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Gambling behavior--a prevalence study and examination of the factors among students.

1. Introduction

Pathological gambling is characterized by persistent and recurrent maladaptive gambling behavior, leading to significant deleterious legal, financial, physical and psychosocial consequences. The prediction of gambling problem is related, inter alia, with the participation in gambling activities.

Gambling is a popular and prevalent behavior among adolescents. In the majority of situations, gambling in adolescence does not appear to have obvious serious negative consequences; however, in a number of cases it does. Despite higher prevalence rates of gambling problem among youth, there are clear empirical and clinical findings suggesting that youth problem and pathological gamblers, similar to adults gamblers, are, in fact, not a homogeneous group (Gupta and Derevensky 1997). Hence, it is possible that different types of adolescents will engage in different gambling activities with different subsequent effects because, gamblers differ in how they respond to the structural and situational characteristics of gambling activities in which they play. So, it is likely that different factors account for the development of gambling problems in different groups. Understanding gambling subtypes is necessary to improve our understanding of the etiology of problem gambling. Therefore studying all gamblers, considering activity types, may be helpful to better understand gambling related problems. As a result, it is important to build a predictive or structural model for class membership, underlying gambling activities' participation. Identifying groups based on similar patterns of behavioral or other characteristics may suggest different etiological processes at work, or may provide different implications for prevention and treatment. It seems, then, that conceptualizing gamblers as a discrete latent variable and using appropriate methods to model gambling behavior may be particularly useful. In doing so, differences that may play an important role in the etiology and prevention of the development of problem and pathological gambling may be discovered.

In a more explanatory study, one may wish to build a predictive or structural model for class membership whereas in a more descriptive study the aim would be to simply profile the latent classes by investigating their association with external variables (covariates) and to examine if some risk or protective factors of problem gambling among adolescents influence gambling problems differently across classes. So, our study might be useful in identifying different subgroups of gamblers in the population and show which characteristics are more commonly associated with a higher risk of developing gambling problems across these subtypes. Similar to drug consumption, gambling activities are highly reinforcing, mainly because of the thrill they provide (Griffiths, 2011).

For young people in particular, the option to "easily" win money represents a major incentive. One consistent finding in the literature is that males are more likely to gamble than females (e.g., Bakken, Gotestam, Grawe, & Wenzel, 2009; Derevensky et al., 2010; Fried, Teichman, & Rahav, 2010; Goldstein, Walton, Cunningham, Resko, & Duan, 2009; Jackson, Dowling, Thomas, Bond, & Patton, 2008; Molde, Pallesen, Bartone, Hystad, & Johnsen, 2009; Moodie & Finnigan, 2006; Moore & Ohtsuka, 1997, 1999a; Welte, Barnes, Tidwell, & Hoffman, 2008; Welte, Barnes, Wieczorek, Tidwell, & Parker, 2002).

Males have more gambling problems than females and spend more time gambling (Chiu & Storm, 2010; Clark & Walker, 2009; Derevensky et al., 2010; Dickson, Derevensky, & Gupta, 2008; Fried et al., 2010; King, Abrams, & Wilkinson, 2010; Molde et al., 2009; Parker, Taylor, Eastabrook, Schell, & Wood, 2008; Turner, Macdonald, Bartoshuk, & Zangeneh, 2008). Derevensky, Sklar, Gupta, and Messerlian (2010) found that of 1,417 Canadian secondary school adolescents, males preferred sports or game-related wagering, whereas females tended to report purchasing lottery scratch tickets, wagering on cards, and playing bingo.

While male problem gamblers primarily seek stimulation and action, female problem gamblers, mainly tend to gamble as a means of escape from emotional strain (Gupta & Derevensky, 1998a). In general, men are more likely to be exposed to gambling during adolescence, place their first bets at a younger age, and begin gambling regularly at earlier ages (Ib'anez et al., 2003; Tavares et al., 2003; Petry, 2002).

Women, however, tend to have a faster progression to problem gambling than men, which is sometimes referred to as the "telescoping effect (Ib'anez et al., 2003; Tavares et al., 2003, 2001; Potenza et al., 2001). Comparison of the results from studies conducted in different countries indicates that participation in different activities is associated with gambling problem in them (Welte, Barnes, Tidwell, & Hoffman, 2009a). For example, in Britain and New Zealand scratch card and EGM gambling are problematic (Clarke & Rossen, 2000; Griffiths, 1995a; Wood & Griffiths, 1998) whereas in the United States it is betting on card games, sports events, and games of skill that appear to be problematic (Engwall, Him ter, & Steinberg, 2004; Welte, Barnes, Tidwell, & Hoffman, 2007; Winters, Stinchfield, & Fulkerson, 1993). One of the most important correlates of gambling and problems with gambling is the use of substances.

