambling disorder (i.e., ‘‘probable pathological gamblers’’) are usually identiﬁed by using a total score of 5 or more as the SOGS cutoff score; the psychometric properties of the SOGS are acceptable (see Lesieur & Blume, 1987).
Procedure
This secondary analysis used the data set obtained by Stewart et al. (2008). In the original study, testing was completed individually. Participants were asked to abstain from alcohol consumption for a period of at least 12 hours prior to their appointment, and breath alcohol tests were used upon arrival at the laboratory in order to conﬁrm abstinence. A computerized reaction time task was completed ﬁrst (see Zack, Stewart, Klein, Loba, & Fragopoulos, 2005, for results). After a short break, participants completed the aforementioned selfreport questionnaires.
Results
Reducing the IGS Data
In the original study by Stewart et al. (2008), prior to cluster analyzing the data from the IGS, factor analysis was performed on the IGS subscale scores in order to reduce the 10 subscales to a more parsimonious number of core types of gambling situations. The factor structure, factor labels, and factor scores for the participants in the original study were retained for the present study. To summarize, Stewart et al. (2008) conducted PCA on the 10 subscale scores of the IGS. The researchers could proceed with PCA on the given data set, as the KaiserMeyerOlkin measure of sampling adequacy was > .50 (i.e., .92). Oblique rotation was selected to permit intercorrelation among factors, and both inspection of the scree plot and use of Kaiser’s eigenvalue > 1 rule indicated a twofactor solution. The twofactor solution obtained demonstrated excellent simple structure, with only one observed complex loading: The Urges and Temptations scale loaded on both factors. Furthermore, there were no hyperplane items, and there were a large number of salient loadings on each factor. It should be noted that the two factors obtained were found to be moderately intercorrelated (r = .64). Together, these two factors were found to account for 81.2% of the variance in IGS item scores. Because the ﬁrst factor showed strong salient loadings on the Unpleasant Emotions, Conﬂict with Others, and Worried Over Debts subscales, it was labelled Negative Situations for gambling. Prior to rotation, the ﬁrst factor was found to account for 70.1% of the variance in IGS subscale scores. Because the second factor showed strong salient loadings from the Pleasant Emotions, Need for Excitement, and Social Pressure subscales, it was labelled Positive Situations for gambling. Prior to rotation, the second factor was found to account for an additional 11.1% of the variance in IGS subscale scores.
Reﬁning the Stewart et al. (2008) Subtypes of Pathological Gamblers With the Alternative Clustering Algorithm
In the original study (Stewart et al., 2008), initial clusters were ﬁrst obtained via Ward’s squared Euclidean distance method by using the factor scores for each participant. The scree plot method indicated a threecluster solution for the number of clusters in the data set. Next, Stewart et al. (2008) conducted a Kmeans cluster analysis by using the IGS factor scores for each participant, and this analysis was constrained to produce a threecluster solution. Euclidean distance was speciﬁed as the distance metric. In the present study, cluster analysis was rerun on the original IGS factor scores with Mahalanobis distance speciﬁed as the distance metric. The Kmeans cluster analysis conducted in the present study was similarly constrained to produce a threecluster solution. Again, a cluster was identiﬁed that was characterized by high scores on both the Negative Gambling Situations factor (mean factor score = 1.128) and the Positive Gambling Situations factor (mean factor score = 0.577), with a notably higher elevation on the Negative Gambling Situations factor; thus, the cluster was inferred to involve gamblers who gamble primarily to cope with negative situations and was thus labelled the coping gamblers cluster (n = 50; 32% of the entire sample). As in the original study, another cluster was identiﬁed that was characterized by negative scores on the Negative Gambling Situations factor (mean factor score = 0.395) and positive scores on the Positive Gambling Situations factor (mean factor score = 0.321); thus, this cluster was again labelled as enhancement gamblers (n = 70; 44% of the entire sample) because of the relatively higher elevation on the Positive Gambling Situations factor. The third cluster was characterized by low scores on both the Negative Gambling Situations (mean factor score = 0.756) and the Positive Gambling Situations (mean factor score = 1.349) factors. This cluster was similar to the third cluster observed in the original study; thus, the cluster was again inferred to be motivated to gamble by reasons other than desires to regulate emotions and was labelled low emotion regulation gamblers (n = 38; 24% of the entire sample) because of their low scores on both factors of the IGS.
