Application of Latent Growth Curve Analysis With Categorical Responses in Social Behavioral Research

Abstract

Latent growth modeling allows social behavioral researchers to investigate within-person change and between-person differences in within-person change. Typically, conventional latent growth curve models are applied to continuous variables, where the residuals are assumed to be normally distributed, whereas categorical variables (i.e., binary and ordinal variables), which do not hold to normal distribution assumptions, have rarely been used. This article describes the latent growth curve model with categorical variables, and illustrates applications using Mplus software that are applicable to social behavioral research. The illustrations use marital instability data from the Iowa Youth and Family Project. We close with recommendations for the specification and parameterization of growth models that use both logit and probit link functions.

Keywords:

• categorical variables
• latent growth curve model
• latent response variable

FUNDING

During the past several years, support for this research has come from multiple sources, including the National Institute of Mental Health (MH00567, MH19734, MH43270, MH48165, MH51361), the National Institute on Drug Abuse (DA05347), the Bureau of Maternal and Child Health (MCJ-109572), the Macarthur Foundation Research Network on Successful Adolescent Development Among Youth in High-Risk Settings, and the Iowa Agriculture and Home Economics Experiment Station (Project 3320).

Notes

¹ The random intercept model is the baseline model for the growth curve model. In Mplus, the model can be specified by using I | Y1@0 Y2@1 Y3@2 Y4@3 Y5@5; under the model command.

² where Prob (Y_i = 1) is the probability of being Y = 1 for individual i. The inverse standard normal function of Prob (Y_i = 1) produces probit values that can be converted to standard normal value z scores.

Additional information

Funding

During the past several years, support for this research has come from multiple sources, including the National Institute of Mental Health (MH00567, MH19734, MH43270, MH48165, MH51361), the National Institute on Drug Abuse (DA05347), the Bureau of Maternal and Child Health (MCJ-109572), the Macarthur Foundation Research Network on Successful Adolescent Development Among Youth in High-Risk Settings, and the Iowa Agriculture and Home Economics Experiment Station (Project 3320).