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…

The fit of an item response model is typically conceptualized as whether a given model could have generated the data. We advocate for an alternative view of fit, "predictive fit", based on the model's ability to predict new data. We derive two predictive fit metrics for item response models that assess how well an estimated item response…

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…

Certain planned-missing designs (e.g., simple-matrix sampling) cause zero covariances between variables not jointly observed, making it impossible to do analyses beyond mean estimations without specialized analyses. We tested a multigroup confirmatory factor analysis (CFA) approach by Cudeck (2000), which obtains a model-estimated…

Many interventions are characterized by repeated observations on the same individuals (e.g., baseline, mid-intervention, two to three post-intervention observations), which offer the opportunity to consider differences in how individuals vary over time. Effective interventions may not be limited to changing means, but instead may also include…

In this article, we propose using the Bayes factors (BF) to evaluate person fit in item response theory models under the framework of Bayesian evaluation of an informative diagnostic hypothesis. We first discuss the theoretical foundation for this application and how to analyze person fit using BF. To demonstrate the feasibility of this approach,…

The multidimensional item response theory (MIRT) models with covariates proposed by Haberman and implemented in the "mirt" program provide a flexible way to analyze data based on item response theory. In this report, we discuss applications of the MIRT models with covariates to longitudinal test data to measure skill differences at the…

The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…

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…

Both ad-hoc robust sandwich standard error estimators (design-based approach) and multilevel analysis (model-based approach) are commonly used for analyzing complex survey data with nonindependent observations. Although these 2 approaches perform equally well on analyzing complex survey data with equal between- and within-level model structures…

The use of standardized test results to drive school administrator evaluations pervades education policymaking in more than 40 states. However, the results of state standardized tests are strongly influenced by non-school factors. The models of best fit (n = 18) from this correlational, explanatory, longitudinal study predicted accurately the…

This paper presents an empirical analysis of similarities and differences between two statistics, G and Phi, which treat genuinely dichotomous data. These results can aid researchers in selecting between these two statistics and in evaluating results from the use of one v the other. (Author)

A correction procedure for estimating correlation coefficients when faced with the problem of a restricted range in the variables due to an explicit selection procedure was empirically investigated. Results indicated that the assumption of linearity is critical, but that homoscedasticity is less important. (JKS)

The relative precision of four methods of estimating missing data in principal components analysis was investigated. Artificial data with known characteristics, obtained from Cattell's "Plasmode: 30-10-4-2," was used with one third of the data on half of the variables being systematically eliminated. The four methods of missing data estimation…

A strategy for comparing two sets of results (one based upon early childhood recollections (ECR) and another upon video taped (VT) group behavior) from the Perceptual Characteristics Rating Scale was developed. The null distribution of the mean deviation was estimated by randomly matching an ECR response vector with a VT response vector. To…