Innovative methods for gambling dataTrends in research methodology: A workshop for early stage investigators

Contact info

• Bethany C. Bray, Ph.D.bcbray@psu.edu

• Research Associate, The Methodology Center, Penn Statehttp://methodology.psu.edu

Goals

• Brief overview of three innovative methods

• Research questions

• Modeling approach

• Tools needed (i.e., software)

• Gambling applications

• Resources for more information

Questions to ask …

• What is my research question?

• What are the data I have to address my research question?

For example …

• Question: What are the risk factors for developing a gambling disorder?

• Data: total number of DSM-5 diagnostic criteria endorsed

• Question: Are there types of gamblers at higher risk for developing gambling disorder compared to others?

• Data: multiple indicators of gambling activity engagement

For example …

• Question: Does the relation between gender and gambling vary across time?

• Data: amount wagered online every day for two years

What do I do when ……

• I want to model a count outcome?• e.g., total number of DSM-5 diagnostic criteria endorsed

• I want to identify types of individuals?• e.g., using multiple indicators of gambling behavior

• I want to model intensively-collected data?• e.g., daily online wagering over time

COUNT OUTCOMES

Research questions

• What are the predictors of number of days gambled?• e.g., measured by total number of days in a month during

which an individual gambled

• What are the predictors of severity of gambling behavior?• e.g., measured by total number of endorsed DSM-5

diagnostic criteria

Research questions

• What are the risk factors (i.e., gambling behaviors, substance abuse, other problem behaviors, sociodemographic characteristics) for disordered gambling? (Welte et al., 2004)

• e.g., frequency of 15 types of gambling, count of diagnostic criteria

• Does the “gambler's fallacy” predict fluctuations in lottery play?• e.g., number of winning bets conditional on the history of draws

(Papachristou, 2004)

Research questions

• Do college student athletes have higher levels of disordered gambling than non-athletes? What are the risk factors for athletes and non-athletes? (Weinstock et al., 2007)

• e.g., gambling frequency

Research questions

• Do gender, age, race/ethnicity, family socioeconomic status, sensation seeking, and participation in risky behaviors predict problematic financial behavior among college students? (Worthy et al., 2010)

• e.g., number of problematic financial behaviors

• At-risk sample

• What would this distribution look like for a general population sample?

Modeling approach

• Poisson regression

• Negative binomial regression

• Zero-inflated Poisson regression

• Zero-inflated negative binomial regression

Modeling approach

• Behaviors like gambling can generate data that are characterized by excess zeros• e.g., much of the population may not engage in the behavior

or not have problems

• These behaviors can also generate data with over-dispersion• Variance substantially exceeds the mean • e.g., because a small number of individuals engage in

extreme levels of the behavior

Modeling approach

• Several closely related models are available for predicting a count variable…• Poisson regression (mean and variance assumed to be equal)• Negative binomial regression (adds over-dispersion)

Modeling approach

• Models can be extended to accommodate excess zeros• Zero-inflated Poisson (ZIP) regression• Zero-inflated NB (ZINB) regression

• These models posit two types of individuals who report zero gambling…• Those who are non-gamblers• And those who have the potential to engage in gambling but

report zero acts during that time

Modeling approach

• Models estimate population-average associations between predictors and gambling

• Can do model comparisons between options to determine which is optimal for examining the association between predictors and outcome• e.g., fit indices like AIC and BIC

Estimated Coefficient(Exponentiated Coefficient)

Intercept(Mean Gambling Count)

0.309**(1.36)

Dispersion Parameter 4.418(n/a)

Community Risk Community Cohesion 0.028*(1.03)

Community Drug/Guns 0.143**(1.15)

School Risk School Prosocial 0.141**(1.15)

Family Risk Family Cohesion 0.112**(1.12)

Family Risk 0.305**(1.36)

Peer Risk Antisocial Peers 0.823**(2.28)

Individual Risk Antisocial Attitudes 0.408**(1.50)

Risky Behaviors 0.436**(1.55)

Modeling approach

• Total number of gambling acts expressed as a function of an intercept, a dispersion parameter, and eight risk indices

• The intercept, 0.309, corresponds to the log of the mean gambling count among all adolescents when all predictors in the model are set to zero• e.g., for adolescents with average levels on all risk indices, the

expected number of gambling acts in the past year was e0.309=1.3

• A positive dispersion parameter (4.418) indicates that the outcome was over-dispersed

Modeling approach

• All risk indices were significantly and positively associated with the number of gambling acts in the overall population

• Coefficients reflect association between each risk index and gambling count, after adjusting for other predictors in the model

