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…

Complex research questions often need large samples to obtain accurate estimates of parameters and adequate power. Combining extant data sets into a large, pooled data set is one way this can be accomplished without expending resources. Measurement invariance (MI) modeling is an established approach to ensure participant scores are on the same…

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…

To date, small sample problems with latent growth models (LGMs) have not received the amount of attention in the literature as related mixed-effect models (MEMs). Although many models can be interchangeably framed as a LGM or a MEM, LGMs uniquely provide criteria to assess global data-model fit. However, previous studies have demonstrated poor…

A new variant of the iterative "data = fit + residual" data-analytical approach described by Mosteller and Tukey is proposed and implemented in the context of item response theory psychometric models. Posterior probabilities from a Bayesian mixture model of a Rasch item response theory model and an unscalable latent class are expressed…

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…

Conventional differential item functioning (DIF) detection methods (e.g., the Mantel-Haenszel test) can be used to detect DIF only across observed groups, such as gender or ethnicity. However, research has found that DIF is not typically fully explained by an observed variable. True sources of DIF may include unobserved, latent variables, such as…

In this study, we reanalyzed the classic Hawai'i Family Study of Cognition (HFSC) data using contemporary multilevel modeling techniques. We used the HFSC baseline data ("N" = 6,579) and reexamined the factorial structure of 16 cognitive variables using confirmatory (restricted) measurement models in an explicit sequence. These models…

The distance between nonparametric and parametric item characteristic curves has been proposed as an index of goodness of fit in item response theory in the form of a root integrated squared error index. This article proposes to use the posterior distribution of the latent trait as the nonparametric model and compares the performance of an index…

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)