For comparative purposes, the three clusters of gamblers obtained in the original study and those obtained in the present study are proﬁled in Figure 1. As can be seen in the ﬁgure, the three proﬁles of gamblers obtained via the Kmeans cluster analysis by using Euclidean distance (original study) were similar to the Kmeans cluster analysis obtained by using Mahalanobis distance (present study). Moreover, there was moderate agreement between the two clustering algorithms (kappa = .59, p < .001; Landis & Koch, 1977). More speciﬁcally, 118 cases (75% of the entire sample) were assigned to similarly labelled clusters by both clustering algorithms.
Validation of the Reﬁned Cluster Analysis with the GMQ
Stewart et al. (2008) performed a factor analysis on the GMQ prior to validating the original IGS cluster solution. Again, these factor analytic results were used for validating the reﬁned IGS cluster solution. To summarize, a PCA with oblique rotation was conducted on the GMQ. This analysis produced the three expected GMQ factors of Enhancement, Social, and Coping motives, using Kaiser’s eigenvalue > 1 rule to determine the number of factors to retain. Scores on the factors for each participant were saved for hypothesis testing, so that each gambling motive score was weighted for the relative contributions of each of the GMQ items. As in the original study, a 3 (reﬁned IGS cluster group) 2 (GMQ subscale) analysis of variance was conducted with the Enhancement and Coping GMQ factor scores entered again as the dependent variables. Consistent with the results of the Stewart et al. (2008) original study, the analysis indicated a main effect of IGS cluster group, F(2, 151) = 27.03, p < .001. As with the original study, this result was qualiﬁed by the predicted signiﬁcant Reﬁned IGS Cluster Group GMQ Subscale interaction F(2, 151) = 15.78, p < .001, which again reﬂected relatively higher GMQ Enhancement factor scores (M = .502; SD = .562) versus GMQ Coping factor scores (M = .113; SD = .774) in the IGS enhancement gambler cluster, as compared with relatively higher GMQ Coping factor scores (M = .990; SD = .765) versus GMQ Enhancement factor scores (M = .578; SD = .634) in the IGS coping gambler cluster. As in the original Stewart et al. (2008) study, there was a signiﬁcant simple effect of reﬁned IGS cluster group membership for the GMQ Enhancement motives factor scores, F(2, 151) = 13.05, p < .001. GamesHowell post hoc tests showed that, as was hypothesized in the original study, the IGS enhancement gambler cluster again obtained signiﬁcantly higher (p < .01) GMQ Enhancement factor scores than did the IGS low emotion regulation gambler cluster (M = 0.085; SD = .810). Similarly, the IGS coping gambler cluster again obtained signiﬁcantly higher GMQ Enhancement factor scores (p < .001) than did the IGS low emotion regulation gambler cluster; however, these clusters did not obtain signiﬁcantly higher GMQ Enhancement factor scores (p > .05) than did the IGS enhancement gambler cluster. Consistent with the original Stewart et al. (2008) study, there was another signiﬁcant simple effect of reﬁned IGS cluster group membership for the GMQ Coping motives factor scores, F(2, 151) = 27.53, p < .001. As was hypothesized in the original study, the IGS coping gambler cluster obtained signiﬁcantly higher GMQ Coping factor scores (p < .001) than did the IGS low emotion regulation gambler cluster (M = .024; SD = .997) and signiﬁcantly higher GMQ Coping factor scores (p < .001) than did the IGS enhancement gambler cluster. As was the case in the original study, GMQ Coping factor scores did not differ signiﬁcantly between the IGS enhancement gambler and low emotion regulation gambler clusters in the present study (p > .05).