Gambling problems have been shown to be correlated with marijuana, cocaine, heroin, and other illicit drug use (Lesieur et al, 1986; Dube et al., 1996). Many researchers in the problem gambling field have noted that gambling and substance use are highly related and that the nature of the predictive relation between the two processes should be investigated, including Barnes et al. (1999, 2002), Griffiths and Sutherland (1998), Kassinove et al. (2000), Nower et al. (2004), Vitaro et al. (1998, 2001), and Winters and Anderson (2000). Moreover, rates of drug's use among adolescents are significant and use of drugs such as marijuana has recently increased (Johnston, O'Malley, Bachman, & Schulenberg, 2010), which reinforces the need to better understand the factors that lead to these outcomes.

Peer group gambling, like other aspects of peer activities during adolescence, is also a significant factor. Adolescent problem gamblers are more likely to have friends who approve of gambling or who gamble excessively themselves (Delfabbro & Thrupp, 2003; Hardoon et al., 2004; Olason et al., 2006). Wickwire et al, 2007. According to Jessor and Jessor (1973) the perceived environment is an adolescent's experience of the influences of his or her parents and peers and is influenced by an adolescent's personality traits and behavior.

The proximal perceived environment consists of perceived parent and peer models and attitudes directly concerning problem behavior and is considered to have a direct impact on the adolescent's behavioral choices. Hardoon and Derevensky (2002) found that peer influence was associated with increasing gambling problems. Adolescents may choose a more risky behavior when peers are actually present (Blakemore and Robbins, 2012). Recently, a research from Smith, Chein and Steinberg (2014) revealed that, participants who believed a peer was observing them, chose to gamble more often than participants who completed the task alone, and this effect was most evident for decisions with a greater probability of loss.

The goal of this paper is to investigate differences in the effects associated with adolescent disordered gambling using regression mixture models. The study will help to examine potential heterogeneity in the effects of gender, substance use and peer influence on problem gambling; specifically, the degree to which these variables have varying levels of influence on adolescent problem gambling across the two latent classes.

Two research questions are addressed:

1. Do gender, substance use and peer influence have a different impact on adolescent problem gambling for different groups of individuals?

2. To what degree and in which direction, gambling on chance or skill-based activities, will predict the differential impact of some variables on adolescent disordered gambling?

Empirically, this paper intends to illustrate the potential use of regression mixture models to assess differential effects, in order to better specify the complex forces leading to gambling behavior as an addictive one.

The paper is designed in 5 sections: section 1 identifies the problem and gives a general view of the gambling behavior in different aspects of different authors, who have treated this problem. Section 2 covers the empirical literature review of gambling behavior. It is focused on the measurements instruments and assessment of model fit such as multivariate statistical techniques that can be used to characterize patterns of gambling. Section 3 deals with the application of quantitative analysis of the issue in case of students of University of Korea. It deals with the methodology used, (a questionnaire) and the data analysis: application of the regression models and interpretation of the results. Section 4 is focused on the recommendations and the conclusions of the study, to be followed by section 5, which deals with references used in the paper. An appendix is attached to the study and it deals only with the questions, whose data are used in the paper, which are part of a longer questionnaire addressed to the students asked on behalf of gambling behavior.

2. Assessing model fit

Latent class analysis (LCA) is a multivariate statistical technique, which can be used to characterize patterns of gambling involvement (Lazarsfeld and Henry 1968; Goodman 1974a/b; McCutcheon, 1987; Vermunt and Magidson 2004; Collins & Lanza, 2010).

Latent class analysis (LCA) is a statistical method used to identify subtypes of related cases using a set of categorical or continuous observed variables. These subtypes are referred to as latent classes. The classes are latent in that, the subtypes are not directly observed; rather, they are inferred from the multiple observed indicators. When the observed variables are categorical, we have traditional latent class analysis (Goodman, 1974). Latent class analysis (LCA) is a person centered approach to data reduction that identifies latent (unobserved) subgroups of individuals within a population based on nominal or ordinal indicators (Vermunt and Magidson, (2004). LCA is similar to factor analysis in that both methods use one or more latent variables to explain associations among a set of observed variables.

