Topic models are mathematical and statistical models used to analyze textual data. The objective of topic models is to gain information about the latent semantic space of a set of related textual data. The semantic space of a set of textual data contains the relationship between documents and words and how they are used. Topic models are becoming…

In random-effects meta-analysis the between-study variance ([tau][superscript 2]) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating [tau][superscript 2] and the overall effect and produce confidence intervals…

The subject of the research is to build methodologies to evaluate the student knowledge by testing. The author points to the importance of feedback about the mastering level in the learning process. Testing is considered as a tool. The object of the study is to create the test system models for defence practice problems. Special attention is paid…

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…

Parallel analysis has been shown to be suitable for dimensionality assessment in factor analysis of continuous variables. There have also been attempts to demonstrate that it may be used to uncover the factorial structure of binary variables conforming to the unidimensional normal ogive model. This article provides both theoretical and empirical…

This study uses simulation techniques to examine the statistical power of the group- randomized design and the matched-pair (MP) randomized block design under various parameter combinations. Both nearest neighbor matching and random matching are used for the MP design. The power of each design for any parameter combination was calculated from…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

Evaluated the performance of several alternative cluster analytic approaches to initial model specification using population parameter analyses and a Monte Carlo simulation. Of the six cluster approaches evaluated, the one using the correlations of item correlations as a proximity metric and average linking as a clustering algorithm performed the…

Prior work has proposed different theoretical mechanisms to explain students' course-taking patterns in schools. On the one hand, there are oversocialized accounts that claim that rules, social background factors, and supply-side factors shape observed career patterns. On the other hand, there are undersocialized accounts that claim that the…

This paper discusses the principles underlying discriminant analysis and constructs a simulated data set to illustrate its methods. Discriminant analysis is a multivariate technique for identifying the best combination of variables to maximally discriminate between groups. Discriminant functions are established on existing groups and used to…

Four measurement designs are presented for use with correlation coefficients corrected, in one variable, for attenuation due to unreliability (partially disattenuated). Associated asymptotic variance/covariance expressions are presented. Empirical simulation results illustrate the satisfactory Type I error control and statistical power of the…

Implications of ignoring correlated error on parameter estimates in some simple structural equation models are examined. It is shown analytically and empirically through simulation that ignoring positive between-construct correlated error overestimates the structural parameter linking the two constructs. Effects become more pronounced with…

The performance of the following four methodologies for assessing unidimensionality was examined: (1) DIMTEST; (2) the approach of P. W. Holland and P. R. Rosenbaum; (3) linear factor analysis; and (4) non-linear factor analysis. Each method is examined and compared with other methods using simulated data sets and real data sets. Seven data sets,…

This paper illustrates the transformation of a raw data matrix into a matrix of associations, and then into a factor matrix. Factor analysis attempts to distill the most important relationships among a set of variables, thereby permitting some theoretical simplification. In this heuristic data, a correlation matrix was derived to display…

This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…