The multidimensional mixture data structure exists in many test (or inventory) conditions. Heterogeneity also relatively exists in populations. Still, some researchers are interested in deciding to which subpopulation a participant belongs according to the participant's factor pattern. Thus, in this study, we proposed three analysis procedures…

In modeling missing data, the missing data latent variable of the confirmatory factor model accounts for systematic variation associated with missing data so that replacement of what is missing is not required. This study aimed at extending the modeling missing data approach to tetrachoric correlations as input and at exploring the consequences of…

Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the…

Survey research frequently involves the collection of data from multiple informants. Results, however, are usually analyzed by informant group, potentially ignoring important relationships across groups. When the same construct(s) are measured, integrative data analysis (IDA) allows pooling of data from multiple sources into one data set to…

Cluster randomized trials involving participants nested within intact treatment and control groups are commonly performed in various educational, psychological, and biomedical studies. However, recruiting and retaining intact groups present various practical, financial, and logistical challenges to evaluators and often, cluster randomized trials…

The relationship between saturated path-analysis models and their fit to data is revisited. It is demonstrated that a saturated model need not fit perfectly or even well a given data set when fit to the raw data is examined, a criterion currently frequently overlooked by researchers utilizing path analysis modeling techniques. The potential of…

The purpose of this study was to investigate the effect of complex structure on dimensionality assessment in noncompensatory multidimensional item response models using dimensionality assessment procedures based on DETECT (dimensionality evaluation to enumerate contributing traits) and NOHARM (normal ogive harmonic analysis robust method). Five…

Type I error rates in multiple regression, and hence the chance for false positive research findings, can be drastically inflated when multiple regression models are used to analyze data that contain random measurement error. This article shows the potential for inflated Type I error rates in commonly encountered scenarios and provides new…

A number of psychometricians have argued for the use of parallel analysis to determine the number of factors. However, parallel analysis must be viewed at best as a heuristic approach rather than a mathematically rigorous one. The authors suggest a revision to parallel analysis that could improve its accuracy. A Monte Carlo study is conducted to…

The purpose of this study was to investigate the application of the parallel analysis (PA) method for choosing the number of factors in component analysis for situations in which data are dichotomous or ordinal. Although polychoric correlations are sometimes used as input for component analyses, the random data matrices generated for use in PA…

Properties of the Spearman correction for attenuation were investigated using Monte Carlo methods, under conditions where correlations between error scores exist as a population parameter and also where correlated errors arise by chance in random sampling. Equations allowing for all possible dependence among true and error scores on two tests at…

While tables and formulas for Fisher's z transformations are commonly included in introductory statistics books, the reverse of this transformation, namely, Fisher's z to r, is not included. Two Fisher's z to r formulas are presented. (Author)

Relative to given scale properties of each of two paired variables, a program for identification and computation of the following indices of relationship is provided: phi, Spearman rank order, Kendall's Tau, Pearson's product moment, biserial, and point biserial. (Author/RC)

Restriction in range is a measurement problem frequently encountered in research studies that utilize correlation coefficients. A FORTRAN program is described that can compute the estimated unrestricted correlation coefficient in either the explicit or implicit case. The user selects the appropriate formula to be employed from five that are…

Formulas and a FORTRAN program for computing Kendall's Tau as well as a generalized Spearman rho coefficient from ordered contingency tables are described. (Author)