Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Multiple group modeling is one of the methods to address the measurement noninvariance issue. Traditional studies on multiple group modeling have mainly focused on item responses. In computer-based assessments, joint modeling of response times and action counts with item responses helps estimate the latent speed and action levels in addition to…

Response-time models are of increasing interest in educational and psychological testing. This article focuses on the lognormal model for response times, which is one of the most popular response-time models, and suggests a simple person-fit statistic for the model. The distribution of the statistic under the null hypothesis of no misfit is proved…

Response-time models are of increasing interest in educational and psychological testing. This paper focuses on the lognormal model for response times (van der Linden, 2006), which is one of the most popular response-time models, and suggests a simple person-fit statistic for the model. The distribution of the statistic under the null hypothesis…

Bayesian item response theory (IRT) modeling stages include (a) specifying the IRT likelihood model, (b) specifying the parameter prior distributions, (c) obtaining the posterior distribution, and (d) making appropriate inferences. The latter stage, and the focus of this research, includes model criticism. Choice of priors with the posterior…

This study analysed polytomous items' psychometric properties according to nonparametric item response theory (NIRT) models. Thus, simulated datasets--three different test lengths (10, 20 and 30 items), three sample distributions (normal, right and left skewed) and three samples sizes (100, 250 and 500)--were generated by conducting 20…

This paper introduces the generalized beta (GB) model as a new modeling tool in the educational assessment area and evaluation analysis, specifically. Unlike normal model, GB model allows us to capture some real characteristics of data and it is an important tool for understanding the phenomenon of learning. This paper develops a contrast with the…

If the diffusion model (Ratcliff & McKoon, 2008) is to account for the relative speeds of correct responses and errors, it is necessary that the components of processing identified by the model vary across the trials of a task. In standard applications, the rate at which information is accumulated by the diffusion process is assumed to be normally…

Being able to characterize the size of raindrops is useful in a number of fields including meteorology, hydrology, agriculture and telecommunications. Associated with this article are data sets containing surface (i.e. ground-level) measurements of raindrop size from two different instruments and two different geographical locations. Students may…

Person-fit assessment may help the researcher to obtain additional information regarding the answering behavior of persons. Although several researchers examined person fit, there is a lack of research on person-fit assessment for mixed-format tests. In this article, the lz statistic and the ?2 statistic, both of which have been used for tests…

The authors assessed correct model identification rates of Akaike's information criterion (AIC), corrected criterion (AICC), consistent AIC (CAIC), Hannon and Quinn's information criterion (HQIC), and Bayesian information criterion (BIC) for selecting among cross-classified random effects models. Performance of default values for the 5…

In light of the emergence of statistical analysis techniques based on data mining in education sciences, and the potential they offer to detect non-trivial information in large databases, this paper presents a procedure used to detect factors linked to academic achievement in large-scale assessments. The study is based on a non-experimental,…

Typically a longitudinal growth modeling based on item response theory (IRT) requires repeated measures data from a single group with the same test design. If operational or item exposure problems are present, the same test may not be employed to collect data for longitudinal analyses and tests at multiple time points are constructed with unique…

W. A. Wallis studied vacancies in the US Supreme Court over a 96-year period (1837-1932) and found that the distribution of the number of vacancies per year could be characterized by a Poisson model. This note updates this classic study.

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…