Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

When estimating causal effects, unmeasured confounding and model misspecification are both potential sources of bias. We propose a method to simultaneously address both issues in the form of a semi-parametric sensitivity analysis. In particular, our approach incorporates Bayesian Additive Regression Trees into a two-parameter sensitivity analysis…

Kulick and Wright concluded, based on theoretical mathematical simulations of hypothetical student exam scores, that assigning exam grades to students based on the relative position of their exam performance scores within a normal curve may be unfair, given the role that randomness plays in any given student's performance on any given exam.…

This study uses simulation techniques to examine the statistical power of the group- randomized design and the matched-pair (MP) randomized block design under various parameter combinations. Both nearest neighbor matching and random matching are used for the MP design. The power of each design for any parameter combination was calculated from…

Multivariate models for the triangular and duo-trio methods are described, and theoretical methods are compared to a Monte Carlo simulation. Implications are discussed for a new theory of multidimensional scaling which challenges the traditional assumption that proximity measures and perceptual distances are monotonically related. (Author/GDC)

This paper studies the general theory of Akaike's Information Criterion (AIC) and provides two analytical extensions. The extensions make AIC asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the two models. The criteria are applied in two Monte Carlo experiments. (Author/GDC)

A Monte Carlo simulation approach was taken to investigate the effect of sample size on a variety of latent growth models. A fully balanced experimental design was implemented, with samples drawn from multivariate normal populations specified to represent 12 unique growth models. The models varied factorially by crossing number of time points,…

A problem that often surfaces in the use of the "t"-test is the absence of critical values for common sample sizes. This problem may cause "guilt" on the part of the professor who must advise students when they encounter discrepancies between their own calculations of the degree of freedom and critical values provided in…

An objective method based on the likelihood ratio procedure is presented for use in selecting a measurement model from among the RASCH, 2-parameter and 3-parameter logistic latent trait models. The procedure may be applied in a straightforward manner to aid in choosing between the 2-parameter and the Rasch models. When choosing between the 3- and…

Proposes a modified version of commonly employed item response models in a fully Bayesian framework and obtains inferences under the model using Markov chain Monte Carlo techniques. Demonstrates use of the model in a series of simulations and with operational data from the North Carolina Test of Computer Skills and the Test of Spoken English…

Three techniques for estimating Kuder Richardson reliability (KR20) coefficients for incomplete data are contrasted. The methods are: (1) Henderson's Method 1 (analysis of variance, or ANOVA); (2) Henderson's Method 3 (FITCO); and (3) Koch's method of symmetric sums (SYSUM). A Monte Carlo simulation was used to assess the precision of the three…

This paper describes a simulation that determines the adequacy of various indices as decision criteria for assessing unidimensionality. Using the sum of absolute residuals from the two-parameter latent trait model, indices were obtained that could discriminate between one latent trait and more than one latent trait. (Author/BW)

Monte Carlo techniques were used to examine regression approaches to external unfolding. The present analysis examined the technique to determine if various characteristics of the points are recovered (such as ideal points). Generally, monotonic analyses resulted in good recovery. (TJH)