Psychologists have long been interested in characterizing individual differences in change over time. It is often plausible to assume that the distribution of these individual differences is continuous in nature, yet theory is seldom so specific as to designate its parametric form (e.g., normal). Semiparametric groups-based trajectory models…

Multiple membership random effects models (MMREMs) have been developed for use in situations where individuals are members of multiple higher level organizational units. Despite their availability and the frequency with which multiple membership structures are encountered, no studies have extended the MMREM approach to hierarchical growth curve…

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common…

The application of multidimensional item response theory models to repeated observations has demonstrated great promise in developmental research. It allows researchers to take into consideration both the characteristics of item response and measurement error in longitudinal trajectory analysis, which improves the reliability and validity of the…

Evaluated multilevel models of growth and change in relation to regression toward the mean artifacts (RTMAs), using simulated data to represent students nested within schools for which there were initial school differences due to selection based on pretest achievement scores. Results demonstrate that multilevel growth models provide no protection…

Used computer simulation methods to examine the sensitivity of model fit criteria to misspecification of the first-level error structure in two-level models of change and to examine the impact of misspecification estimates on the variance parameters, estimates of the fixed effects, and tests of the fixed effects. Discusses problems caused by…

A model for multilevel ordinal response data is described that allows for nonproportional odds for a subset of explanatory variables. The model, the multilevel thresholds of change model, focuses on modeling the K-1 thresholds that delineate membership in the "K" ordered stages. The model is illustrated with data from a cancer prevention study.…

Describes, with examples, three modeling approaches when both "y" and "x" change over time: a conditional approach, an unconditional approach, and an approach based on structural equation modeling. All three can be implemented in a multilevel framework. Also describes how more interesting hypotheses about social processes can…

Dynamic factor models have been used to analyze continuous time series behavioral data. We extend 2 main dynamic factor model variations--the direct autoregressive factor score (DAFS) model and the white noise factor score (WNFS) model--to categorical DAFS and WNFS models in the framework of the underlying variable method and illustrate them with…

Using an approach to the analysis of missing data, this study investigated developmental trends in alcohol, marijuana, and cigarette use among 750 adolescents across 5 years using multiple-group latent growth modeling. Latent variable structural equation modeling and missing data approaches to studying developmental change are explored. (SLD)