Factor analysis clusters observes variables into homogenous groups of indicators, while. LCA clusters individuals into mutually exclusive and exhaustive latent classes (Lazarsfeld PF, Henry NW, 1968). When categorical data are used, the latent class model has the advantage of making no assumptions about the distributions of the indicators other than that of local independence. The use of LCA in applied research has dramatically increased over the past 10 years because LC models assume that the latent variable is categorical, and areas of application are more wide-ranging.

Researchers using latent class (LC) analysis often proceed using the following three steps: 1) a LC model is built for a set of response variables, 2) subjects are assigned to latent classes based on their posterior class membership probabilities, and 3) the association between the assigned class membership and external variables is investigated using simple cross-tabulations or multinomial logistic regression analysis (Vermunt, 2010). In the case of participation in different gambling activities, LCA can be used to empirically sort observations into a smaller number of groups whose members are similar to each other in their patterns of gambling involvement. Several previous studies have used LCA to sort individuals into latent classes based on their gambling activity participation (Boldero, Bell, & Moore, 2010; Faregh & Leth-Steensen, 2011).

There are two fundamental quantities in LCA (Goodman, 1974):

* Latent class probabilities

* Conditional probabilities for each class. Latent class probabilities [[pi].sub.t.sup.X] describe the distribution of classes of the latent variable (X) within which the observed measures are (locally) independent of one another.

Conditional probabilities represent the probability of an individual in a given class of the latent variable being at a particular level of the observed variables. For example, in the case of three categorical observed variables ui, U2, U3, we have

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where [[PI].sup.X.sub.T] denotes the probability of being in latent class t = 1, 2, ..., T of latent variable X;

[[PI].sup.u1/x.sub.it] denotes the conditional probability of obtaining the [i.sup.th] response to item [u.sub.1], from members of class t, i = 1, 2, ..., I; and [[PI].sup.u2/x.sub.jt] [[PI].sup.u3/x.sub.kt], j = 1/ 2, ..., J k = 1, 2, ..., K denote the corresponding conditional probabilities for items u2 and u3 respectively. The goal of LCA is to determine the smallest number of latent classes T that is sufficient to explain away the relationships among observed indicators.

In order to obtain improved description and prediction of the latent variable(s), multinomial or logistic regression models are used to express these probabilities as a function of one or more exogenous variables Z called covariates.

The inclusion of covariates into mixture models allow us to examine relationships of mixture classes and auxiliary information, to understand how different classes relate to risk and protective factors or to examine differences in demographics across the classes. In using real data to estimate a Structural Equation Mixture Model (SEMM) with and without covariates, the model with covariates performed better, as determined by the BIC (Vermunt and Magidson, 2005). But, including covariates in mixture models, latent class variable may have an undesirable shift in the sense that it is no longer measured simply by the original latent class indicator variables, but now it is also measured by the auxiliary variables. (Asparouhov, T & Muthen, B, 2014). However, Wurpts and Geiser (2014) suggest that researchers feels generally comfortable using a larger set of indicators and adding theoretically meaningful covariates to the model. LCA is a measurement model.

A general mixture model has two parts: a measurement model and a structural model. The structural model describes three types of relationships in one set of multivariate regression equations: the relationships among the categorical latent variables, the relationships among observed variables, and the relationships between the categorical latent variables and observed variables that are not latent class indicators. For logistic regression, ordered categorical variables are modeled using the proportional odds specification. Maximum likelihood estimation is used. In mixture modeling, some starting values may result in local solutions that do not represent the global maximum of the likelihood.

To avoid this, different sets of starting values are automatically produced in Mplus and the solution with the best likelihood is reported. When a sample consists of various groups or subtypes of individuals, mixture regression analysis can be performed to examine whether the effects of independent variables on a dependent variable differ across groups, either in terms of intercept or slope.

A purpose of finite mixtures is to approximate the distribution of an outcome using a finite number of classes which each follow some, typically parametric, distribution of the outcome. The model makes no parametric assumptions about the mixed distribution of the outcome, but the distribution of each mixture component (each latent class) is assumed to follow a specific form which is chosen by the analyst.