• For example, a one-standard-deviation increase in family risk corresponds to e0.305=1.36 times more gambling acts, holding all other predictors constant

• For example, associating with antisocial peers had the largest coefficient, corresponding to e0.823=2.28 times more delinquent acts for every one-unit increase

Software

• SPSS• http://www.ats.ucla.edu/stat/spss/dae/poissonreg.htm• http://www.ats.ucla.edu/stat/spss/dae/neg_binom.htm

• SAS• http://www.ats.ucla.edu/stat/sas/dae/poissonreg.htm• http://www.ats.ucla.edu/stat/sas/dae/negbinreg.htm

Gambling applications

• Papachristou, G. (2004). The British gambler's fallacy. Applied Economics, 36, 2073-2077.

• Weinstock, J., Whelan, J. P., Meyers, A. W., & Watson, J. M. (2007). Gambling behavior of student-athletes and a student cohort: What are the odds? Journal of Gambling Studies, 23, 13-24.

Gambling applications

• Welte, J. W., Barnes, G. M., Wieczorek, W. F., Tidwell, M. C. O., & Parker, J. C. (2004). Risk factors for pathological gambling. Addictive behaviors, 29, 323-335.

• Worthy, S. L., Jonkman, J., & Blinn-Pike, L. (2010). Sensation-seeking, risk-taking, and problematic financial behaviors of college students. Journal of Family and Economic Issues, 31, 161-170.

Resources

• Comprehensive texts…

• Agresti, A. (2012). Categorical data analysis. Hoboken, NJ: Wiley.

• Cameron, A. C., & Trivedi, P. K. (2013). Regression analysis of count data. New York, NY: Cambridge University Press.

Resources

• Recommended journal articles…

• Atkins, D. C., & Gallop, R. J. (2007). Rethinking how family researchers model infrequent outcomes: A tutorial on count regression and zero-inflated models. Journal of Family Psychology, 21, 726-735.

• Coxe, S., West, S. G., & Aiken, L. S. (2009). The analysis of count data: A gentle introduction to Poisson regression and its alternatives. Journal of personality assessment, 91, 121-136.

Resources

• Recommended journal articles continued…

• Lanza, S. T., Cooper, B. R., & Bray, B. C. (in press). Population heterogeneity in the salience of multiple risk factors for adolescent delinquency. Journal of Adolescent Health.

IDENTIFYING SUBGROUPS

Research questions

• Are there identifiable patterns of gambling behaviors? If so, what are the related individual characteristics and health consequences? (Boldero et al., 2010; Cunningham-Williams & Hong, 2007; Lloyd et al., 2010)

• Are there identifiable types of gamblers based on the DSM diagnostic criteria? (Carragher & McWilliams, 2011; McBride et al., 2010; Xian et al., 2008)

Modeling approach

• Latent class analysis (LCA)

• Individuals can be divided into subgroups, or latent classes, based on unobservable construct• True class membership is unknown• Classes are mutually exclusive and exhaustive

Modeling approach

• Measurement of construct typically based on several categorical indicators

• There is error associated with the measurement of the latent classes

• Like factor analysis in that you have to identify the number and structure of the classes, but the latent variable is categorical

Modeling approach

• Interested in two sets of parameters…

• Latent class prevalences• e.g., probability of membership in the ‘table and sports

gambling’ latent class

• Item-response probabilities• e.g., probability of responding ‘yes’ to a question about

betting on sports in the past month given membership in the ‘table and sports gambling’ latent class

GamblingClasses

lotto poker sports…

Modeling approach

• Conduct model selection procedure to determine optimal number of latent classes• Use model fit criteria like the AIC and BIC• Somewhat similar to process for exploratory factor analysis

• After model selection, use item-response probabilities to interpret the latent classes

Non-Gamblers

(30%)

LottoOnly

(10%)

Lotto & Cards(25%)

Table & Sports(25%)

Multi-Game(10%)

Lotto .10 .95 .90 .45 .98

Poker .02 .01 .95 .20 .95

Other card games .02 .02 .92 .10 .90

Dice games .01 .05 .30 .85 .90

Other table games .00 .10 .20 .80 .95

Games of personal skill .10 .05 .10 .15 .85

Horse racing .00 .01 .05 .05 .80

Other parimutual betting .00 .02 .03 .05 .70

Sports .05 .20 .25 .95 .98

Modeling approach

Modeling approach

• Might also want to examine group differences in…

• Latent class structure• e.g., test measurement invariance

• Latent class prevalences• e.g., test distribution across groups

• e.g., gender differences in gambling behavior patterns…

Non-Gamblers

(30%)

LottoOnly

(10%)

