Repeated count data showing overdispersion are commonly analysed by using a Poisson model with varying intensity parameter. resulting in a mixed model. A mixed model with a gamma distribution for the Poisson parameter...
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Repeated count data showing overdispersion are commonly analysed by using a Poisson model with varying intensity parameter. resulting in a mixed model. A mixed model with a gamma distribution for the Poisson parameter does not adequately fit a data set on 721 children's spelling errors. An alternative approach is a latent class or mixture model in which the distribution of the intensity parameter is a step function. This gives a solution with many classes that is difficult to interpret. A combination of the two models, resulting in a mixture model with two gamma distributions, however, fits the data very well. Moreover, it yields a substantively satisfactory interpretation: two heterogeneous classes of 'good' and 'poor' spelling children can be identified. Therefore, mixture models for the analysis of overdispersed repeated count data are proposed, where the counts have independent Poisson distributions conditional on the Poisson parameter whose distribution is a mixture of gamma distributions. Combining marginal maximum likelihood methods and the em algorithm leads to straightforward estimations of the models, for which goodness-of-fit tests are also presented.
A full-information item factor analysis model for multidimensional polytomously scored item response data is developed as an extension of previous work by several authors. The model is expressed both in factor-analyti...
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A full-information item factor analysis model for multidimensional polytomously scored item response data is developed as an extension of previous work by several authors. The model is expressed both in factor-analytic and item response theory parameters. Reckase's multidimensional parameters for the model also are discussed as well as the related geometry. An em algorithm for estimation of the model parameters is presented and results of the analysis of item response data by a computer program incorporating this algorithm are presented.
A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized line...
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A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an em algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.
In the design of common-item equating, two groups of examinees are administered separate test forms, and each test form contains a common subset of items. We consider test equating under this situation as an incomplet...
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In the design of common-item equating, two groups of examinees are administered separate test forms, and each test form contains a common subset of items. We consider test equating under this situation as an incomplete data problem-that is, examinees have observed scores on one test form and missing scores on the other. Through the use of statistical data-imputation techniques, the missing scores can be replaced by reasonable estimates, and consequently the forms may be directly equated as if both forms were administered to both groups. In this paper we discuss different data-imputation techniques that are useful for equipercentile equating;we also use empirical data to evaluate the accuracy of these techniques as compared with chained equipercentile equating.
作者：
MARIS, EUNIV NIJMEGEN
NIJMEGEN INST COGNIT & INFORMATDEPT MATH PSYCHOLPOB 91046500 HE NIJMEGENNETHERLANDS
In this paper, some psychometric models will be presented that belong to the larger class of Intent response models (LRMs). First, LRMs are introduced by means of an application in the field of componential item respo...
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In this paper, some psychometric models will be presented that belong to the larger class of Intent response models (LRMs). First, LRMs are introduced by means of an application in the field of componential item response theory (embretson, 1980, 1984). Second, a general definition of LRMs (not specific for the psychometric subclass) is given. Third, some more psychometric LRMs, and examples of how they can be applied, are presented. Fourth, a method for obtaining maximum likelihood (ML) and some maximum a posteriori (MAP) estimates of the parameters of LRMs is presented. This method is then applied to the conjunctive Rasch model. Fifth and last, an application of the conjunctive Rasch model is presented. This model was applied to responses to typical verbal ability items (open synonym items).
An em algorithm was used to analyse data arising from non-linear mixed-effects models. The fixed parameters were determined by maximum likelihood using simplex minimization, and the random effects were estimated using...
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An em algorithm was used to analyse data arising from non-linear mixed-effects models. The fixed parameters were determined by maximum likelihood using simplex minimization, and the random effects were estimated using the em algorithm after linearization with respect to the random effects. Applications to a simple linear model and population pharmacokinetics are described. The use of posterior parameter estimates to investigate covariate relationships is briefly described. The implementation of the estimation-maximization (em) algorithm described here has proved in practice to be robust but slow. We intend to use a Newton-Raphson minimization routine in place of the simplex method to hasten convergence. The alternative linearization of the non-linear mixed effects model suggested by Lindstrom and Bates (Biometrics 46 (1990) 673-687) is much more unstable than the usual linearization, especially during the initial iterations. In the case of indomethacin the two linearizations produced very similar results. The individual posterior parameter estimates provided by the program are very useful for the detection of covariate relationships in population pharmacokinetic studies. In addition, the posterior means can be used in the estimation of pharmacokinetic-pharmacodynamic relationships from sparse pharmacokinetic data where individual modelling is impossible.
The maximum likelihood estimation of parameters of the Poisson binomial distribution, based on a sample with exact and grouped observations, is considered by applying the em algorithm (Dempster et al., 1977). The resu...
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The maximum likelihood estimation of parameters of the Poisson binomial distribution, based on a sample with exact and grouped observations, is considered by applying the em algorithm (Dempster et al., 1977). The results of Louis (1982) are used in obtaining the observed information matrix and accelerating the convergence of the em algorithm substantially. The maximum likelihood estimation from samples consisting entirely of complete (Sprott, 1958) or grouped observations are treated as special cases of the estimation problem mentioned above. A brief account is given for the implementation of the em algorithm when the sampling distribution is the Neyman Type A since the latter is a limiting form of the Poisson binomial. Numerical examples based on real data are included.
We describe two algorithms for computing the minimum χ^2 estimator and the minimum modified χ^2 estimator for frequency tables sampled under complex sampling schemes. The sampling scheme may include sub-samples in w...
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We describe two algorithms for computing the minimum χ^2 estimator and the minimum modified χ^2 estimator for frequency tables sampled under complex sampling schemes. The sampling scheme may include sub-samples in which only some of the original cells are observed and some sub-sets of original cells are grouped together.
The critical step in the drive toward an independent Slovenia was the plebiscite held in December 1990, at which the citizens of Slovenia voted overwhelmingly in favor of a sovereign and independent state. The Sloveni...
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The critical step in the drive toward an independent Slovenia was the plebiscite held in December 1990, at which the citizens of Slovenia voted overwhelmingly in favor of a sovereign and independent state. The Slovenian Public Opinion (SPO) survey of November/December 1990 was used by the government of Slovenia to prepare for the plebiscite. Because the plebiscite counted as “YES voters” only those voters who attended and voted for independence (nonvoters counted as “NO voters”), “Don't Know” survey responses can be thought of as missing data—the true intention of the voter is unknown but must be either “YES” or “NO.” An analysis of the survey data under the missing-at-random assumption for the missing responses provides remarkably accurate estimates of the eventual plebiscite outcome, substantially better than ad hoc methods and a nonignorable model that allows nonresponse to depend on the intended vote.
A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Est...
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A new theoretical point of view is discussed in the framework of density estimation. The multivariate true density, viewed as a prior or penalizing factor in a Bayesian framework, is modelled by a Gibbs potential. Estimating the density consists in maximizing the posterior. For efficiency of time, we are interested in an approximate estimator f̂ = Bπ of the true density f , where B is a stochastic operator and π is the raw histogram. Then, we investigate the discrimination problem, introducing an adaptive bandwidth depending on the k nearest neighbours and chosen to optimize the cross-validation criterion. Our final classification algorithm referred to as APML for approximate penalized maximum likelihood compares favourably in terms of error rate and time efficiency with other algorithms tested, including multinormal, nearest neighbour and convex hull classifiers.
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