When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for…

A heuristic example is presented in which parsimony as typically operationalized in indices of fit may not be desirable. In a simplex model of longitudinal data, the failure to include correlated uniquenesses relating to the same indicators on different occasions will typically lead to systematically inflated estimates of stability. (SLD)

Joreskog's procedure for the analysis of simplex models was used to test Humphreys' assertion that eight semesters of undergraduate grade point averages have a simplex form. The assertion was confirmed, and precise estimates of unattenuated correlations and reliabilities were also obtained. (Author/JKS)

Longitudinal studies of personality traits and intelligence have used an exponential function to relate magnitudes of correlations between occasions to the time interval. This exponential function is shown to be equivalent to a quasisimplex model of a stationary process with constant reliability. (SLD)

The insightful discussions by Raudenbush, Rubin, Stuart and Zanutto (RSZ) and Reckase identify important challenges for interpreting the output of VAM and for its use with test-based accountability. As these authors note, VAM are statistical models for the correlations among scores from students who share common teachers or schools during the…

The use of complex value-added models that attempt to isolate the contributions of teachers or schools to student development is increasing. Several variations on these models are being applied in the research literature, and policy makers have expressed interest in using these models for evaluating teachers and schools. In this article, we…

Newman (1984) examined the causal relations between math self-concept and math achievement in an 8-year longitudinal study using Linear Structural Relations (LISREL) analyses. He concluded that math self-concept did not influence subsequent math achievement. However, the study suffered in that math self-concept was inferred from a single-item…

Education researchers have long been concerned with finding the appropriate method for correlational analysis of hierarchical data. In recent years, the alternative of hierarchical linear modeling (HLM) has come into extensive use. HLM users typically center some or all student-level predictors either at the grand mean or at the school means. This…

The longitudinal interrelations among age, visual and auditory short-term memory, and the concrete operational tasks of class inclusion and combinatorial reasoning were investigated over four testing occasions in a sample of 134 students, initially ranging from 5 to 12 years in age. The Piagetian task battery involved placement of colored…

Forming a sequence covering the various aspects of the simplex model, four articles are presented here under the following titles: "A Simplex Model for Analyzing Academic Growth", "Analyzing Ratings With Correlated Intrajudge Measurement Errors", "The Correlation of States With Gain", and "The Reliability of…

Marsh and Parker (1984) described the big-fish-little-pond effect (BFLPE) whereby equally able students have lower academic self-concepts in high-ability schools than in low-ability schools. The present investigation, a reanalysis of the Youth in Transition data, supported the generality of the earlier findings and demonstrated new theoretical…