The issue of compensation in multidimensional response modeling is addressed. We show that multidimensional response models are compensatory in their ability parameters if and only if they are monotone. In addition, a minimal set of assumptions is presented under which the MLEs of the ability parameters are also compensatory. In a recent series of…

Convergence of the expectation-maximization (EM) algorithm to a global optimum of the marginal log likelihood function for unconstrained latent variable models with categorical indicators is presented. The sufficient conditions under which global convergence of the EM algorithm is attainable are provided in an information-theoretic context by…

The G-DINA ("generalized deterministic inputs, noisy and gate") model is a generalization of the DINA model with more relaxed assumptions. In its saturated form, the G-DINA model is equivalent to other general models for cognitive diagnosis based on alternative link functions. When appropriate constraints are applied, several commonly used…

In an addendum to his seminal 1969 article Joreskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix (Joreskog in "Advances in factor analysis and structural equation models," pp. 40-43, 1979). These condition sets, formulated under…

We offer an introduction to the five papers that make up this special section. These papers deal with a range of the methodological challenges that face researchers analyzing fMRI data--the spatial, multilevel, and longitudinal nature of the data, the sources of noise, and so on. The papers all provide analyses of data collected by a multi-site…

Recent research reflects a growing awareness of the value of using structural equation models to analyze repeated measures data. However, such data, particularly in the presence of covariates, often lead to models that either fit the data poorly, are exceedingly general and hard to interpret, or are specified in a manner that is highly data…

OpenMx is free, full-featured, open source, structural equation modeling (SEM) software. OpenMx runs within the "R" statistical programming environment on Windows, Mac OS-X, and Linux computers. The rationale for developing OpenMx is discussed along with the philosophy behind the user interface. The OpenMx data structures are…

Nested logit models have been presented as an alternative to multinomial logistic models for multiple-choice test items (Suh and Bolt in "Psychometrika" 75:454-473, 2010) and possess a mathematical structure that naturally lends itself to evaluating the incremental information provided by attending to distractor selection in scoring. One potential…

This paper focuses on two estimators of ability with logistic item response theory models: the Bayesian modal (BM) estimator and the weighted likelihood (WL) estimator. For the BM estimator, Jeffreys' prior distribution is considered, and the corresponding estimator is referred to as the Jeffreys modal (JM) estimator. It is established that under…

Latent trait models for response times in tests have become popular recently. One challenge for response time modeling is the fact that the distribution of response times can differ considerably even in similar tests. In order to reduce the need for tailor-made models, a model is proposed that unifies two popular approaches to response time…

Despite wide applications of both mediation models and missing data techniques, formal discussion of mediation analysis with missing data is still rare. We introduce and compare four approaches to dealing with missing data in mediation analysis including list wise deletion, pairwise deletion, multiple imputation (MI), and a two-stage maximum…

In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is…

Starting with Kenny and Judd ("Psychol. Bull." 96:201-210, 1984) several methods have been introduced for analyzing models with interaction terms. In all these methods more information from the data than just means and covariances is required. In this paper we also use more than just first- and second-order moments; however, we are aiming to…

The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we study tests of measurement…

Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the…