The latent class variable "c" is used to model the unknown heterogeneity, whereas, observed variables, that are known to introduce heterogeneity, are treated as covariates. It is considered a regression mixture model, where the intercept and slope of a linear regression (for a continuative y on a covariate x) differs across the latent classes of a categorical latent variable C (divided in K categories or latent classes labeled c = 1,2, ..., K,)

yi | Ci = c = [beta]0c + [beta]1C xi + [r.sub.i], (2)

where: I is the individual (i = 1,2, ..., n) and the residual [r.sub.i] ~ N(0, [theta]c). For parsimony, the residual variance [[theta].sub.c] is often held class invariant. The probability of latent class membership varies as a multinomial logistic regression function of a covariate z,

P ([C.sub.i] = c|[z.sub.i]) = exp([a.sub.c] + [b.sub.c][z.sub.i])/[k.summation over (z=1)] exp([a.sub.z] + [b.sub.s][z.sub.i]) (3)

where for the last class K, the standardization a[kappa] = 0 and b[kappa] = 0 is used to designate this as a reference class. The mixture of normals provides a flexible representation of the distribution of y conditional on x and z. If the covariate z is replaced with x in equation (2), Fig. 1 shows a diagram of the regression mixture model in equations (1) and (2) with observed variables in squares and the latent class variable in a circle. Full arrows represent regression relations. The arrows from x and c to y represent a linear regression of y on these two covariates. The influence of c on y is that of a dummy variable affecting the intercept and therefore the mean of y.

The arrow from x to c indicates a logistic regression. The broken arrows from c to the regression of y on x indicate that the slope varies across the latent classes. The full arrow pointing to y and not originating from another variable represents the residual r in model (1).

X has both an indirect influence on y via the latent class mediator variable c and a direct influence on y.

Regression mixture models have been used primarily in marketing research (Desarbo and Jedidi 2001) and only recently have been applied in the behavioral sciences as a tool for capturing unobserved heterogeneity in the effects of predictors on outcomes. These models provide a potential solution for advancing theory about differential effects of continuous predictors on individuals, consistent with many conceptual models that expect individual or group differences within the population.

Differential effects are typically evaluated through the use of interaction terms which assess whether the effects of one variable on another are moderated by a third variable (Baron & Kenny, 1986). But, with large number of interactions the results are often difficult to interpret. An advantage of regression mixture models is that they potentially provide a parsimonious explanation of complex interactions.

What makes these analyses unique is that, they allow for different effects of a predictor on an outcome to be examined without the need to include a moderator in the analyses. In the regression mixture model, means, variances, and covariance of the outcomes, and the effect of predictors (which may be either continuous or categorical) on outcomes, can all vary between latent classes.

The most commonly used information criteria (IC) in different studies are the penalized information criteria AIC, BIC, and adjusted BIC. The Akaike Information Criterion (AIC) (Akaike, 1987) is defined as

AIC = -2 log L + 2p (4)

where p is the number of free model parameters. The Bayesian Information Criterion (BIC) (Schwartz, 1978) is defined as:

BIC = -2 log L + p log (n) (5)

The adjusted BIC (SABIC), defined by Sclove (1987), replaces the sample size n in the BIC equation above with [n.sup.*] where:

[n.sup.*] = (n + 2)/24. (6)

