A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their "cols :…

Structural equation models offer a valuable tool for delineating the complicated interrelationships among multiple variables, including observed and latent variables. Over the last few decades, structural equation models have successfully analyzed complete and right-censored survival data, exemplified by wide applications in psychological, social,…

Fraction of missing information [lambda][subscript j] is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has…

Intensive longitudinal data (ILD) have become increasingly common in the social and behavioral sciences; count variables, such as the number of daily smoked cigarettes, are frequently used outcomes in many ILD studies. We demonstrate a generalized extension of growth mixture modeling (GMM) to Poisson-distributed ILD for identifying qualitatively…

Although structural equation modeling software packages use maximum likelihood estimation by default, there are situations where one might prefer to use multiple imputation to handle missing data rather than maximum likelihood estimation (e.g., when incorporating auxiliary variables). The selection of variables is one of the nuances associated…

Missing data are common in studies that rely on multiple informant data to evaluate relationships among variables for distinguishable individuals clustered within groups. Estimation of structural equation models using raw data allows for incomplete data, and so all groups can be retained for analysis even if only 1 member of a group contributes…

Multilevel modeling (MLM) is a popular way of assessing mediation effects with clustered data. Two important limitations of this approach have been identified in prior research and a theoretical rationale has been provided for why multilevel structural equation modeling (MSEM) should be preferred. However, to date, no empirical evidence of MSEM's…

Some nonlinear developmental phenomena can be represented by using a simple piecewise procedure in which 2 linear growth models are joined at a single knot. The major problem of using this piecewise approach is that researchers have to optimally locate the knot (or turning point) where the change in the growth rate occurs. A relatively simple way…

Valuable methods have been developed for incorporating ordinal variables into structural equation models using a latent response variable formulation. However, some model parameters, such as the means and variances of latent factors, can be quite difficult to interpret because the latent response variables have an arbitrary metric. This limitation…

The purpose of this simulation study was to assess the performance of latent variable models that take into account the complex sampling mechanism that often underlies data used in educational, psychological, and other social science research. Analyses were conducted using the multiple indicator multiple cause (MIMIC) model, which is a flexible…

Incomplete nonnormal data are common occurrences in applied research. Although these 2 problems are often dealt with separately by methodologists, they often cooccur. Very little has been written about statistics appropriate for evaluating models with such data. This article extends several existing statistics for complete nonnormal data to…

A well-known ad-hoc approach to conducting structural equation modeling with missing data is to obtain a saturated maximum likelihood (ML) estimate of the population covariance matrix and then to use this estimate in the complete data ML fitting function to obtain parameter estimates. This 2-stage (TS) approach is appealing because it minimizes a…