Bayesian Modal Estimation for the One-Parameter Logistic Ability-Based Guessing (1PL-AG) Model

The calibration of the one-parameter logistic ability-based guessing (1PL-AG) model in item response theory (IRT) with a modest sample size remains a challenge for its implausible estimates and difficulty in obtaining standard errors of estimates. This article proposes an alternative Bayesian modal estimation (BME) method, the Bayesian Expectation-Maximization-Maximization (BEMM) method, which is developed by combining an augmented variable formulation of the 1PL-AG model and a mixture model conceptualization of the three-parameter logistic model (3PLM). By comparing with marginal maximum likelihood estimation (MMLE) and Markov Chain Monte Carlo (MCMC) in JAGS, the simulation shows that BEMM can produce stable and accurate estimates in the modest sample size. A real data example and the MATLAB codes of BEMM are also provided.

Latent D-Scoring Modeling: Estimation of Item and Person Parameters

This study presents a latent (item response theory–like) framework of a recently developed classical approach to test scoring, equating, and item analysis, referred to as D-scoring method. Specifically, (a) person and item parameters are estimated under an item response function model on the D-scale (from 0 to 1) using marginal maximum-likelihood estimation and (b) analytic expressions are provided for item information function, test information function, and standard error of estimation for D-scores obtained under the proposed latent treatment of the D-scoring method. The results from a simulation study reveal very good recovery of item and person parameters via the marginal maximum-likelihood estimation method. Discussion and recommendations for practice are provided.

Modeling Responses and Response Times in Rating Scales With the Linear Ballistic Accumulator

In this article, a new model is proposed for the responses and the response times in attitudinal or personality inventories with graded response format. The model is based on the lognormal race model ( Heathcote & Love, 2012 ) and assumes two accumulators that aggregate evidence in favor of and against the statement made by an item of an inventory. The accumulator that first reaches a response threshold determines the direction of the response (agreement/disagreement). The strength of the response, which is indicated by the choice of a graded response option, is a function of the difference between the two accumulators when responding. By relating the accumulators to latent traits, the model can be embedded into a latent trait model that accounts for individual differences. The model can be fit to data with marginal maximum likelihood estimation. A test of model fit is described, and it is shown how the model can be used for attitudinal and personality assessment. Finally, the application of the model is demonstrated with a real dataset.