Traditional network research analyzes relational ties within a single group of actors: the models presented in this paper involve relational ties exist beteen two distinct sets of actors. Statistical models for traditional networks in which relations are measured within a group simplify when modeling unidirectional relations measured between groups. The traditional paradigm results in a one-mode socionatrix; the network paradigm considered in this paper results in a two-mode socionatrix; A statistical model is presented, illustrated on a sample data set, and compared to its traditional counterpart. Extensions are discussed, including those that model multivariate relations simultaneously, and those that allow for the inclustion of attributes of the individuals in the group.

The intraclass correlation, ρ, is a parameter featured in much psychological research. Two commonly used estimators of ρ, the maximum likelihood and least squares estimators, are known to be negatively biased. Olkin and Pratt (1958) derived the minimum variance unbiased estimator of the intraclass correlation, but use of this estimator has apparently been impeded by the lack of a closed form solution. This note briefly reviews the unbiased estimator and gives a FORTRAN 77 subroutine to calculate it.

The conventional method of measuring ability, which is based on items with assumed true parameter values obtained from a pretest, is compared to a Bayesian method that deals with the uncertainties of such items. Computational expressions are presented for approximating the posterior mean and variance of ability under the three-parameter logistic (3PL) model. A 1987 American College Testing Program (ACT) math test is used to demonstrate that the standard practice of using maximum likelihood or empirical Bayes techniques may seriously underestimate the uncertainty in estimated ability when the pretest sample is only moderately large.

The recent development of probabilistic Thurstonian choice models for analyzing preference data has been motivated by the need to describe both inter- and intra-individual difference, the multidimensional nature of choice objects, and the effects of similarity and comparability among choice objects. A common feature of these models is that they focus on a single preference judgment. It is customary, however, to ask subjects not only for an overall preference judgment but also for additional paired comparison responses regarding specific attributes. This paper proposes a generalization of Thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships. The approach is illustrated by modeling data from two multivariate preference experiments.

In introducing the LISREL model for systems of linear structural equations, Jöreskog and Sörbom proposed two goodness-of-fit indices, GFI and AGFI. Their asymptotic distributions and some statistical properties are discussed.

We derive several relationships between communalities and the eigenvalues for a p × p correlation matrix Σ under the usual factor analysis model. For suitable choices of j, λj(Σ), where λj(Σ) is the j-th largest eigenvalue of Σ, provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - λp (Σ) improves on the use of squared mulitiple correlation coefficient as a lower bound.

Consider a multivariate context with p variates and k independent samples, each of size n. To test equality of the k population covariance matrices, the likelihood ratio test is commonly employed. Box's F-approximation to the null distribution of the test statistic can be used to compute p-values, if sample sizes are not too small. It is suggested to regard the F-approximation as accurate if the sample sizes n are greater than or equal to 1+0.0613p2 + 2.7265p -1.4182p0.5 + 0.235p1.4* In (k), for 5≤ p ≤30, k ≤20.