Lotto & Cards(25%)

Table & Sports(25%)

Multi-Game(10%)

Males 25% 5% 20% 35% 15%

Females 35% 15% 30% 15% 5%

Modeling approach

Modeling approach

• Lots of extensions to these models…

• e.g., add covariates to predict subgroup membership

• e.g., use subgroup membership to predict a distal outcome

• e.g., examine changes in subgroup membership over time

GamblingClasses

casino games sports lotto…

GenderDrug Use

GamblingClasses

casino games sports lotto…

Mental Heath

Disorders

Time 1GamblingClasses

Time 2GamblingClasses

Software options

• SAS (PROC LCA)http://methodology.psu.edu/downloads

• Mplushttp://www.statmodel.com/

• Latent Goldhttp://statisticalinnovations.com/products/latentgold.html

Gambling applications

• Boldero, J. M., Bell, R. C., & Moore, S. M. (2010). Do gambling activity patterns predict gambling problems? A latent class analysis of gambling forms among Australian youth. International Gambling Studies, 10, 151-163.

• Carragher, N., & McWilliams, L. A. (2011). A latent class analysis of DSM-IV criteria for pathological gambling: Results from the National Epidemiologic Survey on Alcohol and Related Conditions. Psychiatry Research, 187, 185-192.

Gambling applications

• Cunningham-Williams, R. M., & Hong, S. I. (2007). A latent class analysis (LCA) of problem gambling among a sample of community-recruited gamblers. The Journal of Nervous and Mental Disease, 195, 939-947.

• Lloyd, J., Doll, H., Hawton, K., Dutton, W. H., Geddes, J. R., Goodwin, G. M., & Rogers, R. D. (2010). Internet gamblers: A latent class analysis of their behaviours and health experiences. Journal of Gambling Studies, 26, 387-399.

Gambling applications

• McBride, O., Adamson, G., & Shevlin, M. (2010). A latent class analysis of DSM-IV pathological gambling criteria in a nationally representative British sample. Psychiatry Research, 178, 401-407.

• Xian, H., Shah, K. R., Potenza, M. N., Volberg, R., Chantarujikapong, S., True, W. R., ... & Eisen, S. A. (2008). A latent class analysis of DSM-III-R pathological gambling criteria in middle-aged men: Association with psychiatric disorders. Journal of addiction medicine, 2, 85-95.

Resources

• Comprehensive text…

• Collins, L. M., & Lanza, L. M. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. New York, NY: Wiley.

Resources

• Recommended journal articles…

• Lanza, S. T., Bray, B. C., & Collins, L. M. (2013). An introduction to latent class and latent transition analysis. In J. A. Schinka, W. F. Velicer, & I. B. Weiner (Eds.), Handbook of psychology (2nd ed., Vol. 2, pp. 691-716). Hoboken, NJ: Wiley.

• Lanza, S. T., Collins, L. M., Lemmon, D. R., & Schafer, J. L. (2007). PROC LCA: A SAS procedure for latent class analysis. Structural Equation Modeling, 14, 671-694.

Resources

• Recommended journal articles continued…

• Lanza, S. T., Collins, L. M., Lemmon, D. R., & Schafer, J. L. (2007). PROC LCA: A SAS procedure for latent class analysis. Structural Equation Modeling, 14(4), 671-694.

• Lanza, S. T. & Rhoades, B. L. (2013). Latent class analysis: An alternative perspective on subgroup analysis in prevention and treatment. Prevention Science, 14, 157-168.

Resources

• Recommended journal articles continued…

• Lanza, S. T., Rhoades, B. L., Nix, R. L., Greenberg, M. T., & the Conduct Problems Prevention Research Group (2010). Modeling the Interplay of Multilevel Risk Factors for Future Academic and Behavior Problems: A Person-Centered Approach. Development and Psychopathology, 22, 313-335.

Resources

• Recommended journal article on power in latent class models that is helpful for grant applications…

• Dziak, J. J., Lanza, S. T., & Tan, X. (in press). Effect size, statistical power and sample size requirements for the bootstrap likelihood ratio test in latent class analysis. Structural Equation Modeling.

INTENSIVE LONGITUDINAL DATA

Research questions

• Do baseline characteristics like gender exert differential effects at various points in the gambling onset process?

• How do we deal with excessive wins and losses in understanding the onset process?

Research questions

• Does pharmacological treatment for gambling disorder continue to suppress craving over the long-term?

• Which psychological characteristics like depression present greatest risk for relapse?• Do these differed based on duration of cessation?

What are EMA data?

