Latent Growth Models for Count Outcomes: Specification, Evaluation, and Interpretation

Abstract

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the Poisson or negative binomial distribution and their zero-inflated extensions to account for excess zero counts. This article demonstrates how to specify, evaluate, and interpret LGMs for count outcomes using the Mplus program in the structural equation modeling framework. The foundations of LGMs for count outcomes are discussed and illustrated using empirical count data on self-reported criminal offenses of adolescents (N = 1,664; age 15–18). Annotated syntax and output are presented for all model variants. A negative binomial LGM is shown to best fit the crime growth process, outperforming Poisson, zero-inflated, and hurdle LGMs.

Keywords:

• Count data
• latent growth models
• Mplus
• Poisson and negative binomial
• structural equation modelling

Notes

Data Availability Statement

The data and Mplus input files used in this paper are openly available in an online repository: https://osf.io/r3mnb/.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 A discussion of modeling change in count outcomes from a generalized linear model perspective using other software can be found in Grimm and Stegmann (2019).

2 Effects of time-invariant covariates can also be specified directly onto the count outcomes (Stoel et al., 2004).

3 Mplus estimates intercepts for latent binary and unordered dependent variables and thresholds for observed dependent variables in logit and probit models. Thresholds should have opposite signs to the intercepts.