Student modeling can help guide the behavior of a cognitive tutor system and provide insight to researchers on understanding how students learn. In this context, Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge inference models due to its predictive accuracy, interpretability and ability to infer student knowledge. However,…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

Use of linear combinations of Fisher's "z" transformations as a combined test for the common correlation parameter based on "k" independent sample correlations has been previously studied. This article considers additional "z" additive properties and methods of combining independent studies when planning the number of…

Three separate papers are included in this report. The first describes a two-stage procedure for choosing from among several instructional programs the one which maximizes the probability of passing the test. The second gives the exact sample sizes required to determine whether a squared multiple correlation coefficient is above or below a known…

A large number of seemingly diverse coefficients have been proposed as indices of dependability, or reliability, for domain-referenced and/or mastery tests. In this paper, it is shown that most of these indices are special cases of two generalized indices of agreement: one that is corrected for chance, and one that is not. The special cases of…

Five issues relative to the use of different Ordinary Least Squares (OLS) and Hierarchical Linear Modeling (HLM) models to identify effective schools and teachers were examined using data from all students in the Dallas (Texas) public schools in grade 3 in 1994 and grade 4 in 1995. OLS models using first- and second-order interactions produced…

The focus of this study is on the estimation procedures implemented in BILOG, a computer program. One purpose is to compare the item parameter estimates produced by various procedures available in BILOG. Four different models are used: the one, two, and three parameter model and a three parameter model with common guessing parameters. The results…

Analyses for results of a series of studies examining intercorrelations among a set of as many as p+1 variables are presented. Several estimators of a pooled or average correlation vector and its variances are derived for cases in which some studies do not report complete correlation matrices. A test of the homogeneity (consistency) of the…

Researchers have been limited in their ability to examine multiple constructs simultaneously due to the constraints imposed by traditional statistical methods. The most notable limitations include the need for a relatively large sample size while restricting the variables to a relatively small number. The application of a newly discovered…