This Monte Carlo study examined the validity of the chi-square test for model evaluation in different instances of misspecification and sample size. The usefulness of the chi-square difference statistic to compare competing structures and improvement in fit is also addressed. (Author/BS)

Three correlation matrices (PEARSON, POLYCHORIC, and TOBIT) were used to obtain reliability estimates on ordered polytomous variable models. A Monte Carlo study with different levels of variable asymmetry and 400 sample correlation matrices demonstrated that the PEARSON matrix did not perform as well as did the other 2 matrices. (SLD)

A detailed investigation is provided of Stout's statistical procedure (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary item response data from a psychological test. Three refinements achieve greater power. The revised approach is validated using real data sets.…

Believing that examinee-by-item interaction should be conceptualized as true score variability rather than as a result of errors of measurement, Lu proposed a modification of Hoyt's analysis of variance reliability procedure. Via a computer simulation study, it is shown that Lu's approach does not separate interaction from error. (Author/RL)

A method is proposed for constructing a population covariance matrix as the sum of a particular model plus a nonstochastic residual matrix, with the stipulation that the model holds with a prespecified lack of fit. The procedure is considered promising for Monte Carlo studies. (SLD)

Two sets of real sorting data from 50 college students are used to compare results of multidimensional scaling of raw co-occurrence frequencies or dissimilarity measures (D) and profile distances (delta) to determine which yields a better representation of the underlying structure of 2 sets of stimuli. Slight differences are discussed. (SLD)

A Monte Carlo study explores the robustness assumption in structural equation modeling of using a full information normal theory generalized least-squares estimation procedure on Type I censored data. The efficacy of the following proposed alternate estimation procedures is assessed: asymptotically distribution free estimator and a latent…

The regression-discontinuity design involving a treatment interaction effect (TIE), pretest-posttest functional form specification, and choice of point-of-estimation of the TIE are examined. Formulas for controlling the magnitude of TIE in simulations can be used for simulating the randomized experimental case where estimation is not at the…

Changes in information retention resulting from changes in reliability and number of intervals in scale construction were studied to provide quantitative information to help in decisions about choosing intervals. Information retention reached a maximum when the number of intervals was about 8 or more and reliability was near 1.0. (SLD)

The relationship between levels of reliability and the power of two bias and differential item functioning (DIF) detection methods is examined. Both methods, the Mantel-Haenszel (MH) procedure of P. W. Holland and D. T. Thayer (1988) and the Simultaneous Item Bias (SIB) procedure of R. Shealy and W. Stout (1991), use examinees' raw scores as a…

A Monte Carlo study was conducted to estimate the small sample standard errors and statistical bias of psychometric statistics commonly used in the analysis of achievement tests. The statistics examined in this research were: (1) the index of item difficulty; (2) the index of item discrimination; (3) the corrected item-total point-biserial…

In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…

In an experiment manipulating artificial data in a factorial design, model misspecification and varying levels of error in measurement and in model structure are shown to have significant effects on LISREL parameter estimates in a modified peer influence model. (Author/LMO)

A solution to the problem of specification error due to excluded variables in statistical models of treatment effects in nonrandomized (nonequivalent) control group designs is presented. It involves longitudinal observation with at least two pretests. A maximum likelihood estimation program such as LISREL may provide reasonable estimates of…

Forming the matching variable for the Mantel-Haenszel differential item functioning (DIF) procedure through use of the total score as the matching variable (thin) and forming the matching variable by pooling total score levels (thick) were compared in a Monte Carlo study. Reasons thick matching is superior are discussed. (SLD)