Multilevel Modeling in Single-Case Studies With Zero-Inflated Count Data

• In Event: Analysis and Meta-Analysis of Single-Case Experimental Data: Methodological Developments

Abstract

Single-case experiment design (SCED) plays an important role in research on behavioral modification and evaluation of a given intervention. Frequency count and interval proportions of target behaviors are common types of outcome measurements in SCEDs, where the normality assumed by the traditional multilevel modeling approach (e.g., linear mixed models) is often violated (Declercq et al., 2019; Shadish & Sullivan, 2011). As a flexible approach, generalized linear mixed models (GLMMs) are introduced to accommodate various nonnormal SCED data (Shadish, Kyse, & Rindskopf, 2013). This approach has been recently demonstrated and evaluated to account for overdispersed count and proportion data caused by autocorrelation or true extra noise in SCEDs (Li et al., 2021). However, overdispersion can also be caused by excessive zero observations, which is not uncommon in the SCED context (Shadish, Kyse, & Rindskopf, 2013). This phenomenon is referred to as zero-inflation but is seldom studied and often ignored in the empirical SCED analysis.
For frequency count, zero inflation occurs when there is an excess of zeros in the observed data than would be expected if the data were generated by a Poisson distribution (DesJardins, 2016). Count data are prevalent in the social and behavioral sciences, especially in research involving substance use, antisocial behavior, and other low base rate events. Much of these data involve counts of events that are rare, and thus with many zero observations dominate the distribution (Ferrer et al., 2016). In a recent review, Pustejovsky et al. (2019) found that of the 311 data series with positive-valence count outcomes in SCEDs, 27% had mean baseline levels very close to zero (<.01), indicating that zero-inflation can be frequently encountered for count data in SCEDs. Previous studies found that ignoring zero-inflation would lead to poor model fit, and biased parameter estimates and standard errors (Lambert, 1992; Zuur et al., 2009), however, basic GLMMs, such as Poisson or negative binomial models are not capable to handle these excessive zeros.
The present study aims to introduce two methods to address this zero-inflation issue on the analysis of SCED data. We first provide a colloquial illustration for two types of GLMMs that can account for inflated zeros in SCEDs. The first type is called the zero-inflated Poisson model and the second type is referred to as the Poisson hurdle model. Both models can handle zero-inflation with subtle but important differences. For demonstration purposes, we will illustrate with a real example of SCED data. The focus is to explain the differences in terms of research questions and applications, model specifications, and results interpretation. Following the demonstration, a small Monte-Carlo simulation will be conducted with conditions based on the empirical setting to evaluate the performance of both models.

Authors

• Haoran Li, Texas A&M University - College Station

• Wen Luo, Texas A&M University - College Station

• Eunkyeng Baek, Texas A&M University - College Station

• Christopher G. Thompson, Texas A&M University - College Station

• Kwok Hap Lam, Texas A&M University - College Station