A smaller AIC and BIC for a particular model suggests that the trade-off between fit and parsimony is preferable. AIC is not a good indicator for class enumeration for LCA models with categorical outcomes (Yang, 2006). Based on the results of some studies, BIC is superior to all other ICs (Nylund, 2007). The BIC and the adjusted BIC are comparatively better indicators of the number of classes than the AIC. Comparing across all the models and sample sizes, there seems to be strong evidence that the BIC is the best of the ICs considered (Collins, Fidler, Wugalter, & Long, 1993; Hagenaars & McCutcheon, 2002; Magidson & Vermunt, 2004). Jedidi, Jagpal, and DeSarbo (1997) found that among commonly used model selection criteria, the BIC picked the correct model most consistently in the finite mixture structure equation model. The Lo-Mendell Rubin adjusted (LMR) test and the bootstrapped likelihood ratio test (BLRT) methods are able to distinguish between the k-g and k class models (g<k), which is how they are commonly used in practical applications. The LMR (Lo et al, 2001; see also Vuong, 1989) test compares the improvement in fit between neighboring class models (i.e., comparing k-1 and k class models) and provides a p-value that can be used to determine if there is a statistically significant improvement in fit for the inclusion of one more class. A low p-value rejects the k-1 class model in favor of the k class model. Similar to the LMR, the BLRT (McLachlan & Peel, 2000) provides a p-value that can be used to compare the increase in model fit between the k-1 and k class models. Results indicated that the BLRT outperformed the other ICs. But, if there is a miss predication in the model or the distributions of the variables, the replicated data sets will not be similar in nature to the original data set, which leads to incorrect p-value estimation. For example, if data within a class are skewed but modeled as normal, the BLRT p-value might be incorrect. Thus, the LMR may be preferable in such contexts. BLRT has not commonly been implemented in mixture modeling software, so it is not commonly used in LCA. If LMR has indicated that a two-class model is most fitting, it might be more difficult to somehow increase the number of classes. Based on experience and the findings of some study, (Nyland, 2007), preliminary results suggest the first time the p value of the LMR is no significant might be a good indication to stop increasing the number of classes. M plus reports the relative entropy of the model, which is a rescaled version of entropy. The relative entropy is defined on [0, 1], with values near one indicating high certainty in classification and values near zero indicating low certainty.

3. Methodology and data analysis

To apply Regression mixture models, some raw data are gathered through simple random selection techniques. The population is the students of University of Korea - Albania (undergraduate). The questionnaire is designed with open and ended questions, multiple choice questions, translated in numerical and categorical variable (the appendix is only a part of the questionnaire, which refers only to the data used for this study purpose). It is used a pilot phase, before the final questionnaire is distributed. The study included 726 students (60.5% females, 39.5% males) from the University of Korga, ranged from 18 to 23 years old. The survey was conducted between June and July, 2015. Data were collected using a self-reported questionnaire.

We focused only on respondents who had played in at least one of the survey gambling activities on at least one occasion during the last 12 months. Participants were given a questionnaire during regular class time assessing their past gambling history, frequency of gambling behavior and other addictive behaviors, types and number of gambling activities in which they engaged, and PGSI items. The total time required for completion of the questionnaire was approximately 20 minutes.

Our conceptual framework, illustrated in Fig. 2, uses a moderating factor, which captures differences in the effects of gender, substance use and peer influence on adolescent problem gambling.

One important aspect of this conceptual framework is that it relaxes the assumption of structural homogeneity (Richters, 1997) which states that if there are differences in contextual effects, all of the moderators responsible for those differences are included in the model.

Data is analyzed using SPSS and M plus software packages. The term "gambling" is used to describe a widely varying array of activities. These activities included lotteries, bingo, scratch cards, sport betting, EGMs, race, poker, roulette, internet gambling, dice and other gambling activities outside of a casino. For each of the eleven gambling activities, respondents answered on a six-alternative scale: 0-never; 1-less than once monthly; 2-less than once weekly; 3-1-2 times a week; 4-3-5 times a week; 5-6-7 times a week. In the analysis, three measures were used as independent variables: 1. Gender, as binary categorical variable; 2. Peer influence, as ordered categorical variable with four categories; 3. Drug use, as ordered categorical variable with four categories.

The scores are coded positively with high scores in the last two variables indicating higher frequency in gambling involvement and drug use, respectively. Gambling problems among students are measured using the nine-item questionnaire of the Problem Gambling Severity Index (PGSI) measurement instrument. Among a lot of measurement instruments, the consensus in the literature is that the PGSI (Ferris and Wynne, 2001) is the most appropriate measure of disordered gambling in terms of psychometric properties (Jackson, Wynne, Dowling, Tomnay, & Thomas, 2009; McMillen & Wenzel, 2006;

Svetieva & Walker, 2008).So, a continuous variable, taking into account the sum and the frequency of the endorsed items, was obtained, with values ranged from 1 to 36. The latent class categorical variable was obtained from eleven gambling activities with six categories, as latent class indicators.

Regression mixture models are estimated with Mplus version 6.12 (Muthen & Muthen, 2011). To deal with the no normality of the data, a robust maximum likelihood estimator (MLR) is used.

