Regression estimation and poststratification are methods used in survey sampling to estimate a population mean, when additional information is available for some auxiliary variables. The extension of these methods to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISREL framework.

Conjunctive item response models are introduced such that (a) sufficient statistics for latent traits are not necessarily additive in item scores; (b) items are not necessarily locally independent; and (c) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are special cases. Simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well. Conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability. It is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure. It is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence, multidimensionality, and item response function form.

Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.

A test is proposed for the equality of the variances of k ≥ 2 correlated variables. Pitman's test for k = 2 reduces the null hypothesis to zero correlation between their sum and their difference. Its extension, eliminating nuisance parameters by a bootstrap procedure, is valid for any correlation structure between the k normally distributed variables. A Monte Carlo study for several combinations of sample sizes and number of variables is presented, comparing the level and power of the new method with previously published tests. Some nonnormal data are included, for which the empirical level tends to be slightly higher than the nominal one. The results show that our method is close in power to the asymptotic tests which are extremely sensitive to nonnormality, yet it is robust and much more powerful than other robust tests.

In a variety of measurement situations, the researcher may wish to compare the reliabilities of several instruments administered to the same sample of subjects. This paper presents eleven statistical procedures which test the equality of m coefficient alphas when the sample alpha coefficients are dependent. Several of the procedures are derived in detail, and numerical examples are given for two. Since all of the procedures depend on approximate asymptotic results, Monte Carlo methods are used to assess the accuracy of the procedures for sample sizes of 50, 100, and 200. Both control of Type I error and power are evaluated by computer simulation. Two of the procedures are unable to control Type I errors satisfactorily. The remaining nine procedures perform properly, but three are somewhat superior in power and Type I error control.

In this—partly—expository paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation will be considered from a system theoretic perspective. The general dynamic model covers (dynamic) factor analytic models, (dynamic) MIMIC models and Jöreskog's linear structural model as special cases. Its reduced form is—under a slightly different specification—known in system theory and econometrics as the stochastic, stationary version of the state-space model. By using concepts and methods from system theory, such as the observability and controllability concept, the (steady-state) Kalman filter and a general nonlinear ML-estimation procedure known as prediction-error estimation the general dynamic model will be identified. It will be shown that Jöreskog's LISREL-procedure is a special case of the prediction-error estimation procedure.

Proximity data can be represented by an extended tree, which generalizes traditional trees by including marked segments that correspond to overlapping clusters. An extended tree is a graphical representation of the distinctive features model. A computer program (EXTREE) that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data.

Experiments are considered where each of a sample of subjects is assigned to one of C categories separately by each of a fixed or varying group of observers. Building on earlier publications, general procedures are proposed to analyze agreements and disagreements among observers. In the case of a varying group of observers, it is shown that it is not necessary to demand a constant number of observers per subject. In the case of a fixed group of observers, the problem of missing data is considered.

The procedures are illustrated within the context of two clinical diagnosis examples. In the first example it is investigated which categories are relatively hard to distinguish from one another; a new theorem is applied that shows a useful property of the statistic kappa. In the second example it is investigated if a subgroup of observers can be found with a significantly higher degree of interobserver agreement.

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. This hypothesis is basic to the writings of several prominent theorists, such as Gagné and Piaget. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative example is also provided.

Under the assumption of normality, a formula is derived for the reliability of the maximum score. It is shown that the maximum score is more reliable than each of the single observations, but less reliable than their composite score.

The name “Roy's largest root” and similar names are used in practice to label two different but functionally related statistics—one proportional to anF, and the other, a squared canonical correlation. This note presents the logic that leads to the two formulations, states which statistic some popular statistical packages use, and shows the possible source of this inconsistency in the original work of Roy (1953) and Heck (1960).

An algorithm for assessing additivity conjunctively via both axiomatic conjoint analysis and numerical conjoint scaling is described. The algorithm first assesses the degree of individual differences among sets of rankings of stimuli, and subsequently examines either individual or averaged data for violations of axioms necessary for an additive model. The axioms are examined at a more detailed level than has been previously done. Violations of the axioms are broken down into different types. Finally, a nonmetric scaling of the data can be done based on either or both of two different badness-of-fit scaling measures. The advantages of combining all of these features into one algorithm for improving the diagnostic value of axiomatic conjoint measurement in evaluating additivity are discussed.