On Latent Change Model Choice in Longitudinal Studies

Abstract

An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R ² indexes associated with repeatedly followed measures in longitudinal studies. In addition to facilitating evaluation of local model fit, the approach is helpful for purposes of differentiating between plausible models stipulating different patterns of change over time, and in particular in empirical situations characterized by large samples and high statistical power. The procedure is also applicable in cross-sectional studies, as well as with general structural equation models. The method is illustrated using data from a nationally representative study of older adults.

Keywords:

• confidence interval
• latent change analysis
• linear change
• model choice
• nonlinear change

Notes

¹When a member of a set of rival latent change models for a given data set is found in this sense not to be plausible for the latter, that model can be excluded from further considerations and the process of model selection.

²As could be implied from the earlier discussion, this article does not consider the process of model choice to be concerned with identification of the true model, but rather with the selection of the most useful model from a given set of competing models as rival means for description of a particular data set. This selection, as pursued in the current section of this article, is best based on substantive considerations, research questions, and an extended set of statistical indexes (including in particular the R ² indexes for observed dependent variables and their CIs) relative to routine applications of LCA in contemporary empirical behavioral and social research. Specifically, by selecting the quadratic change model as preferable to the linear change model for the analyzed BMI data, a researcher is also in a position to adequately model in subsequent analyses nonlinear change over time in BMI, which can also be seen as suggested by an examination of the trend in its mean (see Table 1). This model choice conclusion is also based on the reported finding of the R ² CIs for the observed variables in the quadratic model being positioned markedly above, and overlapping little if at all, with their counterparts in the linear model (see Table 2 and preceding discussion in this section, as well as last note to Appendix A with regard to a more complex growth model).