Aiming the evaluation of the presence of differential effects in gambling activities on problem gambling, regression mixture models are used to identify latent classes representing differential effects of gambling activities subtypes on adolescent problem gambling. This involved selecting the number of latent classes to be interpreted and determining whether or not classes are differentiated by differences in the types of gambling activities participated, on gambling problems. The optimal number of classes is determined by estimating models with an increasing number of classes, K, and then comparing those models using information criteria, classification criteria, the interpretability of each class, and the LMR and BLRT tests, requesting TECH11 and TECH14 respectively in the OUTPUT command of the Mplus syntax. We investigated models that include between one and seven latent classes. Lower values of the Akaike information criterion (AIC), Bayesian information criterion (BIC), and adjusted BIC are preferred. Because the AIC has been found to perform poorly in regression mixture models (Van Horn et al, 2009), and simulation studies have demonstrated that the AIC typically overestimates the number of classes needed (Nylund et al, 2007), our interpretation of the results relied primarily on the BIC and adjusted BIC. We also use the bootstrapped likelihood ratio test (BLRT) to determine the number of classes (McLachlan & Peel, 2000).This tests the null hypothesis that a given model fits no better than a model with one less class. Failing to reject this test provides evidence for the model with one fewer class.

Analysis: a key interest in an exploration of population heterogeneity is to determine the number of latent classes that best fit the data. The analysis was performed using Mplus 6.12. A latent class analysis of past year involvement in 11 different gambling activities was performed to classify the participants into latent groups. A variety of tools was used together for model selection, including the likelihood-ratio [chi square] statistic, Akaike's Information Criterion (AIC) and Bayesian Information Criterion (BIC) and adjusted BIC (SABIC). LRTSTARTS and OPTSEED options were used to avoid warnings about log likelihoods not being replicated in the bootstrap draws (local optima) and to reduce the computational time.

Taking into account an early research (Nylund et al., 2007), we did not use the usual likelihood ratio chi-square test (2 times the log likelihood difference) to test a k-1 versus k class model because 2 times the log likelihood difference was not chi-square distributed in that situation. Two alternatives were used in M plus, TECH11 and TECH14. In addition, students' gender, peer influence and substance use were included as covariates. They are used to increase the classification accuracy of individuals into each latent class and to examine their influence on the outcome variable of problem gambling. Since the scores of dependent variable were continuous, the appropriate regression mixture model was a linear analysis.

Results: a latent model consisting of two (2) classes was obtained. The two-class solution had the lowest Bayesian information criterion (BIC). The LMR test suggested that each successive model above a two-class model did not provide a model statistical improvement.

The Lo-Mendell-Rubin adjusted LRT test had a p-value of .0000 and the bootstrapped parametric likelihood ratio test had a p value of 0.0000, so these test suggested that two classes are indeed better than the one class. Having non-normal data in our study, the approximate p-value from BLRT test may not be trustworthy. Significant drop in the entropy from the two (2) class model to the three (3) class model was observed. The Lo-Mendell-Rubin test had a significance value of p = .0000 for the two-class solution, suggesting a significantly better fit of the two-class solution over the one-class solution. The three-class solution had a Lo-Mendell-Rubin test significance value of .8066 suggesting that the three-class model is not advantageous over the two-class model. Therefore, based upon the BIC, the entropy and the Lo-Mendell-Rubin test, the two-class solution emerged as the optimal one (Table 1)

The next step was to interpret the meaning of the two classes. The largest class (Table 2) contained about 77% of the respondents, who had preferences on chance-based gambling activities. * The second class, comprising about 23% of the students, is characterized by preferring skill-based activities. There was a statistically significant difference in the means between the two latent classes with the students in the second class to have higher thresholds values and higher values in the probability scale for the most categories of gambling activities. Figures 3-4 show estimated probabilities for the two classes of students for the categories 2-5 of responses related to gambling activities playing frequencies.

Incorporating covariates in the model, stepwise or simultaneously, the accuracy of the model was improved, increasing also the probability of being in the latent class with the highest mean (class 2), as in Table 2

The results of Regression Mixture Analysis, as shown in table 3, indicated that some of the variables influenced gambling problems among adolescents differently across the two latent classes. Specifically, within the first class, only the use of substances resulted to significantly influence problem gambling, while, within the second class, only the peer influence resulted to have a statistically significant impact on problem gambling. The second class had higher mean and residual variances compared with the first class.

