In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with cond...
详细信息
In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with conditional independence interpretations are also discussed. Using an incomplete data point of view, the relationships between the incomplete and complete data likelihoods, assuming normality, are highlighted. For computing maximum likelihood estimates, the em algorithm and alternatives are surveyed. For the alternative algorithms, simplified expressions for computing function values and derivatives are given. Likelihood ratio tests based on complete and incomplete data are related, and an example on using their relationship to improve the fit of a model is given.
Estimation of the parameters of the Rasch model, a one-parameter item response model, is considered when both the item parameters and the ability parameters are considered random quantities. It is assumed that the ite...
详细信息
Estimation of the parameters of the Rasch model, a one-parameter item response model, is considered when both the item parameters and the ability parameters are considered random quantities. It is assumed that the item parameters are drawn from a N(γ, τ2) distribution, and the abilities are drawn from a N(0, σ2) distribution. A variation of the em algorithm is used to find approximate maximum likelihood estimates of γ, τ, and σ. A second approach assumes that the difficulty parameters are drawn from a uniform distribution over part of the real line. Real and simulated data sets are discussed for illustration.
Missing data complicate the analysis of paired categorical data. This paper considers with the use of the em algorithm, the maximum likelihood estimation and likelihood ratio test for incomplete square tables with mis...
详细信息
Missing data complicate the analysis of paired categorical data. This paper considers with the use of the em algorithm, the maximum likelihood estimation and likelihood ratio test for incomplete square tables with missing data. An example involving the susceptibility of micro-organisms to antimicrobial drugs illustrates the procedure.
Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate ...
详细信息
Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the em algorithm. The procedure is illustrated by data from a mathematics test.
This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed,...
详细信息
This article describes a Bayesian framework for estimation in item response models, with two-stage prior distributions on both item and examinee populations. Strategies for point and interval estimation are discussed, and a general procedure based on the em algorithm is presented. Details are given for implementation under one-, two-, and three-parameter binary logistic IRT models. Novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest. Improved estimation in a moderately small sample is demonstrated with simulated data.
An Expectation-Maximization (em)-algorithm procedure is presented that extends Cheliak et al. (1983) method of maximum-likelihood estimation of mating system parameters of mixed mating system models. The extension per...
详细信息
An Expectation-Maximization (em)-algorithm procedure is presented that extends Cheliak et al. (1983) method of maximum-likelihood estimation of mating system parameters of mixed mating system models. The extension permits the estimation of the rate of self-fertilization (s) and allele frequencies (Pi) at loci in outcrossing pollen, at marker loci having recessive null alleles. The algorithm makes use of maternal and filial genotypic arrays obtained by the electrophoretic analysis of cohorts of progeny. The genotypes of maternal plants must be known. Explicit equations are given for cases when the genotype of the maternal gamete inherited by a seed can (gymnosperms) or cannot (angiosperms) be determined. The procedure can accommodate any number of codominant alleles, but only one recessive null allele at each locus. An example, using actual data from Pinus banksiana, is presented to illustrate the application of this em algorithm to the estimation of mating system parameters using marker loci having both codominant and recessive alleles.
The problem of missing data for categorical variables is examined from the perspective of modeling the mechanisms of nonresponse. Log-linear causal models, as formulated by Goodman, are studied for the relationship of...
详细信息
The problem of missing data for categorical variables is examined from the perspective of modeling the mechanisms of nonresponse. Log-linear causal models, as formulated by Goodman, are studied for the relationship of the survey variables to response; under some conditions several such models are estimable from the observed data. For nested patterns of nonresponse, a specific causal model represents exactly the assumption of ignorable response. Most causal models, however, imply nonignorable response mechanisms and yield alternative estimates for the distribution of the survey variables. [ABSTRACT FROM AUTHOR]
A new method is proposed for imputation of missing values in sample survey data. The procedure uses standard statistical methodology, permits a general specification of the nonresponse process, and does not impose spe...
详细信息
A new method is proposed for imputation of missing values in sample survey data. The procedure uses standard statistical methodology, permits a general specification of the nonresponse process, and does not impose specific model assumptions. Prior information from past similar surveys or from other sources may be incorporated in a routine manner. [ABSTRACT FROM AUTHOR]
作者：
Dinse, Gregg E.Senior Staff Fellow
Biometry and Risk Assessment Program National Institute of Envimnmental Health Sciences P.O. Box 12233 Research Triangle Park NC 27709
Age-specific prevalence and mortality estimators are important descriptors of disease development and the subsequent effects of a disease on longevity. Nonparametric maximum likelihood estimators for the prevalence an...
详细信息
Age-specific prevalence and mortality estimators are important descriptors of disease development and the subsequent effects of a disease on longevity. Nonparametric maximum likelihood estimators for the prevalence and mortality functions are available for the case in which incidental and fatal occurrences of a disease can always be distinguished. This article generalizes these methods to allow the role of a disease in causing death to be uncertain for a subset of the animals dying with the disease. The proposed analysis makes no assumptions about the degree of disease lethality. Data from sacrificed animals can be incorporated easily, although sacrifices are not necessary if a certain representativeness assumption holds. No restrictions are imposed on the distribution of survival times, but the prevalence function is held constant over time intervals for stabilization purposes. Variances are estimated by inverting the observed information matrix. An em algorithm simplifies the analysis when the prevalence function is constrained to be monotone or when cause of death is classified into ordered categories, according to how likely it was that the disease was responsible for death. The proposed methods are illustrated with some data on nonrenal vascular disease in female RFM mice. [ABSTRACT FROM AUTHOR]
Capture—recapture models assume that individuals in the population are captured one at a time and independently of each other. There are often situations, however, where individuals are captured in small clusters or ...
详细信息
Capture—recapture models assume that individuals in the population are captured one at a time and independently of each other. There are often situations, however, where individuals are captured in small clusters or groups. This article provides a model that allows individuals to be captured in groups; the em algorithm is used to estimate parameters in the model that include capture probabilities and the size of the population under study.
暂无评论