Using the item response model as developed on the multinomial distribution, asymptotic variances are obtained for residuals with response patterns and first- and second-order marginal frequencies of manifest variables. A limited-information test of fit is developed by using residuals defined for the first- and second-order marginals. (Author/SLD)

This paper describes a PASCAL program that computes both different types of transitions and learning statistics suitable for learning experiments in which a two-stage Markov model is used. The frequency counts of the different transitions are used for estimating the parameters of the two-stage Markov model. (Author/LMO)

Coefficient alpha, the most commonly used estimate of internal consistency, is often considered a lower bound estimate of reliability, though the extent of its underestimation is not typically known. Many researchers are unaware that coefficient alpha is based on the essentially tau-equivalent measurement model. It is the violation of the…

A Rasch measurement model can be constructed to meet the requirements of rank ordered data. If multiple rankings of the same objects are available, then the parameters of the objects can be estimated, along with their standard errors and also with statistics summarizing the fit of the data to the measurement model. This paper summarizes the…

The Werts-Linn procedure for dealing with categorical errors of measurement in "Comments on Boyle's 'Path Analysis and Ordinal Data'" in The American Journal of Sociology, volume 76, number 6, May 1971, is shown to be inappropriate to the problem of ordered categories. (For related document, see TM 002 301.) (DB)

Study compares the Rasch and the Guttman models of measurement and thus adds to the description of the characteristics of Rasch's logistic model. Such knowledge is of importance in making decisions as to which model and which statistics should be used in evaluations of tests. (Author/CB)

A probabilistic hypothesis testing procedure to assess the fit of hypothesized hierarchical structures for test item data is discussed. Statistical procedures are presented which are useful for evaluating the fit of data of a certain class of probabilistic models. These models apply to sets of dichotomous (O,1) responses for which there are…

When repeated observations are taken at equal time intervals, a simple form of a stationary time series structure may be fitted to the observations. Use of correction factors is discussed. A computer simulation method is used to investigate power advantages of fitting a serial correlation pattern to repeated observations. (TJH)

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

In all latent trait models there is an equation which describes the probabilistic outcome of the interaction of a person with a known ability and an item with a known difficulty. This modeled outcome can be compared to the observed outcome, and the residuals can be summed over the items to assess the fit of the person to the model. Various…

A stochastic disturbance term appears to be essential for structural models in the social sciences. The analysis of such models is considered from the perspective of Joreskog's (1970) general model for the analysis of covariance structure. (For related document, see TM 002 301.) (Author)

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…

Often, all of the variables in a model are latent, random, or subject to measurement error, or there is not an obvious dependent variable. When any of these conditions exist, an appropriate method for estimating the linear relationships among the variables is Least Principal Components Analysis. Least Principal Components are robust, consistent,…

This paper is part of a series of applied statistics monographs intended to provide supplementary reading for applied statistics students. In the present paper, derivations of the unbiased standard error of estimate for both the raw score and standard score linear models are presented. The derivations for raw score linear models are presented in…

This study examined how four commonly used test equating procedures (linear, equipercentile, Rasch Model, and three-parameter) would respond to situations in which the properties or the two tests being equated were different. Data for two tests plus an external anchor test were generated from a three parameter model in which mean test differences…