A tutorial on count regression and zero-altered count models for longitudinal substance use data.

Critical research questions in the study of addictive behaviors concern how these behaviors change over time: either as the result of intervention or in naturalistic settings. The combination of count outcomes that are often strongly skewed with many zeroes (e.g., days using, number of total drinks, number of drinking consequences) with repeated assessments (e.g., longitudinal follow-up after intervention or daily diary data) present challenges for data analyses. The current article provides a tutorial on methods for analyzing longitudinal substance use data, focusing on Poisson, zero-inflated, and hurdle mixed models, which are types of hierarchical or multilevel models. Two example datasets are used throughout, focusing on drinking-related consequences following an intervention and daily drinking over the past 30 days, respectively. Both datasets as well as R, SAS, Mplus, Stata, and SPSS code showing how to fit the models are available on a supplemental website.

[1]  J. V. Ver Hoef,et al.  Quasi-Poisson vs. negative binomial regression: how should we model overdispersed count data? , 2007, Ecology.

[2]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[3]  Scott M. Lynch,et al.  Introduction to Applied Bayesian Statistics and Estimation for Social Scientists , 2007 .

[4]  J. Simons,et al.  Risk for Marijuana-Related Problems among College Students: An Application of Zero-Inflated Negative Binomial Regression , 2006, The American journal of drug and alcohol abuse.

[5]  S. West,et al.  The Analysis of Count Data: A Gentle Introduction to Poisson Regression and Its Alternatives , 2009, Journal of personality assessment.

[6]  Donald Hedeker,et al.  Longitudinal Data Analysis , 2006 .

[7]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[8]  Sophia Rabe-Hesketh,et al.  Multilevel and Longitudinal Modeling Using Stata , 2005 .

[9]  N. Goldman,et al.  Improved estimation procedures for multilevel models with binary response: a case‐study , 2001 .

[10]  Jarrod D. Hadfield,et al.  MCMC methods for multi-response generalized linear mixed models , 2010 .

[11]  D. Draper.  Bayesian Multilevel Analysis and MCMC , 2008 .

[12]  J. H. Schuenemeyer,et al.  Generalized Linear Models (2nd ed.) , 1992 .

[13]  H. White,et al.  Towards the assessment of adolescent problem drinking. , 1989, Journal of studies on alcohol.

[14]  J. Singer,et al.  Applied Longitudinal Data Analysis , 2003 .

[15]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[16]  Stephen W. Raudenbush,et al.  Many Small Groups , 2008 .

[17]  J. Simons,et al.  Evaluations and expectancies of alcohol and marijuana problems among college students. , 2007, Psychology of addictive behaviors : journal of the Society of Psychologists in Addictive Behaviors.

[18]  Mollie E. Brooks,et al.  Generalized linear mixed models: a practical guide for ecology and evolution. , 2009, Trends in ecology & evolution.

[19]  A. Zeileis,et al.  Regression Models for Count Data in R , 2008 .

[20]  B. Muthén,et al.  Integrating person-centered and variable-centered analyses: growth mixture modeling with latent trajectory classes. , 2000, Alcoholism, clinical and experimental research.

[21]  J. Simons,et al.  Inference in Regression Models of Heavily Skewed Alcohol Use Data: A Comparison of Ordinary Least Squares, Generalized Linear Models, and Bootstrap Resampling , 2007, Psychology of addictive behaviors : journal of the Society of Psychologists in Addictive Behaviors.

[22]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[23]  Scott L. Zeger,et al.  Marginalized Multilevel Models and Likelihood Inference , 2000 .

[24]  Joseph Hilbe,et al.  Data Analysis Using Regression and Multilevel/Hierarchical Models , 2009 .

[25]  David C. Atkins,et al.  Efficacy of web-based personalized normative feedback: a two-year randomized controlled trial. , 2010, Journal of consulting and clinical psychology.

[26]  David C. Atkins,et al.  Event-specific drinking among college students. , 2011, Psychology of addictive behaviors : journal of the Society of Psychologists in Addictive Behaviors.

[27]  David C. Atkins,et al.  Examining the associations among severity of injunctive drinking norms, alcohol consumption, and alcohol-related negative consequences: the moderating roles of alcohol consumption and identity. , 2010, Psychology of addictive behaviors : journal of the Society of Psychologists in Addictive Behaviors.

[28]  J. Hilbe.  Negative Binomial Regression: Index , 2011 .

[29]  J. Jaccard.  Interaction effects in logistic regression , 2001 .

[30]  G. Molenberghs,et al.  Models for Discrete Longitudinal Data , 2005 .

[31]  J. Hilbe.  Negative Binomial Regression: Preface , 2007 .

[32]  David C. Atkins,et al.  Rethinking how family researchers model infrequent outcomes: a tutorial on count regression and zero-inflated models. , 2007, Journal of family psychology : JFP : journal of the Division of Family Psychology of the American Psychological Association.

[33]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[34]  Melinda Beeuwkes Buntin,et al.  Too much ado about two-part models and transformation? Comparing methods of modeling Medicare expenditures. , 2004, Journal of health economics.

[35]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .