Extends the Triadic Relations Model of C. Bond, E. Horn, and D. Kenny (1997) to analyze the covariances between triadic variables. Specifies a bivariate version of the model and presents estimation methods that can be used to decompose the covariance between 2 triadic variables into 33 covariance components. (Author/SLD)

The perturbation theory of the generalized eigenproblem is used to derive influence functions of each squared canonical correlation coefficient and the corresponding canonical vector pair. Three sample versions of these functions are described, and some properties are noted. Two obvious applications, multiple correlation and correspondence…

A new version of the standardized estimated parameter change that is invariant to the original metrics of the measured and latent variables is suggested for use in model modification. A multivariate estimated parameter change for a set of fixed parameters to be freed simultaneously is also introduced. (SLD)

An Expectation-Maximization (EM) algorithm in a maximum likelihood framework is developed to estimate finite mixtures of multivariate regression and simultaneous equation models with multiple endogenous variables. A dataset with cross-sectional observations for a diverse sample of businesses illustrates the semiparametric approach. (SLD)

A method is presented for approximating the amount of bias in estimators with complex sampling distributions that are influenced by a variety of properties. The model is illustrated in the contexts of the bootstrap method and redundancy analysis. (SLD)

Methods for studying relationships between patterns of change on different variables are considered, showing how the multilevel modeling framework, often used to study univariate change, can be extended to the multivariate case to yield estimates of covariances of parameters representing aspects of change for different variables. (SLD)

An analysis of repeated measures designs is proposed that uses an empirical Bayes estimator of the covariance matrix. The proposed analysis behaves like a univariate analysis when sample size is small or sphericity nearly satisfied, but behaves like multivariate analysis when sample size is large or sphericity is strongly violated. (SLD)

Computational formulas are developed for recovering measures of strength of association from approximate "F" tests and chi-square tests associated with four multivariate test statistics. The four statistics include Wilke's Lambda; Pillai's Trace "V"; Hotelling's Trace "T"; and Roy's greatest characteristic root…

The Gibbs sampling algorithms presented by M. H. Seltzer (1993) are fully generalized to a broad range of settings in which vectors of random regression parameters in the hierarchical model are assumed multivariate normally or multivariate "t" distributed across groups. The use of a fully Bayesian approach is discussed. (SLD)

It is demonstrated that, in the presence of population information, a linear combination of true scores can be estimated more efficiently than by the same linear combination of the observed scores. Three criteria for optimality are discussed, but they yield the same solution, described as a multivariate shrinkage estimator. (Author/SLD)

The source of an event-related brain potential (ERP) is estimated from multivariate measures of ERP on the head under several mathematical and physical constraints on the parameters of the source model. Statistical aspects of estimation are discussed, and new tests are proposed. (SLD)

A general model for two-level multivariate data, with responses possibly missing at random, is described. The model combines regressions on fixed explanatory variables with structured residual covariance matrices. The likelihood function is reduced to a form enabling computational methods for estimating the model to be devised. (Author)

Generalizability or invariance procedures have been known for over three decades. Through the years, these procedures have not been widely discussed or employed. One reason for the lack of use is that most of the articles on invariance procedures have been mathematically oriented. The mathematical orientation of research articles and the lack of…

A class of two-stage models is developed to accommodate three common characteristics of behavioral data: (1) its multivariate nature; (2) the typical small sample size; and (3) the possibility of missing observations. The model, as illustrated, permits estimation of the full spectrum of plausible measurement error structures. (SLD)

This article presents a didactic discussion on the role of asymptotically independent test statistics and separable hypotheses as they pertain to issues of specification error, power, and model misspecification in the covariance structure modeling framework. A small population study supports the major findings. (SLD)