We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n x 1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a…

A distinction is proposed between measures and predictors of latent variables. The discussion addresses the consequences of the distinction for the true-score model, the linear factor model, Structural Equation Models, longitudinal and multilevel models, and item-response models. A distribution-free treatment of calibration and…

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…

In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of "fungible weights" (Waller, Psychometrica, "in press") that yields identical "SSE" (sum of squared errors) and R[superscript 2] values. When the R[superscript 2] using the alternate weights is a fixed value, fungible…

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for…

Characterizations of local homogeneity and the homogeneous monotone item response theory (IRT) model are provided. The characterization theorem states that the joint condition of experimental independence and pairwise nonnegative association in every nonnegligible subpopulation is necessary and sufficient for the homogenous monotone IRT model.…

An algorithm for assessing the correspondence of one or more attribute rating variables to a symmetric matrix of dissimilarities is presented. It is useful as an alternative to fitting property variables into a multidimensional scaling space. The relation between the matrix and the variables is determined by evaluating pairs of pairs relations.…

Three dimensional contingency tables in which one variable is considered to be a factor and the other two variables have a natural relationship (such as left and right eye vision) are analyzed. Models involving symmetry and proportional symmetry between the related variables are also presented. (Author/JKS)

A Fisher's Z transformation is developed for the corrected correlation for conditions when the criterion data are missing because of selection on the predictor and when the criterion was missing at random, not because of selection. The two Z transformations were evaluated in a computer simulation and found accurate. (SLD)

A model is proposed for investigating test validity as a predictor of a criterion variable when there are both missing and censored scores in the data set. Implications for maximum likelihood estimation are discussed, and the method is illustrated with hypothetical data sets. (SLD)

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent…

Using an infinite item test framework, it is argued that the usual assumption of local independence should be replaced by a weaker assumption--essential independence. The usual assumption of unidimensionality is replaced by a weaker and more appropriate statistically testable assumption of essential unidimensionality. (TJH)

In recent years, latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest. Such models summarize shared features of the multiple indicators as an underlying categorical variable, and the indicators' substantive associations with predictors are built directly and indirectly…

Formulas for the asymptotic biases of the parameter estimates in structural equation models are provided in the case of the Wishart maximum likelihood estimation for normally and nonnormally distributed variables. When multivariate normality is satisfied, considerable simplification is obtained for the models of unstandardized variables. Formulas…

A method is suggested to estimate the relationship between a latent trait and one or more manifest predictors without estimating subject parameters. The method, developed for the Rasch model, can be generalized to two-parameter and three-parameter logistic latent trait models. The model is illustrated with simulated and empirical data. (SLD)