The social relations model (SRM) is a mathematical model that can be used to analyze interpersonal judgment and behavior data. Typically, the SRM is applied to one (i.e., univariate SRM) or two variables (i.e., bivariate SRM), and parameter estimates are obtained by employing an analysis of variance method. Here, we present an extension of the SRM…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

This article reproduces correspondence between Georg Rasch of The University of Copenhagen and Benjamin Wright of The University of Chicago in the period from January 1966 to July 1967. This correspondence reveals their struggle to operationalize a unidimensional measurement model with sufficient statistics for responses in a set of ordered…

This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under certain circumstances, meet legal criteria of causation.…

The present article considers a fundamental question in evaluation research: "By how much do program effects vary across sites?" The article first presents a theoretical model of cross-site impact variation and a related estimation model with a random treatment coefficient and fixed site-specific intercepts. This approach eliminates…

This article presents our response to Oud and Folmer's "Modeling Oscillation, Approximately or Exactly?" (2011), which criticizes aspects of our article, "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011). In this response, we present a conceptual explanation of the derivative-based estimation…

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

Maximum likelihood is an important approach to analysis of two-level structural equation models. Different algorithms for this purpose have been available in the literature. In this paper, we present a new formulation of two-level structural equation models and develop an EM algorithm for fitting this formulation. This new formulation covers a…

A computationally efficient three-stage estimator of thresholds and covariance structure parameters is prepared for analysis of structural equation models with polytomous variables. The method is based on partition maximum likelihood and generalized least squares estimation. An analysis of questionnaire responses of 739 young adults illustrates…

A two-stage approach based on the rationale of maximum likelihood and generalized least-squares methods is developed to analyze the general structural equation model for continuous and polytomous variables. Some illustrative examples and a small simulation study (50 replications) are reported. (SLD)

A model based on latent trait theory, with maximum likelihood parameter estimates and associated asymptotic tests, is presented. Latent curve analysis is a method for representing development and is an alternative to repeated measures analysis of variance and first-order auto-regressive models. (SLD)

Consistent, asymptotically efficient and asymptotically normal stepwise estimators are given for a subclass of the uniparametric and multiparametric exponential families. Estimators are derived from the Robbins-Monro stochastic approximation procedure with certain families of random variables arising from the normalized log-likehood. Three…

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative hypothesis is provided. (Author/LMO)

A maximum likelihood procedure is developed for multidimensional scaling where similarity or dissimilarity measures are taken by such ranking procedures as the method of conditional rank orders or the method of triadic combinations. An example is given. (Author/JKS)