Maximum Likelihood Item Easiness Models for Test Theory Without an Answer Key

Marginal Maximum Likelihood Estimation of Item Response Models in R

Item response theory (IRT) models are a class of statistical models used by researchers to describe the response behaviors of individuals to a set of categorically scored items. The most common IRT models can be classified as generalized linear fixedand/or mixed-effect models. Although IRT models appear most often in the psychological testing literature, researchers in other fields have success...

A comparison of algorithms for maximum likelihood estimation of Spatial GLM models

In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two n...

Item response theory and classical test theory: an empirical comparison

Despite theoretical differences between item response theory (IRT) and classical test theory (CTT), there is a lack of empirical knowledge about how, and to what extent, the IRTand CTT-based item and person statistics behave differently. This study empirically examined the behaviors of the item and person statistics derived from these two measurement frameworks. The study focused on two issues:...

Boosting and Maximum Likelihood for Exponential Models

We derive an equivalence between AdaBoost and the dual of a convex optimization problem, showing that the only difference between minimizing the exponential loss used by AdaBoost and maximum likelihood for exponential models is that the latter requires the model to be normalized to form a conditional probability distribution over labels. In addition to establishing a simple and easily understoo...

Parameter Estimation with Mixture Item Response Theory Models: A Monte Carlo Comparison of Maximum Likelihood and Bayesian Methods