This note is concerned with the benefits that can result from the use of the maximal reliability and optimal linear combination concepts in educational and psychological research. Within the widely used framework of unidimensional multi-component measuring instruments, it is demonstrated that the linear combination of their components that…

Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

Ordinary least squares (OLS) regression provides optimal linear predictions of a dependent variable, y, given an independent variable, x, but OLS regressions are not symmetric or reversible. In order to get optimal linear predictions of x given y, a separate OLS regression in that direction would be needed. This report provides a least squares…

Ordinary least squares (OLS) regression and orthogonal regression (OR) address different questions and make different assumptions about errors. The OLS regression of Y on X yields predictions of a dependent variable (Y) contingent on an independent variable (X) and minimizes the sum of squared errors of prediction. It assumes that the independent…

The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown…

In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and…

Exploratory factor analysis (EFA) has long been used in the social sciences to depict the relationships between variables/items and latent traits. Researchers face many choices when using EFA, including the choice of rotation criterion, which can be difficult given that few research articles have discussed and/or demonstrated their differences.…

The problem of factor score indeterminacy implies that the factor and the error scores cannot be completely disentangled in the factor model. It is therefore proposed to compute Harman's factor score predictor that contains an additive combination of factor and error variance. This additive combination is discussed in the framework of classical…

Assessing measurement equivalence in the framework of the common factor linear models (CFL) is known as factorial invariance. This methodology is used to evaluate the equivalence among the parameters of a measurement model among different groups. However, when dichotomous, Likert, or ordered responses are used, one of the assumptions of the CFL is…

Latent state-trait (LST) analysis is frequently applied in psychological research to determine the degree to which observed scores reflect stable person-specific effects, effects of situations and/or person-situation interactions, and random measurement error. Most LST applications use multiple repeatedly measured observed variables as indicators…

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found.…

This chapter addresses the psychometric challenges in assessing English language learners (ELLs) and students with disabilities (SWDs). The first section addresses some general considerations in the assessment of ELLs and SWDs, including the prevalence of ELLs and SWDs in the student population, federal and state legislation that requires the…

The purpose of the present study was to examine the reliability, factorial validity and measurement invariance (across gender, age and physical activity participation) of a Portuguese version of the Rosenberg Self-Esteem Scale (RSES). The sample consisted of 1,763 Portuguese youngsters (731 male and 1,032 female) with ages between 15 and 20 years.…

The purpose of this study was to investigate the "g" loadings and specific effects of the core and diagnostic composite scores from the Differential Abilities Scales, Second Edition (DAS-II; Elliott, 2007a). Scores from a subset of the DAS-II standardization sample for ages 3:6 to 17:11 were submitted to principal factor analysis. Four…

We investigated various structural models of phonological processing and the relationship of phonological processing abilities to basic reading. Data were collected on 116 kindergarten and first grade students. The specific ability model, which included phonological awareness, phonological memory, and rapid automatized naming as separate…