For comparative purposes, the GMQ Coping and Enhancement motives factor scores for the clusters of gamblers obtained with the IGS in the original study and the clusters of gamblers obtained in the present study with the IGS are plotted in Figure 2. (Note that the ns for each cluster in Figures 1 and 2 are not identical because full data on the GMQ were unavailable for four participants.) As can be seen in Figure 2, consistent with the results of the original study, the clusters of gamblers identiﬁed with the IGS in the present study were similarly crossvalidated by a discriminating elevation in GMQ Coping motives in coping gamblers and by noteworthy elevations in GMQ Enhancement motives in both enhancement and coping gamblers.
Determining Proﬁle Goodness of Fit for Individual Cases of Pathological Gambling
The method used by Turk and Rudy (1988), and later by McKillop and Nielson (2011), for comparing a respondent’s scores on the MPI (Kerns et al., 1985) with three MPI psychosocial proﬁles—dysfunctional, interpersonally distressed, and adaptive coper—was used in the present study to compare a gambler’s scores on the IGS with the reﬁned IGS enhancement, coping, and low emotion regulation gambler proﬁles. More speciﬁcally, generalized squared distances (D^{2}) were calculated for each gambler by comparing his or her scores on the IGS factors with the three reﬁned gambler proﬁles. These calculations yielded three D^{2} values for each gambler, the lowest value representing the best proﬁle ﬁt for the gambler. D^{2} is deﬁned as follows:
McKillop (2010) provided a description of the steps required for calculating D^{2}, as well as an example of how to compare a respondent’s proﬁle of scores on the MPI to the adaptive coper proﬁle. In a similar manner, the following example describes the comparison of a gambler’s proﬁle of IGS factor scores to the coping gambler proﬁle to demonstrate these calculations in the context of the present study. More speciﬁcally, in the preceding formula, the terms xi and xj represent any two points in multivariate space, and the term S 1 represents the inverse covariance matrix of the IGS factor scores. The term xi represents a vector or proﬁle of factor scores for any particular gambler. As an example, assume that a gambler’s Negative Gambling Situations factor score and Positive Gambling Situations factor score on the IGS are 2.196 and 1.566, respectively. Again, assume that this gambler’s proﬁle is being compared to the coping gambler proﬁle, which has mean values of 1.128 and 0.577 on the Negative Gambling Situations and Positive Gambling Situations factors, respectively. Thus, in matrix algebra form, (x_{i} – x_{j})^{l} is expressed as follows:
The next step is to premultiply this vector by the inverse covariance matrix, which is expressed as follows:
Then, postmultiply to obtain the distance value between the gambler’s profile and the coping gambler profile:
Generalized squared distance approximates a chisquare (w2) distribution with degrees of freedom being equal to the number of proﬁle or vector variables (McKillop, 2010). Thus, goodness of ﬁt for this particular example can be expressed as follows:
For the present study, a spreadsheet was created to automate the calculations for generalized squared distances (D^{2}) for each gambler on the basis of his or her IGS factor scores. Thus, the spreadsheet also determined the best proﬁle ﬁt for each gambler, as the lowest of the three obtained D^{2} values indicated his or her best proﬁle ﬁt. This spreadsheet and the user guidelines are available from the authors upon request. In the same manner as McKillop and Nielson (2011), we compared the best D^{2} for each gambler with the reﬁned Kmeans cluster assignment for each gambler. Classiﬁcation agreement was perfect, as none of the gamblers were misclassiﬁed (kappa = 1.0, p < .001), indicating that generalized D^{2} approximated the reﬁned cluster solution with precision.
Discussion
The coping, enhancement, and low emotion regulation subtypes of pathological gamblers derived by Stewart et al. (2008) were reﬁned when the data used to derive them were subjected to an extended cluster analysis by using an alternative clustering algorithm—an algorithm that used Mahalanobis distance speciﬁed as the distance metric instead of Euclidean distance. Consistent with the results from the original study, enhancement gamblers appeared to gamble purely for positive reinforcement; coping gamblers appeared to gamble for both positive and negative reinforcement, but primarily for negative reinforcement; and low emotion regulation gamblers appeared to gamble for reasons other than the direct modulation of mood. There seemed to be a moderate level of agreement between the clustering algorithm used in the original study and the algorithm used in the present study, suggesting that the results of the original study were not overly distorted by the use of Euclidean distance. The results obtained in the present study, however, could be considered somewhat reﬁned because the cluster analysis that relied on Mahalanobis distance took into account the correlated nature of the clustering variables: gambling in negative situations and gambling in positive situations.
