Tests for Overdispersion and Zero Inflation in SCED (Single-Case Experimental Design) Count Data: A Multistage Model-Selection Procedure (Poster 7)

• In Event: Methodological Innovations and Complexities in the Analysis and Meta-Analysis of Single-Subject Experimental Design Data

Abstract

Single-case experimental designs (SCEDs) play an important role in research on behavioral modification and evaluation of a given intervention by repeatedly measuring an outcome over time. As direct observations of target behaviors are very common in SCEDs, the outcomes are often measured in a count metric (e.g., frequency counts and rates). To deal with clustering and the non-normal nature of count data, generalized linear mixed models (GLMMs) have been shown as a promising approach (Li et al., 2022a).
One of the statistical decisions in the analysis of SCED count data via GLMMs is to determine an appropriate distribution. The basic GLMMs for count outcome assume a Poisson distribution where the conditional mean is equal to conditional variance. However, when the data exhibit excessive variance than what a Poisson can deal with, overdispersion occurs. Overdispersion can be caused by autocorrelated measurements or true extra noises. Li et al. (2022a) has shown that the negative binomial model can yield accurate estimates and inferential results for the treatment effect, while the Poisson model leads to inflated type I error rates.
On the other hand, overdispersion can also be caused by excessive zeros, which is called zero-inflation. In the SCED context, although some methodology studies cautioned that zero-inflation is not rare in empirical studies with count outcomes (Declercq et al., 2019; Shadish et al., 2013), it is often ignored and not appropriately addressed. Previous studies found that negative binomials would lead to poor model fit, and biased parameter estimates and standard errors when overdispersion is caused by zero-inflation, while zero-inflated models had better performance (Lambert, 1992; Li et al., 2022b; Zuur, 2012). Hence, tests for overdispersion and zero inflation is essential in the selection of an appropriate model. The purpose of this study is to examine the performance of a multi-stage model selection procedure in the SCED context, which is originally proposed by Campbell (2021). The general idea of this procedure is to determine an appropriate distribution by testing overdispersion in the first stage and testing zero-inflation in the second stage.
We will conduct a simulation study in which overdispersed and/or zero-inflated count data are generated based on the multiple baseline design. We will vary the following design factors: series length, number of cases, immediate treatment effect, treatment effect on trend, overdispersion, probability of excessive zeros. To test for overdispersion, a likelihood ratio test with a mixture of two Chi-squared distributions (Self & Liang, 1987; Stram & Li, 1994) and a Pearson Chi-squared test (Bolker et al., 2009) will be adopted. To test for zero-inflation, two parametric bootstrap approaches will be included. Therefore, four variants of the multi-stage model selection procedure will be examined. In addition, information criteria such as AIC and BIC will also be evaluated. The relative bias, coverage rates, empirical Type I error rate and power will be calculated for the immediate treatment effect and treatment effect on the trend.

Authors

• Haoran Li, University of Minnesota

• Wen Luo, Texas A&M University

• Eunkyeng Baek, Texas A&M University

• Kwok Hap Lam, Texas A&M University

• Zoey Du, Texas A&M University