Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading…

Cognitive diagnosis models (CDMs) are latent class multidimensional statistical models that help classify people accurately by using a set of discrete latent variables, commonly referred to as attributes. These models require a Q-matrix that indicates the attributes involved in each item. A potential problem is that the Q-matrix construction…

Lagrange multiplier (LM) or score tests have seen renewed interest for the purpose of diagnosing misspecification in item response theory (IRT) models. LM tests can also be used to test whether parameters differ from a fixed value. We argue that the utility of LM tests depends on both the method used to compute the test and the degree of…

Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits…

In Ramsay curve item response theory (RC-IRT) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the…

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

A latent variable modeling approach that can be used to examine whether several psychometric tests are parallel is discussed. The method consists of sequentially testing the properties of parallel measures via a corresponding relaxation of parameter constraints in a saturated model or an appropriately constructed latent variable model. The…

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…

Estimation problems associated with the correlated-trait correlated-method (CTCM) parameterization of a multitrait-multimethod (MTMM) matrix are widely documented: the model often fails to converge; even when convergence is achieved, one or more of the parameter estimates are outside the admissible parameter space. In this study, the authors…

This article reports a study that investigated the effects of Q-matrix misspecifications on parameter estimates and misclassification rates for the deterministic-input, noisy "and" gate (DINA) model, which is a restricted latent class model for multiple classifications of respondents that can be useful for cognitively motivated diagnostic…

Two models for scaling of paired comparison data are compared to the Thurstone case III model. Two goodness of fit indices are presented for each model for five data sets. The results illustrate the inability of the Thurstone model to adequately account for data when the scale includes extreme stimuli. (Author)

Component analysis provides an attractive alternative to factor analysis, since component scores are easily determined while factor scores can only be estimated. The correct method of determining component scores is presented as well as several illustrations of how commonly used incorrect methods distort the meaning of the component solution. (RC)

The first eigenvalue of a correlation matrix indicates the maximum amount of the variance of the variables which can be accounted for with a linear model by a single underlying factor. The first eigenvalue measures the primary cluster in the matrix, its number of variables and average correlation. (Author/RL)

A procedure for estimating the reliability of a factorially complex composite is considered. An application of its use with Scholastic Aptitude Test data is provided. (Author/JKS)

In traditional factor analysis, the variance-covariance matrix or the correlation matrix has often been a form of inputting data. In contrast, in Bayesian factor analysis, the entire data set is typically required to compute the posterior estimates, such as Bayes factor loadings and Bayes unique variances. We propose a simple method for computing…