Latent class analysis is formulated as a problem of estimating parameters in a finite mixture distribution. The EM algorithm is used to find the maximum likelihood estimates, and the case of categorical variables with more than two categories is considered. (Author)

Studied whether the standard z-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. An example illustrates that neither the factor loading estimates nor the standard error estimates possess scale…

Two methods of estimating parameters in the Rasch model are compared. The equivalence of likelihood estimations from the model of G. J. Mellenbergh and P. Vijn (1981) and from usual unconditional maximum likelihood (UML) estimation is demonstrated. Mellenbergh and Vijn's model is a convenient method of calculating UML estimates. (SLD)

Discusses whether the tradition of accepting point-symmetric item characteristic curves is justified by uncovering the inconsistent relationship between the difficulties of items and the order of maximum likelihood estimates of ability. In this context, proposes a family of models, called the logistic positive exponent family, that provides…

This paper presents a detailed description of maximum parameter estimation for item response models using the general EM algorithm. In this paper the models are specified using a univariate discrete latent ability variable. When the latent ability variable is discrete the distribution of the observed item responses is a finite mixture, and the EM…

It has previously been shown that the Bock-Aitkin procedure (R. Bock and M. Aitkin, 1981) is an instance of the EM algorithm when trying to find the marginal maximum likelihood estimate for a discrete latent ability variable (latent trait). In this paper, it is shown that the Bock-Aitkin procedure is a numerical implementation of the EM algorithm…

Misspecification of mean and covariance structures for metric endogenous variables is considered. Maximum likelihood estimation of model parameters and the asymptotic covariance matrix of the estimates are discussed. A Haussman test for misspecification is developed, which is sensitive to misspecification not detected by the test statistics…

This paper is concerned with estimation and hypothesis testing of treatment effects in nonequivalent control group designs with the assumption that in the absence of treatment effects, natural growth conforms to a particular class of continuous growth models. Point estimation, interval estimation, and hypothesis testing procedures were developed…

Reparameterization is used to find the maximum likelihood estimates of parameters in a multivariate model having some component variable observable only in polychotomous form. Maximum likelihood estimates are found by a Fletcher Powell algorithm. In addition, the partition maximum likelihood method is proposed and illustrated. (Author/GDC)

A constrained quadratic spline is proposed as an estimator of the hazard function of a random variable. A maximum penalized likelihood procedure is used to fit the estimator to a sample of psychological response times. (Author/LMO)

Item response theory (IRT) has proven to be a very powerful and useful measurement tool. However, most of the IRT models that have been proposed, and all of the models commonly used, require the assumption of unidimensionality, which prevents their application to a wide range of tests. The few models that have been proposed for use with…

Two linearly constrained models based on the Rasch model are discussed. Necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimators are derived. Methods for hypothesis testing within this framework are proposed. (Author/JKS)

An extension of the model for measuring reading speed proposed by G. Rasch (1960) is presented. In this approach, subject parameters are treated as random variables having a common gamma distribution. From this marginal, maximum-likelihood estimators are derived for test difficulties and the parameters of latent subject distribution. (SLD)

D. R. Divgi (1986) demonstrated that the bias of unconditional maximum likelihood (UCON) item-parameter estimates is not removed by the factor (n-1)/n. D. Andrich (1989) argued that the demonstration was faulty. In this note, a complete proof of Divgi's conclusion is presented. (Author/TJH)

A new estimation method, Weighted Likelihood Estimation (WLE), is derived mathematically. Two Monte Carlo studies compare WLE with maximum likelihood estimation and Bayesian modal estimation of ability in conventional tests and tailored tests. Advantages of WLE are discussed. (SLD)