• Ecological• Real-world environments and experiences• Provides ecological validity

• Momentary• Real-time assessments• Avoids recall bias

• Assessment• Self-report or automatic• Repeated, intensive, longitudinal

(Stone & Shiffman, 1994)

What are EMA data?

• Key idea is that…

…these data allow analysis of psychological, behavioral, and/or physiological processes over time

(Stone & Shiffman, 1994)

What are EMA data?

• Collected using…• Tablets• Smartphones• Biological/physiological devices

(Stone & Shiffman, 1994)

What are EMA data?

• Also called intensive longitudinal data (ILD)• e.g., repeated internet-based assessments• e.g., daily or weekly assessments over a long period of time• e.g., longitudinal burst designs

• bwin gambling data available from The Transparency Project (www.thetransparencyproject.org)

What are EMA data?

• Traditional longitudinal data

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

Times

Sub

ject

Traditonal Longitudinal Data

• Irregular longitudinal data

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

Times

Sub

ject

Sparse Irregular Longitudinal Data

What are EMA data?

• Irregular longitudinal data

What are EMA data?

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

Times

Sub

ject

Intensive Longitudinal Data

Modeling approach

• Time-varying effect model (TVEM)(methodology.psu.edu/ra/inten-longit-data)

• Examines the time-varying relation between an outcome and predictor(s)

• Let’s consider two examples…

Modeling approach

• Does gender exert differential effects across time on amount of money wagered after the opening of an online gambling account?• e.g., time-invariant predictor

• What varies across time?• Mean amount of money wagered (i.e., intercept function)• Effect of gender

Modeling approach

• The complex function is approximated using non-parametric smoothing techniques

• Coefficients are not single-number summaries, but are expressed as functions over time• Interpretation must take time into account

• Look at time-varying effects using graphs

Treatment

Placebo

Days since account opening

poker

casinogames

Time-varying intercept function by activity.

Days since account opening

poker

casinogames

Time-varying effect of gender by activity.

Modeling approach

• When does depression present the greatest risk for gambling disorder relapse after cessation?• e.g., time-varying predictor

• What varies over time?• Engagement in gambling behavior (i.e., intercept function)• Effect of depression

Days since cessation attempt

malesfemales

Time-varying effect of depression by gender.

Software

• SAS suite of %TVEM macros • Binary outcomes• Normally-distributed continuous outcomes• Count outcomes (Poisson)• Zero-inflated count outcomes (ZIP)

• Yang, J., Tan, X., Li, R., & Wagner, A. (2012). TVEM (time-varying effect model) SAS macro suite users' guide (Version 2.1.0). University Park: The Methodology Center, Penn State. Retrieved from http://methodology.psu.edu

• methodology.psu.edu/downloads

Modeling approach

• TVEM enables us to think differently about effects

• Effects of predictors can strength or weaken with time

• In particular, note that the effect of “baseline” characteristics can change over time

• Could lead not only to tailoring interventions and treatment, but also to adaptive treatment designs

Gambling applications

• None to date

• But, there are applications of TVEM to other behaviors like smoking and smoking cessation that may provide inspiration!

Resources

• No comprehensive text, but…

• Walls, T. A., & Schafer. J. L. (2006). Models for intensive longitudinal data. New York, NY: Oxford University Press.

Resources

• Recommended journal articles…

• Lanza, S. T., Vasilenko, S., Liu, X., Li, R., & Piper, M. (2013). Advancing the understanding of craving during smoking cessation attempts: A demonstration of the time-varying effect model. Nicotine and Tobacco Research. doi: 10.1093/ntr/ntt128

• Liu, X., Li, R., Lanza, S. T., Vasilenko, S., & Piper, M. (in press). Understanding the role of cessation fatigue in the smoking cessation process. Drug and Alcohol Dependence.

Resources

• Recommended journal articles continued…

• Shiyko, M. P., Lanza, S. T., Tan, X., Li, R., & Shiffman, S. (2012). Using the time-varying effect model (TVEM) to examine dynamic associations between negative affect and self-confidence on smoking urges: Differences between successful quitters and relapsers. Prevention Science, 13, 288-299. doi: 10.1007/s11121-011-0264-z

• Tan, X., Shiyko, M. P., Li, R., Li, Y., & Dierker, L. (2012). A time-varying effect model for intensive longitudinal data. Psychological Methods, 17, 61-77. doi:10.1037/a0025814

Resources

• Recommended journal articles continued…

• Vasilenko, S., & Piper, M., Liu, X., Lanza, S. T., & Li, R. (in press). Time-varying processes involved in smoking lapse in a randomized trial of smoking cessation therapies. Nicotine and Tobacco Research.

THANK YOU!!