One of the most vexing challenges facing developmental researchers today is the statistical modeling of two or more behaviors as they unfold jointly over time. Although quantitative methodologists have studied these issues for more than half a century, no widely agreed-upon principled strategy exists to empirically analyze codevelopmental…

Log-linear models for contingency tables are a key tool for the study of categorical inequalities in sociology. However, the conventional approach to model selection and specification suffers from at least two limitations: reliance on oftentimes equivocal diagnostics yielded by fit statistics, and the inability to identify patterns of association…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

In recent years the use of expert judgement to set and maintain examination standards has been increasingly criticised in favour of approaches based on statistical modelling. This paper reviews existing research on this controversy and attempts to unify the evidence within a framework where expertise is utilised in the form of comparative…

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family that includes many useful models. A three-step procedure is presented for analyzing data sets by generalized bilinear models. (SLD)

A recursive dynamic programing strategy for reorganizing the rows and columns of square proximity matrices is discussed. The strategy is used when the objective function measuring the adequacy of the reorganization has a fairly simple additive structure. (Author/JKS)

Model modification problems in covariance structure analysis are examined. The Modification Index, suggesting modifications based on a test statistic's largest drop in overall value, and the Expected Parameter Change, suggesting modifications based on the removal of large specification errors, are applied to two specifications of the Wisconsin…

When the highest-way association is present in a 3-way cross-classification of frequencies, standard logit and loglinear models have an many parameters as there are cells in the table; that is, the models are "saturated." Extensions of logit and loglinear models are described here that provide more parsimonious alternatives to saturated…

This study analytically examined the multiple comparison procedures for testing a combined set of planned and post hoc comparisons. To establish a practical guideline, the following issues were investigated: (1) when the generalized sequentially rejective Bonferroni method (GSRB) is and is not applicable; (2) the required alpha levels for the GSRB…

B. De Finetti's "Fundamental Theorem of Probability" is reformulated as a computable linear programming problem. The theorem is substantially extended, and shown to have fundamental implications for the theory and practice of statistics. It supports an operational meaning for the partial assertion of prevision via asserted bounds. The…

A method based on homogeneity analysis (multiple correspondence analysis or multiple scaling) is proposed to reduce many categorical variables to one variable with "k" categories. The method is a generalization of the sum of squared distances cluster analysis problem to the case of mixed measurement level variables. (SLD)

This note shows that the formula suggested by N. D. Bryant and S. Gokhale (1972) for correcting indirectly restricted correlations when no information is available on the third (directly restricted) variable is accurate only in one special instance. A more general correction formula is illustrated. (SLD)

The partial credit model (PCM) (G. N. Masters, 1982) can be viewed as a generalization of the Rasch model for dichotomous items to the case of polytomous items. In many cases, the PCM is too restrictive to fit the data. Several generalizations of the PCM have been proposed. In this paper, a generalization of the PCM (GPCM), a further…

Conditional observed score (COS) and latent trait (LT) definitions of differential item functioning (DIF) are explored to determine when they are equivalent. COS methods rely solely on observed measurements, and LT methods model the response to an item as a function of an unobserved hypothetical latent ability or trait. For the case of dichotomous…