Multilevel structural equation (MSEM) models allow researchers to model latent factor structures at multiple levels simultaneously by decomposing within- and between-group variation. Yet the extent to which the sampling ratio (i.e., proportion of cases sampled from each group) influences the results of MSEM models remains unknown. This paper…

There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included…

This study explored motivation and engagement among North American (the United States and Canada; n = 1,540), U.K. (n = 1,558), Australian (n = 2,283), and Chinese (n = 3,753) secondary school students. Motivation and engagement were assessed via students' responses to the Motivation and Engagement Scale-High School (MES-HS). Confirmatory factor…

In current research on achievement goal theory, most researchers differentiate between performance-approach and performance-avoidance goal orientations. Evidence from prior research and from several previously published data sets is used to highlight that the correlation is often rather large, with a number of studies reporting correlations above…

This article reports results of a confirmatory factor analysis performed to cross-validate the factor structure of the Educators' Attitudes Toward Educational Research Scale. The original scale had been developed by the author and revised based on the results of an exploratory factor analysis. In the present study, the revised scale was given to…

Exploratory factor analysis (EFA) is generally regarded as a technique for large sample sizes ("N"), with N = 50 as a reasonable absolute minimum. This study offers a comprehensive overview of the conditions in which EFA can yield good quality results for "N" below 50. Simulations were carried out to estimate the minimum required "N" for different…

When conducting an exploratory factor analysis, the decision regarding the number of factors to retain following factor extraction is one that the researcher should consider very carefully, as the decision can have a dramatic effect on results. Although there are numerous strategies that can and should be utilized when making this decision,…

A factor analysis of the correlation matrix for the subsets of WPPSI was carried out for each of the age groups between 4 and 6 1/2 years. (Editor)

The degree of indeterminacy of the factor score estimates is biased and can lead to erroneous conclusion regarding the nature of the results. The magnitude of this bias is illustrated and guidelines for describing factor analytic studies using factor scores are offered. (Author/PN)

A modification of Horn's parallel analysis is introduced that is based on the Monte Carlo simulation of the null distributions of the eigenvalues generated from a population correlation identity matrix. This modification reduces the tendency of the parallel analysis procedure to overextract or to extract poorly defined factors. (SLD)

The oblimax, promax, maxplane, and Harris-Kaiser techniques are compared. (Author)

The most widely used procedures to harness the power of a concomitant (nuisance) variable are block designs and analysis of covariance (ANCOVA). This study attempted to provide a scientific foundation on which to base decisions on whether to block or covary and how many blocks to be used if blocking is selected. Monte Carlo generated data were…

Use of parallel analysis (PA), a selection rule for the number-of-factors problem, is investigated from the viewpoint of permutation assessment through a Monte Carlo simulation. Results reveal advantages and limitations of PA. Tables of sample eigenvalues are included. (SLD)

Under some circumstances, it is desirable to compare the factor patterns obtained from different factor analyses. To date, the best method of simultaneously achieving simple structure and maximum similarity is the technique devised by Bloxom (1968). This technique simultaneously rotates different factor patterns to maximum similarity and varimax…

A common problem in the behavioral sciences is to determine if a set of observed variables can be more parsimoniously represented by a smaller set of derived variables. To address this problem, the performance of five methods for determining the number of components to retain (Horn's parallel analysis, Velicer's Minimum Average Partial (MAP),…