This paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data. These choice models are derived by s...
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This paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data. These choice models are derived by specifying elements of the choice process at the individual level. Probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior. Due to the explicit consideration of random effect sources, the choice models are parsimonious and readily interpretable. An easy to implement em algorithm is presented for parameter estimation. Two applications illustrate the proposed approach.
A probabilistic choice model is developed for paired comparisons data about psychophysical stimuli. The model is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured o...
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A probabilistic choice model is developed for paired comparisons data about psychophysical stimuli. The model is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured on a small number of physical variables. The utility of a stimulus is related to its values on the physical variables either by means of an additive univariate spline model or by means of multivariate spline model. In the additive univariate spline model, a separate univariate spline transformation is estimated for each physical dimension and the utility of a stimulus is assumed to be an additive combination of these transformed values. In the multivariate spline model, the utility of a stimulus is assumed to be a general multivariate spline function in the physical variables. The use of B splines for estimating the transformation functions is discussed and it is shown how B splines can be generalized to the multivariate case by using as basis functions tensor products of the univariate basis functions. A maximum likelihood estimation procedure for the Thurstone Case V model with spline transformation is described and applied for illustrative purposes to various artificial and real data sets. Finally, the model is extended using a latent class approach to the case where there are unreplicated paired comparisons data from a relatively large number of subjects drawn from a heterogeneous population. An em algorithm for estimating the parameters in this extended model is outlined and illustrated on some real data.
Copas's model for contamination in binary regression structures is translated into the sampling paradigm approach that is familiar in discriminant analysis. A parallel treatment of the two models is afforded by a ...
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Copas's model for contamination in binary regression structures is translated into the sampling paradigm approach that is familiar in discriminant analysis. A parallel treatment of the two models is afforded by a common expression of the log-likelihood. Resistant parameter estimation is discussed for prevalence rates and for parameters, including discriminant functions, within component distributions. The methods are illustrated on a breast cancer example.
Presents a new algorithm for efficient estimation of order-restricted parameters of correspondence models for two-way contingency tables. Attention to correspondence analysis (CA) of contingency tables; Negative assoc...
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Presents a new algorithm for efficient estimation of order-restricted parameters of correspondence models for two-way contingency tables. Attention to correspondence analysis (CA) of contingency tables; Negative association between the underling variables; Incompatibility of obtained order between the estimated scores with the inherent order of the categories.
The following problem arises in Computer vision, diagnostic medical imaging, and remote sensing: At each pixel in an image a vector of observations is measured, and the distribution of these measurements is approximat...
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The following problem arises in Computer vision, diagnostic medical imaging, and remote sensing: At each pixel in an image a vector of observations is measured, and the distribution of these measurements is approximated by a mixture model. The goal is to estimate the mixing proportions of the classes by pixel in the image together with any unknown parameters in the latent distributions. In many problems of this type, it is appropriate to incorporate constraints on mixing proportions. This article deals with spatial smoothness constraints, which have been found useful in analyzing sequences of emission tomography images. An estimation methodology using penalized likelihood with multiple smoothing parameters is proposed. Numerical methods for implementing this methodology are developed. This includes an importance sampling technique for approximating the effective degrees of freedom of the solution. The methodology is illustrated with an application to the analysis of a dynamic emission tomography study using aC11-labeled thymidine tracer. Some simulations motivated by this example are also presented.
A longstanding difficulty in multivariate statistics is identifying and evaluating nonnormal data structures in high dimensions with high statistical efficiency and low search effort. Here the possibilities of using s...
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A longstanding difficulty in multivariate statistics is identifying and evaluating nonnormal data structures in high dimensions with high statistical efficiency and low search effort. Here the possibilities of using sample moments to identify mixtures of multivariate normals are investigated. A particular system of moment equations is devised and then shown to be one that identifies the true mixing distribution, with some limitations (indicated in the text), and thus provides consistent estimates. Moreover, the estimates are shown to be quickly calculated in any dimension and to be highly efficient in the sense of being close to the values of the parameters that maximize the likelihood function. This is shown by simulation and the application of the method to Fisher's iris data. While establishing these results, we discuss certain limitations associated with moment methods with regard to uniqueness and equivariance and explain how we addressed these problems.
In many practical situations dealing with parallel systems, the failure times of the components are not observable unless that is the last one resulting in the failure of the system. Based on observation on the life t...
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In many practical situations dealing with parallel systems, the failure times of the components are not observable unless that is the last one resulting in the failure of the system. Based on observation on the life time of the system, nonparametric estimation of the life time distributions of the components is considered. Dealing with a parallel system with two components, a competing risks framework is developed and an algorithm of the em type for maximum likelihood estimation is obtained. The method is illustrated with a simulated data set.
A three-state illness–death model provides a useful way to represent data from rodent tumorigenicity experiments. Some of the earliest proposals use fully parametric models based on, for example, Weibull distribution...
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A three-state illness–death model provides a useful way to represent data from rodent tumorigenicity experiments. Some of the earliest proposals use fully parametric models based on, for example, Weibull distributional assumptions. Recently, nonparametric versions of this model have been proposed, but these generally require large data sets with frequent interim sacrifices to yield stable estimates. As a compromise between these extremes, others have considered semiparametric models. In this paper, we develop a model that assumes a multiplicative relationship between death rates with and without tumour and a piecewise exponential model for the base-line transition rates. The model can be fitted with information from a single sacrifice. An em algorithm provides a useful way to fit the model, since the likelihood corresponds to that from a standard piecewise exponential survival model when time to tumour onset is known. We discuss the relationship between the piecewise exponential model and other recent proposals and illustrate the method with data from two carcinogenicity studies.
A maximum likelihood method is used for the estimation of the proportion of gene mutations that are selectively neutral. Random samples, including both neutral and deleterious alleles, are simulated by computer, and t...
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A maximum likelihood method is used for the estimation of the proportion of gene mutations that are selectively neutral. Random samples, including both neutral and deleterious alleles, are simulated by computer, and the allele frequencies are determined. The estimation method is tried out on each sample, as if the latter were for a single locus. Assuming that it is not known which alleles are neutral in the sample (as would often be the case in practice), the estimation method usually leads to the erroneous conclusion that all alleles are neutral at that locus. When it is known which alleles are neutral in the sample (and such is the case for the simulated data), the method attempts to estimate the rates of neutral and deleterious mutations and the selective disadvantage of the latter class. The estimates are somewhat biased and have relatively high variances. The results are compared, were possible, with those for an estimation method introduced by Kimura. The method is not, here, extended to samples from many independent loci. Presumably, if such samples were available and could all be assumed to be homogeneous with respect to the mutation and selection parameters, then the maximum likelihood estimation method would achieve better results.
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