In the original study, the obtained cluster solution was based on gamblers’ selfreported primary antecedents for gambling, as measured by the IGS (LittmanSharp et al., 2009), and was validated with a measure of selfreported gambling motives, as measured by the GMQ (Stewart & Zack, 2008). Consistent with these original results, the cluster solution obtained in the present study also was ‘‘crossvalidated’’ by selective elevations in GMQ Coping motives in coping gamblers and by elevations in GMQ Enhancement motives in both enhancement and coping gamblers (Stewart et al., 2008, p. 263). Given these ﬁndings, readers may ask: why not subtype gamblers according to their GMQ scores? Certainly this is a possibility that could be empirically tested. It should be pointed out, however, that one advantage of subtyping gamblers according to the method described here is that it does not require them to have insight into their gambling motives. Rather, it requires only that they have memory or knowledge of the situation(s) in which they have gambled most heavily.
Borrowing from the literature that described a method for matching chronic pain patients to dysfunctional, interpersonally distressed, or adaptive coper proﬁles on the basis of their responses to a multiitem pain inventory (McKillop & Nielson, 2011; Turk & Rudy, 1988), we used generalized squared distance (D^{2}) in the present study to determine each individual gambler’s best proﬁle ﬁt in relation to the reﬁned coping, enhancement, and low emotion regulation gambler proﬁles. On this point, and consistent with the favourable results observed in the pain literature, D^{2} approximated the reﬁned cluster solution with precision. User guidelines and the spreadsheet that was created to determine each gambler’s best proﬁle ﬁt are available from the authors upon request. This tool provides a means for making objective and empirically based decisions for classifying gamblers according to the reﬁned subtypes; thus, it could be used by researchers or practitioners with an understanding of psychometric theory and skills in clinical assessment to determine other pathological gamblers’ best proﬁle ﬁt for various purposes. On this point, it is worth mentioning that, because D^{2} approximates a chisquare (w2) distribution, with degrees of freedom being equal to the number of proﬁle variables (McKillop, 2010), a bonus of using D^{2} is that it allows the user to comment on the signiﬁcance of the values obtained (an option that is not available with the use of Euclidean distance). Given that the reﬁned subtyping scheme is based on scores from a fairly brief selfreport measure that is available for professional use at no cost (i.e., the IGS), classiﬁcation of pathological gamblers according to these subtypes could be incorporated into clinical practice with relative ease. From the evidence from randomized controlled trials supporting the efﬁcacy of motivationmatched treatments for substance misuse developed in recognition of subtyping schemes that incorporated underlying motivations and personality factors (e.g., Conrod et al., 2000), it has been hypothesized that motivationmatched treatments for pathological gamblers might help improve treatment outcomes (Stewart et al., 2008). Clinicians who specialize in the provision of gambling treatment could use this tool to match their clients to the aforementioned proﬁles and then tailor their treatments accordingly. As another example of its potential use, researchers could use the tool to identify the subtypes of gamblers in order to study their possible etiologies, as this provides one method of operationally deﬁning them.
The potential limitations of the original study that were addressed by Stewart et al. (2008) still apply to the ﬁndings concerning the reﬁned subtyping scheme (e.g., reliance on selfreport measures, crosssectional study design, use of a sample of participants who drank alcohol at least 50% of the time when they gambled) and are not discussed in detail again here. With regard to limitations of the method used to match gamblers to the reﬁned proﬁles, this method requires crossvalidation on samples of gamblers that are independent of the development sample; thus, research aimed at crossvalidation would be a logical step forward, ideally on even larger samples of gamblers.
