The factor structure of the "KeyMath--Revised Normative Update" (KMR-NU) "Form A" was analyzed using data from a sample of 130 students. The KMR-NU is composed of 13 subtests that are purported to measure three important aspects of math ability: Basic Concepts, Operations, and Applications. A confirmatory factor analysis…

An important class of applications of measurement error or constrained factor analytic models consists of comparing models for several populations. In such cases, it is appropriate to make explicit statistical tests of model similarity across groups and to constrain some parameters of the models to be equal across groups using a priori substantive…

Using several data sets, the relative performance of the beta binomial model and two more general strong true score models in estimating several indices of classification consistency is examined. It appears that the beta binomial model can provide inadequate fits to raw score distributions compared to more general models. (TJH)

Coefficient alpha, the most commonly used estimate of internal consistency, is often considered a lower bound estimate of reliability, though the extent of its underestimation is not typically known. Many researchers are unaware that coefficient alpha is based on the essentially tau-equivalent measurement model. It is the violation of the…

A five by five covariance matrix representing longitudinal measurements at five occasions is used to illustrate that markedly different types of learning curves may generate indistinguishable covariance structures. An excellent fit of a simplex structure can be misleading. Common uses of covariance structure models for growth studies are…

Maximum likelihood factor analysis provides an effective method for estimation of factor matrices and a useful test statistic in the likelihood ratio for rejection of overly simple factor models. A reliability coefficient is proposed for analysis of factor solution. (Author/RK)

Implications of ignoring correlated error on parameter estimates in some simple structural equation models are examined. It is shown analytically and empirically through simulation that ignoring positive between-construct correlated error overestimates the structural parameter linking the two constructs. Effects become more pronounced with…

Derivations of several item selection algorithms for use in fitting test items to target information functions (IFs) are described. These algorithms, which use an average growth approximation of target IFs, were tested by generating six test forms and were found to provide reliable fit. (SLD)

Five comparisons were made relative to the quality of estimates of ability parameters and item calibrations obtained from the one-parameter and three-parameter logistic models. The results indicate: (1) The three-parameter model fit the test data better in all cases than did the one-parameter model. For simulation data sets, multi-factor data were…

A general process for testing the feasibility of applying alternative mathematical or statistical models to the solution of a practical problem is presented and flowcharted. The system is used to compare five models for test equating: (1) anchor test equating using classical test theory; (2) anchor test equating using the one-parameter logistic…

This paper outlines the development of a quantitative instrument designed to measure students' multiple achievement goals and key aspects of their cognitive engagement in Australian educational settings. The paper demonstrates the use of congeneric measurement models in assessing and improving the validity of the scales comprising the Goal…

The Rasch model for test analysis is described and compared with two-parameter and three-parameter latent-trait models. Conditional maximum likelihood equations for estimating item parameters are derived, and estimates of person parameters are described together with their confidence intervals. Goodness of fit tests are discussed, including a…

The stability of Rasch test item difficulty parameters was investigated under varying conditions. Data were taken from a mathematics achievement test administered to over 2,000 Australian students. The experiments included: (1) relative stability of the Rasch, traditional, and z-item difficulty parameters using different sample sizes and designs;…