Comparing Mixed-Effects Poisson, Zero Inflated and Hurdle Models for Analyzing Longitudinal Count Data with Many Zeros

• In Event: 1-009 - Advanced Analytics for Large, Secondary, and Open Source Data

Abstract

Count data with excessive zeros and over-dispersion are prevalent in a wide variety of disciplines, such as public health, psychology, and education (Atkins et al., 2012; De Smet et al., 2011; Desjardins, 2016). Analyzing this type of data poses a challenge. It is well known that classical linear models using either non-transformed or logarithmic transformed counts are inappropriate for zero inflated count data due to the violation of normality and constant variance assumptions (Loeys et al., 2012). Alternative models have been proposed to handle this type of data (Agresti, 2002): Poisson regression (Poisson), negative binomial regression (NB), zero-inflated Poisson regression (ZIP), zero-inflated negative binomial regression (ZINB), and zero-altered Poisson regression (Hurdle). Moreover, count regression models assume independent observations, which is problematic when using a longitudinal design (i.e., repeated observations on the same individual are correlated). To accommodate non-independence of observations, Poisson, NB, ZIP, ZINB, and hurdle models have been extended to the mixed model including random effects. The goals of the current research were to review and compare five mixed-effects Poisson family models commonly used to analyze count data with a high proportion of zeros. For purposes of illustration, we examined the number of heavy alcohol-use days over four waves from the National Longitudinal Study of Adolescent to Adult Health (Add Health; Harris, 2013).
Our analytic procedures included comparing fit indices across models. The SAS nonlinear mixed model procedure (PROC NLMIXED) yields four model fit indices: the likelihood value statistic (−2LL), the Akaike Information Criterion (AIC), the finite sample corrected AIC (AICC) and the Bayesian Information Criterion (BIC). Results revealed that the ZINB model had the best fit, indicating better performance than the other models (Table 1). The Poisson model had the worst fit to the data. Beyond fit, highlights of the results of the ZINB analyses revealed a negative quadratic time trend indicating that the number of heavy alcohol-use days increased over time, but at a slightly decelerating rate, conditional on random effects (Table 1). The discussion will focus on recommendations for using analytic procedures in relation to count data. In particular, results from this study support that when over-dispersion exists in zero-inflated longitudinal count data, the ZINB model tends to produce better model fit and has the least discrepancy on its AIC values compared with other preferred models.

Authors

• Yage Guo, University of Nebraska–Lincoln
  Presenting Author

• Lorey A Wheeler, University of Nebraska–Lincoln