On these notes, the promising ﬁndings from the present study suggest that the proposed method for classifying subtypes should hold up well on crossvalidation. However, the development sample was not necessarily representative of all problem gamblers given the inclusion criteria (e.g., drinking regularly while gambling; Stewart et al., 2008). For example, coping gamblers might be overrepresented in this sample of problem gamblers who regularly drink while gambling because prior work has shown that coping gamblers drink more frequently and problematically than other >gambler subtypes (Stewart et al., 2008). Thus, future research should focus on the extent to which the method used to classify gamblers according to the present subtyping scheme can be used with other samples, including nonproblem gamblers and those who do not regularly drink while gambling.
Intuitively appealing subtyping schemes for those with gambling disorders have not been incorporated routinely into clinical practice, perhaps because ‘‘easytouse’’ assessment methods for classifying gamblers have not been provided (Stewart et al., 2008, p. 258). It is our hope that the method of classiﬁcation described in this article, along with the tool offered that automates classiﬁcation according to gamblers’ affective motivations for gambling, may make the option of subtyping those with gambling problems more of a possibility for practitioners who would like to use this research to inform their clinical work. We also hope that dissemination of this classiﬁcation method facilitates future research on these subtypes, as well as research on other subtyping schemes in general. Future investigations may reveal better models for subtyping pathological gamblers, better statistical procedures for subtyping them, and better methods for classifying them; however, we believe that the present work represents a positive step forward in dealing with the complex heterogeneity of those with gambling disorders in both research and practice.
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Submitted September 30, 2015; accepted August 11, 2016. This article was peer reviewed. All URLs were available at the time of submission.
For correspondence: Sherry H. Stewart, PhD, Department of Psychology & Neuroscience, P.O. Box 15000, Dalhousie University, Halifax, NS, B3H 4R2. Email: sstewart@dal.ca
Competing interests: None declared (both authors).
Ethics approval: This study involved secondary data analysis of deidentiﬁed data.
Acknowledgements: This research was supported by a generous grant cofunded by the Ontario Problem Gambling Research Centre and the Nova Scotia Gaming Foundation (now Gambling Awareness Nova Scotia). S.H.S. was supported through an Investigator Award from the Canadian Institutes of Health Research and by a Killam Professorship from the Dalhousie Faculty of Science at the time this research was conducted. M.J. was supported by the Social Sciences and Humanities Research Council of Canada and by the Nova Scotia Health Research Foundation during the undertaking of the present study. The authors would like to acknowledge the contributions of Martin Zack to the original study from which these data are derived, the contributions of Pamela Collins and Fofo Fragopoulos for their assistance in data collection, and the contributions of Maureen Balcom in data entry.
The authors also wish to thank Jeff McKillop for conceptual and statistical assistance in the undertaking of the present study.
Appendix A
The supplementary material for this article is a spreadsheet that assists in the determination of whether a probable pathological gambler who meets the same study inclusion criteria described in the Method section of this article may be best considered an enhancement gambler, a coping gambler, or a low emotion regulation gambler (ﬁrst described by Stewart et al., 2008) according to the gambler’s raw responses to the Inventory of Gambling Situations (IGS; LittmanSharp et al., 2009) and according to the reﬁned proﬁles of IGS Negative Gambling Situations and Positive Gambling Situations factor scores for the enhancement, coping, and low emotion regulation subtypes described in the Results section of this article.
More speciﬁcally, the spreadsheet calculates generalized squared distances (D^{2}) for a gambler by computing and comparing the gambler’s scores on the IGS factors with the IGS factor scores for the three reﬁned enhancement, coping, and low emotion regulation gambler proﬁles. Thus, the spreadsheet produces three D^{2} values for the gambler. The lowest of these three D^{2} values represents the best proﬁle ﬁt for the gambler. Interested users may refer to the Results section of this article for an example of how to perform these calculations manually.
Because the spreadsheet calculates D^{2} by using IGS factor scores, it calculates IGS Negative Gambling Situations and Positive Gambling Situations factor scores for each gambler that are based on input of his or her raw responses to the individual IGS items and that are based on the results of the principal components analysis (PCA) described in the Results section of this article (also see Stewart et al., 2008). As an intermediary step, because this PCA was performed on IGS subscale scores (e.g., Conﬂict with Others, Urges and Temptations, Need for Excitement), the spreadsheet also calculates the gambler’s IGS subscale scores on the basis of his or her raw responses to the individual IGS items (interested users may refer to LittmanSharp et al., 2009, for instructions on how to manually calculate and interpret these scores).
