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…

We propose the use of the latent change and latent acceleration frameworks for modeling nonlinear growth in structural equation models. Moving to these frameworks allows for the direct identification of "rates of change" and "acceleration" in latent growth curves--information available indirectly through traditional growth…

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…

Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following…

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…

Proposes a test for change in composite reliability as a result of scale revision or modification. The test, which is useful for examining whether a revision changes the population reliability of a scale undergoing development, is illustrated with two examples. (SLD)

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…

The usefulness of structural equation modeling methodology for studying change is explored, considering individual and group change model classes. The relationship between the constant rate of change and simplex models as representatives of either class is examined, and both models are shown to be special cases of comprehensive latent curve…

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…

Two Statistical Analysis System (SAS) macros are presented that perform the modified principal components approach of L. R. Tucker (1966) to modeling generalized learning curves analysis up to a rotation of the components. Three SAS macros are described that rotate the factor patterns to have characteristics Tucker considered desirable. (SLD)

Methods for studying relationships between patterns of change on different variables are considered, showing how the multilevel modeling framework, often used to study univariate change, can be extended to the multivariate case to yield estimates of covariances of parameters representing aspects of change for different variables. (SLD)

Offers reflections on the peer review process, the errors of some reviewers and editors, and recommendations to improve peer review that will increase the quality of science. Discusses issues of review process, the primacy of research results, and the responsibilities of editors. (SLD)