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…

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…

Whenever you think you have an idea of how something works, you have a mental model. That is, in effect, a layman's way of talking about having an hypothesis. The hypothesis needs to be tested for how closely it fits reality--and reality is the data collected from an experiment. So the data is collected on the few and compared with a few…

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,…

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…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

The purpose of this report is to demonstrate loglinear smoothing using SAS PROC GENMOD. The results from four published examples, which include the smoothing of a) univariate distributions, b) bivariate distributions, c) distributions with teeth, and d) bivariate distributions with structural zeros, are reproduced to show the flexibility of the…

The two purposes of this paper are to provide a SAS IML macro that performs loglinear smoothing and to apply this macro to loglinear smoothing problems that have not been extensively discussed in the test-equating literature. The SAS macro is demonstrated on univariate, bivariate, and trivariate smoothing problems. The univariate and bivariate…

The Libby-Novick class of three-parameter generalized beta distributions is shown to provide a rich class of prior distributions for the binomial model that removes some restrictions of the standard beta class. A numerical example indicates the desirability of using these wider classes of densities for binomial models. (Author/BW)

Several techniques have been developed for creating continuous smooth distributions of test norms. This paper describes two studies that explore the behavior of cubic splines in order to determine their appropriateness for use in test norming. The first study uses data from the Curriculum Referenced Tests of Mastery (CRTM) and employs two…