The spreadsheet was created by using Microsoft Ofﬁce Excel 2003 and should function with later versions of this program. The spreadsheet may be distributed and shared without permission, but it cannot be resold or distributed for proﬁt.
Instructions

Download and open the Microsoft Excel Worksheet ﬁle named ‘‘Gambler Proﬁle Match.’’ Rightclick on icon next to Appendix A title.

Type the gambler’s responses to the individual IGS items into the cells directly below those labelled ‘‘igs1’’ through ‘‘igs63.’’ For example, if the gambler circled the number 2, indicating that he or she ‘‘rarely’’ gambled heavily in response to the ﬁrst item on the IGS (i.e., ‘‘When I almost won and felt that I would win very soon’’; LittmanSharp et al., 2009), then type the number 2 into cell A4 of the spreadsheet. If the gambler circled the number 3 in response to the second item, then type the number 3 into cell B4, and so on.

After the gambler’s responses to all of the IGS items have been typed into the spreadsheet, press the Enter button.
It should be noted that the spreadsheet is meant to handle data from a gambler who provides a response to all of the IGS items. It should also be noted that the spreadsheet does not ﬂag data entry errors on the part of the user (e.g., entering a value of 40 instead of 4 as a response to an individual IGS item). Furthermore, copying and pasting a gambler’s data from another spreadsheet or data set has been found to result in calculation errors; thus, manual entry of a gambler’s responses to the IGS items is recommended.
Interpreting Output
After the gambler’s raw responses to all of the IGS items have been entered into the spreadsheet and doublechecked, the spreadsheet automatically calculates the gambler’s IGS subscale scores and displays them in cells E20 through E29. As mentioned previously, interested users may refer to the work of LittmanSharp et al. (2006) for direction on how to interpret IGS subscale scores.
The spreadsheet also automatically calculates the gambler’s IGS Negative Gambling Situations and Positive Gambling Situations factor scores according to the PCA described in the present article and in Stewart et al. (2008). The gambler’s IGS Negative Gambling Situations and Positive Gambling Situations factor scores are displayed in cells B35 and C35, respectively.
Finally, the spreadsheet automatically calculates D^{2} for the gambler by comparing his or her scores on the IGS factors with the three reﬁned gambler subtype IGS proﬁles (Steps 1 through 3 within the spreadsheet are provided for users who are interested in how the spreadsheet performs these calculations). The spreadsheet produces three D^{2} values for the gambler in cells I33, I34, and I35 under the ‘‘Chisquare’’ heading. It should be noted that D^{2} approximates a chisquare (w2) distribution, with degrees of freedom being equal to the number of proﬁle variables (McKillop, 2010; i.e., two proﬁle variables in this context). Cells I33, I34, and I35 are D^{2} values in relation to the enhancement gambler proﬁle, low emotion regulation gambler proﬁle, and coping gambler proﬁle, respectively. The lowest of the three D^{2} values in these cells represents the best proﬁle ﬁt for the gambler. Thus, if the lowest value is in cell I33, then the gambler may be best considered an enhancement gambler. Alternatively, if the lowest value is in cell I34, then the gambler may be best considered a low emotion regulation gambler, or, if the lowest value is in cell I35, then the gambler may be best considered a coping gambler.
The values produced in cells J33, J34, and J35 are corresponding p values for the chisquare values displayed in cells I33, I34, and I35, respectively, which could be used to comment on the signiﬁcance of proﬁle ﬁt if desired.
As an example, the default values saved within the spreadsheet upon ﬁrst downloading it represent those of a hypothetical low emotion regulation gambler, as the lowest D^{2} value can be seen in cell I34. Thus, goodness of ﬁt for this hypothetical gambler can be expressed as follows:
x^{2}(2) = 0.575, p = 0.75
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