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Gross, Alan L.; Torres-Quevedo, Rocio – Psychometrika, 1995
The posterior distribution of the bivariate correlation is analytically derived given a data set where "X" is completely observed, but "Y" is missing at random for a portion of the sample. Interval estimates of the correlation are constructed from the posterior distribution in terms of the highest density regions. (SLD)
Descriptors: Bayesian Statistics, Correlation, Equations (Mathematics), Estimation (Mathematics)

Camilli, Gregory – Psychometrika, 1995
This paper demonstrates that two major tests for two-by-two tables, Fisher's exact and Pearson's chi-square tests, are highly related from a Bayesian perspective. A formal similarity is demonstrated in small samples, and reasons for the relationship are discussed. (SLD)
Descriptors: Bayesian Statistics, Chi Square, Equations (Mathematics), Probability

Lenk, Peter J.; DeSarbo, Wayne S. – Psychometrika, 2000
Presents a hierarchical Bayes approach to modeling parameter heterogeneity in generalized linear models. The approach combines the flexibility of semiparametric latent class models that assume common parameters for each subpopulation and the parsimony of random effects models that assume normal distributions for the regression parameters.…
Descriptors: Bayesian Statistics, Monte Carlo Methods, Simulation, Statistical Distributions

Bockenholt, Ulf – Psychometrika, 1993
A flexible class of stochastic mixture models is introduced and illustrated for analysis and interpretation of individual differences in recurrent choice and other types of count data. These models are derived by specifying elements of the choice process at the individual level. An easy-to-implement algorithm is presented for parameter estimation.…
Descriptors: Bayesian Statistics, Decision Making, Equations (Mathematics), Estimation (Mathematics)

Vijn, Peter – Psychometrika, 1983
The use of Bayesian theory to connect ordinal data and ordered scale points with the theory of order statistics is presented. Exact and approximate multivariate and marginal densities for the scale points are derived. (Author/JKS)
Descriptors: Bayesian Statistics, Data Analysis, Latent Trait Theory, Measurement

Swaminathan, Hariharan; Gifford, Janice A. – Psychometrika, 1985
A Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model. Joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described. (Author/LMO)
Descriptors: Bayesian Statistics, Estimation (Mathematics), Latent Trait Theory, Mathematical Models

Lin, Miao-Hsiang; Hsiung, Chao A. – Psychometrika, 1994
Two simple empirical approximate Bayes estimators are introduced for estimating domain scores under binomial and hypergeometric distributions respectively. Criteria are established regarding use of these functions over maximum likelihood estimation counterparts. (SLD)
Descriptors: Adaptive Testing, Bayesian Statistics, Computation, Equations (Mathematics)

Swaminathan, Hariharan; Gifford, Janice A. – Psychometrika, 1986
A joint Bayesian estimation procedure for estimating parameters in the three-parameter logistic model is developed. Simulation studies show that the Bayesian procedure (1) ensures that the estimates stay in the parameter space and (2) produces better estimates than the joint maximum likelihood procedure. (Author/BS)
Descriptors: Bayesian Statistics, Estimation (Mathematics), Goodness of Fit, Latent Trait Theory

Mislevy, Robert J. – Psychometrika, 1984
Assuming vectors of item responses depend on ability through a fully specified item response model, this paper presents maximum likelihood equations for estimating the population parameters without estimating an ability parameter for each subject. Asymptotic standard errors, tests of fit, computing approximations, and details of four special cases…
Descriptors: Bayesian Statistics, Estimation (Mathematics), Goodness of Fit, Latent Trait Theory

Jansen, Margo G. H.; van Duijn, Marijtje A. J. – Psychometrika, 1992
A model developed by G. Rasch that assumes scores on some attainment tests can be realizations of a Poisson process is explained and expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. How additional between-subject and within-subject factors can be incorporated is discussed. (SLD)
Descriptors: Achievement Tests, Bayesian Statistics, Equations (Mathematics), Estimation (Mathematics)
Lee, Sik-Yum; Xia, Ye-Mao – Psychometrika, 2006
By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the…
Descriptors: Maximum Likelihood Statistics, Statistical Distributions, Structural Equation Models, Robustness (Statistics)