4. Conclusions

Considering that different types of adolescents will engage in different gambling activities with different subsequent effects because, gamblers differ in how they respond to the structural and situational characteristics of gambling activities in which they play. So, it is likely that different factors account for the development of gambling problems in different groups. Understanding gambling subtypes is necessary to improve our understanding of the etiology of problem gambling. Therefore studying all gamblers, considering activity types, may be helpful to better understand gambling related problems.

Using some statistical techniques such as Regression Mixture Modeling could be helpful to better understand the way, how several factors influence gambling problems among adolescents, because gamblers are not a homogenous group.

Our study might is considered to be useful in identifying different subgroups of gamblers in the population and show which characteristics are more commonly associated with a higher risk of developing gambling problems across these subtypes.

This paper is an effort of the authors to build a predictive or structural model for class membership, underlying gambling activities' participation. Identifying groups based on similar patterns of behavioral or other characteristics may suggest different etiological processes at work, or may provide different implications for prevention and treatment. In doing so, differences that may play an important role in the etiology and prevention of the development of problem and pathological gambling may be discovered.

Latent class analysis (LCA) is a multivariate statistical technique, which is used to characterize patterns of gambling involvement. It is free of assumptions and considered that the latent variable is categorical, and areas of application are more wide-ranging.

Using Regression mixture models provided a potential solution for advancing theory about differential effects of continuous predictors on individuals, consistent with many conceptual models that expect individual or group differences within the population.

Based upon the BIC, the entropy and the Lo-Mendell-Rubin test, and using raw data base on self administered questionnaires among students of University of Korea--Albania, the two-class solution emerged as the optimal one: The largest class (77% of the respondents) who had preferences on chance-based gambling activities and the second one (23%)is characterized by preferring skill-based activities. The results of Regression Mixture Analysis indicated that some of the variables influenced gambling problems among adolescents differently across the two latent classes. Specifically, within the first class, only the use of substances resulted to significantly influence problem gambling, while, within the second class, only the peer influence resulted to have a statistically significant impact on problem gambling.

The findings of this study revealed that the use of substances among students might cause more problems with gambling for those individuals who have preferences on chance-based gambling activities, while the peer influence might be dangerous for individuals who gamble on skill-based or strategic gambling activities and this is consistent with previous research according to which, adolescents may choose a more risky behavior when peers are actually present.

The limitation of the study consist of the fact that the data are no-normal distributive and the approximate p-value from BLRT test may not be trustworthy, but in a further step, this can be corrected with non-parametric techniques applied in the model.

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APPENDIX 1

Questionnaire (related to adolescent problem gambling)

1. Gender: female [] male []

2. Age years old--

3. Have you gambled during the past 12 months? Yes [] No []

4. Indicate, in which activity or activities have you gambled, and with which frequency?

5. How many of your close friends play on gambling activities? None [] Some of them [] Most of them [] All of them []

6. How often, do you use substances? Never [] Once a month [] Once a week [] Almost every day []

7. Have you bet more than you could really afford to lose? 1 2 3 4

8. Have you needed to gamble with larger amounts of money to get the same feeling of excitement? 1 2 3 4

9. When you gambled, did you go back another day to try to win back the money you lost? 1 2 3 4

10. Have you borrowed money or sold anything to get money to gamble? 1 2 3 4

11. Have you felt that you might have a problem with gambling? 1 2 3 4

12. Has gambling caused you any health problems, including stress or anxiety? 1 2 3 4

13. Have people criticized your betting or told you that you had a gambling problem, regardless of whether or not you thought it was true? 1 2 3 4

14. Has your gambling caused any financial problems for you or your household? 1 2 3 4

15. Have you felt guilty about the way you gamble or what happens when you gamble? 1 2 3 4
Gambling        Never    Less      Less     1-2      3-5      6-7
activities               than      than    times    times    times
                         once      once    weekly   weekly   weekly
                        a month   a week

Lottery
Bingo
Scratch cards
Sport betting
EGMs
Race (horses,
dogs, autos)
Poker
Roulette
Internet
Gambling
Dice
Other activity
(specify)


EMIL FRASHERI (1), BESA SHAHINI (2)

(1) PhD candidate, Department of Management, Faculty of Economy, University "Fan S. Noli", email: efrasheri6@hotmail.co.uk

(2) Prof. asoc. dr., Department of Applied Statistics and Informatics, Faculty of Economy, University of Tirana--Albania, tel: +355684018309, email: besa.shahini@unitir.edu.al and besashahini@yahoo.com

