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. 2013 Mar;27(1):166-77.
doi: 10.1037/a0029508. Epub 2012 Aug 20.

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

David C Atkins  1 , Scott A Baldwin, Cheng Zheng, Robert J Gallop, Clayton Neighbors
Affiliations

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

David C Atkins et al. Psychol Addict Behav. 2013 Mar.

Erratum in

  • Psychol Addict Behav. 2013 Jun;27(2):379

Abstract

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.

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Figures

Figure 1
Figure 1
Plots of Frequency Counts of Daily Drinks from Timeline Follow-Back (TLFB; upper left) and Rutgers Alcohol Problems Index (RAPI; upper right). Residuals from fitting an ordinary least squares regression to the RAPI or log-transformed RAPI are in lower left and lower right, respectively.
Figure 2
Figure 2
Means and 95% Confidence Intervals for Drinking on Drinking Days (top row) and Proportion of Individuals Drinking (bottom row). Means are stratified by weekend vs. weekday, male vs. female, and fraternity / sorority member or not.
Figure 3
Figure 3
Means and 95% Confidence Intervals for Number of Problems when there are any problems (left) and Proportion of Individuals reporting any drinking-related problems (right). Means are stratified by assessment period and gender.
Figure 4
Figure 4
Plots of frequency counts of data simulated from Poisson distributions with three different means (top row). The bottom row contains frequency counts of data simulated from negative binomial distributions with the same mean but varying dispersion.
Figure 5
Figure 5
RAPI scores plotted over time for 8 randomly selected individuals (top row). Distribution of intercepts (bottom left) and slopes (bottom right) from fitting separate Poisson regressions to each individual's data.
Figure 6
Figure 6
Predicted (unit-specific) RAPI scores from Poisson GLMM for men and women over time, with specific values noted in text.
Figure 7
Figure 7
Predicted (marginal) drinks for each unique combination of gender, weekend (WE) vs. weekday (WD), and fraternity / sorority status from count submodel of over-dispersed Poisson hurdle mixed model.
See this image and copyright information in PMC

References

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