In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing LVMs with the usual linear covariate effects by including nonparametric components for nonlinear…

The practicality and usefulness of variational Monte Carlo calculations to atomic structure are demonstrated. It is found to succeed in quantitatively illustrating electron shielding, effective nuclear charge, l-dependence of the orbital energies, and singlet-tripetenergy splitting and ionization energy trends in atomic structure theory.

The randomized response technique ensures that individual item responses, denoted as true item responses, are randomized before observing them and so-called randomized item responses are observed. A relationship is specified between randomized item response data and true item response data. True item response data are modeled with a (non)linear…

Reading and Mathematics tests of multiple-choice items for grades Kindergarten through 9 were vertically scaled using the three-parameter logistic model and two different scaling procedures: concurrent and separate by grade groups. Item parameters were estimated using Markov chain Monte Carlo methodology while fixing the grade 4 population…

This study presents an extended children-of-twins model, which allowed the authors to test the direction of the association between parenting and child adjustment. Three mechanisms were examined: direct phenotypic influence of parenting on child behavior (controlling for both parental and child genotype), passive genotype-environment correlation,…

This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the…

The authors propose a concise formula to evaluate the standard error of the estimated latent variable score when the true values of the structural parameters are not known and must be estimated. The formula can be applied to factor scores in factor analysis or ability parameters in item response theory, without bootstrap or Markov chain Monte…

Tests of model misfit are often performed to validate the use of a particular model in item response theory. Douglas and Cohen (2001) introduced a general nonparametric approach for detecting misfit under the two-parameter logistic model. However, the statistical properties of their approach, and empirical comparisons to other methods, have not…

Covariance and correlation structure analytic techniques can be used to test whether a specified correlation structure is an adequate model of the population correlation structure. These procedures include: (1) normal theory (NT) and asymptotically distribution free (ADF) covariance structure analysis techniques; and (2) NT and ADF correlation…

A procedure proposed by H. F. Kaiser (1968) for averaging coefficients using the first eigenvalue of an intercorrelation matrix was studied via Monte Carlo methods. The study also assessed a modification of the Kaiser procedure and the use of Fisher's "z." Applications to sample size effects are discussed. (TJH)

While violation of the homogeneity of variance assumption has received considerable attention, violation of the assumption of normally distributed data has not received as much attention. As a result, researchers may have the mistaken impression that as long as the assumptions of independence of observations and homogeneity of variance are…

A likelihood ratio test, using Monte Carlo methods, is conducted to determine the number of classes appropriate to a certain data set when applying latent class analysis. Results confirm that the usually assumed null distribution is inappropriate. (TJH)

Two Monte Carlo studies investigated the effects of within-group covariance structure on subgroup recovery by 10 hierarchical clustering methods using 100 bivariate observations from 2 subgroups. Superior recovery was associated with within-group correlation that matched the direction of subgroup separation. (SLD)

Studied Type I error rates and relative power of structural means, multiple-indicator, multiple-cause, and multivariate analysis of variance approaches for testing construct mean differences within a one-factor, two-group design. Used Monte Carlo methods to investigate Type I error rates and a population analysis approach to study the power of…