Structural equation modeling (SEM) is being applied to ever more complex data types and questions, often requiring extensions such as regularization or novel fitting functions. To extend SEM, researchers currently need to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we introduce…

Proposes a marginal Bayesian estimation procedure to improve item parameter estimates for the three parameter logistic model. Computer simulation suggests that implementing the marginal Bayesian estimation algorithm with four-parameter beta prior distributions and then updating the priors with empirical means of updated intermediate estimates can…

The Gibbs sampling algorithms presented by M. H. Seltzer (1993) are fully generalized to a broad range of settings in which vectors of random regression parameters in the hierarchical model are assumed multivariate normally or multivariate "t" distributed across groups. The use of a fully Bayesian approach is discussed. (SLD)

It is shown that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Analysis of several thousand solutions to Bayesian problems showed that when information was presented in frequency formats, statistically naive participants derived up to 50% of inferences by Bayesian…

An adaptive testing algorithm is presented based on an alternative modeling framework, and its effectiveness is investigated in a simulation based on real data. The algorithm uses a latent class modeling framework in which assessed latent attributes are assumed to be categorical variables. (SLD)

The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are estimation bias due to measurement error and the estimation of the effects of the individual's hierarchical social milieu. This paper…

Type I error rates of F. M. Lord's chi square test for differential item functioning were investigated using Monte Carlo simulations with marginal maximum likelihood estimation and marginal Bayesian estimation algorithms. Lord's chi square did not provide useful Type I error control for the three-parameter logistic model at these sample sizes.…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…