Caption: Fig. 1. Diagram of Regression Mixture Source: D & J, 2001

Caption: Fig. 2. Conceptual Framework Source: Richters 1997

Caption: Fig. 3. Probabilities for gambling less than once a month (Source: Authors' calculation)

Caption: Fig. 4. Probabilities for gambling less than once a week (Source: Authors' calculation)
Table 1
Fit Indecis

Nr. of classes          1           2           3           4

Loglikelihood       -7824.029   -6865.726   -6738.472    -6636.893
# of parameters        55          111         167          223
AIC                 14678.059   13953.452   13810.472    13719.785
BIC                 14930.374   14462.670   14.577.065   14742.809
SSABIC              14755.732   14110.211   14046.790    14034.716
Entropy                NA         .839        .789         .802
LMR-LRT 2 x log L      NA        832.781     253.789      202.866
k-1 vs. k
LMR-LRT                NA         .0000       .7905        .7687
p-value
BLRT                             836.612     254.503      203.426
2 x log L
k-1 vs. k
BLRT approx.                      .0000       .0000        .0000
p-value

Nr. of classes          5           6           7

Loglikelihood       -6548.059   -6494.133   -6449.762
# of parameters        279         335         391
AIC                 13654.118   13658.866   13681.523
BIC                 14934.045   15195.095   15475.255
SSABIC              14048.135   14131.369   14233.712
Entropy               .832        .851        .835
LMR-LRT 2 x log L    200.804     153.429     145.254
k-1 vs. k
LMR-LRT               .7640       .8352       .7603
p-value
BLRT                 201.358     153.845     145.648
2 x log L
k-1 vs. k
BLRT approx.          .0000       .0000       .0000
p-value

Source: Authors' calculations

Table 2
The improved model

                  2 classes   2 classes   2 classes   2 classes
                                with      with peer   with drug
                               gender     influence      use

Loglikelihhod     -6865.726   -6775.034   -6818.522   -6807.564
AIC               13953.452   13774.068   13861.045   13839.129
BIC               14462.670   14287.873   14374.850   14352.934
SSABIC            14110.211   13932.240   14019.217   13997.301
Entropy             .839        .839        .851        .861
OR c#1 on            NA        37.037       4.962      16.393
gender, peer
infl., drug use
Class counts       C#1=557     C#1=440     C#1=549     C#1=554
                   C#2=169     C#2=286     C#2=177     C#2=172

                  2 classes with      2 classes        2 classes
                    gender and     with peer infl.   with drug use
                    peer infl.      and drug use      and gender

Loglikelihhod       -6756.562         -6781.674        -6751.246
AIC                 13739.124         13789.349        13728.493
BIC                 14257.517         14307.742        14246.886
SSABIC              13898.708         13948.933        13888.077
Entropy                .838             .864             .828
OR c#1 on           24.582(g)       3.194 (p. i)       18.519(g)
gender, peer       3.588 (p. i)      13.683 (d)       11.905 (d)
infl., drug use
Class counts         C#1=468           C#1=539          C#1=498
                     C#2=258          C#2=18 7          C#2=228

                  2 classes with
                   gender, peer
                  inf., drug use

Loglikelihhod       -6738.344
AIC                 13704.687
BIC                 14227.668
SSABIC              13865.683
Entropy                .836
OR c#1 on           15.781 (g)
gender, peer       2.927 (p. i)
infl., drug use     11.107 (d)
Class counts         C#1=490
                     C#2=236

Source: Authors' calculations

Table 3
Regression mixture analysis

     Latent Class 1                    Two-tailed
Problem Gambling ON        Est.    S.E.   Est / S.E.   P-Value

Drug use                   .217    .049     4.443       .000
Gender                     -.020   .026     -.769       .442
Peer infl.                 .132    .074     1.784       .074
Intercept of PG            .788    .088     8.961       .000
Residual variances of PG   .176    .033     5.386       .000

Latent Class 2
Problem Gambling ON
Drug use                   .087    .081     1.070       .285
Gender                     .073    .056     1.306       .191
Peer influence             .260    .102     2.546       .011
Intercept of PG            1.389   .208     6.674       .000
Residual variances of PG   .854    .090     9.453       .000
Mean of C#1                .841    .177     4.749       .000

Source: Authors' calculations
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Author:Frasheri, Emil; Shahini, Besa
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