A widely and readily applicable covariance structure modeling approach is outlined that allows point and interval estimation of scale reliability with fixed components. The procedure employs only linear constraints introduced in a congeneric model, which after reparameterization permit expression of composite reliability as a function of…

Curriculum-based measurement of oral reading fluency (CBM-R) is an established procedure used to index the level and trend of student growth. A substantial literature base exists regarding best practices in the administration and interpretation of CBM-R; however, research has yet to adequately address the potential influence of measurement error.…

The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…

A simple errors-in-variables regression model is given in this article for illustrating the method of marginal maximum likelihood (MML). Given suitable estimates of reliability, error variables, as nuisance variables, can be integrated out of likelihood equations. Given the closed form expression of the resulting marginal likelihood, the effects…

With respect to the often-present covariance between error terms of correlated variables, D. W. Zimmerman and R. H. Williams's (1977) adjusted correction for attenuation estimates the strength of the pairwise correlation between true scores without assuming independence of error scores. This article focuses on the derivation and analysis of…

R. D. Howell, E. Breivik, and J. B. Wilcox (2007) have argued that causal (formative) indicators are inherently subject to interpretational confounding. That is, they have argued that using causal (formative) indicators leads the empirical meaning of a latent variable to be other than that assigned to it by a researcher. Their critique of causal…

The constraints of conducting evaluations in real-world settings often necessitate the implementation of less than ideal designs. Unfortunately, the standard method for estimating the precision of a result (i.e., confidence intervals [CI]) cannot be used for evaluative conclusions that are derived from multiple indicators, measures, and data…

Because persons with mental retardation cannot be executed for murder, the diagnosis becomes a life and death matter. The American Association on Mental Retardation (now the American Association on Intellectual and Developmental Disabilities) and other associations agree that IQ alone is an insufficient criterion and adaptive functioning also…

This study empirically investigates the effectiveness of Distributed Leadership Teacher Training (DLT) program on improving student's academic achievement. In addition, it both tests the assumption that the year 1 impacts are stable across calendar years and examines the importance of properly accounting for the fact that the standard error of the…

This study examined the extent of measurement invariance of the Basic Psychological Needs in Exercise Scale responses (BPNES; Vlachopoulos & Michailidou, 2006) across male (n = 716) and female (n = 1,147) exercise participants. BPNES responses from exercise participants attending private fitness centers (n = 1,012) and community exercise programs…

Past estimates of the effect of family income on child development have often been plagued by endogeneity and measurement error. In this paper, we use two simulated instrumental variables strategies to estimate the causal effect of income on children's math and reading achievement. Our identification derives from the large, non-linear changes…

Full account of the latent regression model for the National Assessment of Educational Progress is given. The treatment includes derivation of the EM algorithm, Newton-Raphson method, and the asymptotic standard errors. The paper also features the use of the adaptive Gauss-Hermite numerical integration method as a basic tool to evaluate…

The procedures required to obtain the approximate posterior standard deviations of the parameters in the three commonly used item response models for dichotomous items are described and used to generate values for some common situations. The results were compared with those obtained from maximum likelihood estimation. It is shown that the use of…

A series of computer programs was written for computing the conditional standard errors of measurement (CSEM) for both rights-scored and formula-scored tests based on a method suggested by F. M. Lord (1984), commonly known as Lord's Method IV or the compound binomial method. These programs estimate the CSEM for both raw and scaled scores, average…

Sampling error refers to variability that is unique to the sample. If the sample is the entire population, then there is no sampling error. A related point is that sampling error is a function of sample size, as a hypothetical example illustrates. As the sample statistics more and more closely approximate the population parameters, the sampling…