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Some statistical properties of the G...

Kakuma, Tatsuyuki.

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Some statistical properties of the GOM model: A fuzzy classification method for multivariate discrete data.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Some statistical properties of the GOM model: A fuzzy classification method for multivariate discrete data./
Author:	Kakuma, Tatsuyuki.
Description:	85 p.
Notes:	Source: Dissertation Abstracts International, Volume: 51-08, Section: B, page: 3651.
Contained By:	Dissertation Abstracts International51-08B.
Subject:	Biology, Biostatistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9101271

Some statistical properties of the GOM model: A fuzzy classification method for multivariate discrete data.
Kakuma, Tatsuyuki.

Some statistical properties of the GOM model: A fuzzy classification method for multivariate discrete data. - 85 p.

Source: Dissertation Abstracts International, Volume: 51-08, Section: B, page: 3651.

Thesis (Ph.D.)--Yale University, 1990.

Information collected in large scale epidemiological and public health surveys often yields a form of multivariate discrete data which may be generated from a heterogeneous population. A class of latent variable models is frequently used to analyze such data.Subjects--Topical Terms:

1018416
Biology, Biostatistics.

Some statistical properties of the GOM model: A fuzzy classification method for multivariate discrete data.
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100 1 $a Kakuma, Tatsuyuki. $3 1254586
245 1 0 $a Some statistical properties of the GOM model: A fuzzy classification method for multivariate discrete data.
300 $a 85 p.
500 $a Source: Dissertation Abstracts International, Volume: 51-08, Section: B, page: 3651.
502 $a Thesis (Ph.D.)--Yale University, 1990.
520 $a Information collected in large scale epidemiological and public health surveys often yields a form of multivariate discrete data which may be generated from a heterogeneous population. A class of latent variable models is frequently used to analyze such data.
520 $a A new statistical model, called 'Grade of Membership' model (henceforth GOM model), first introduced by Woodbury et al. (1974, 1978), is examined. The GOM model has already been applied to problems of medical classification (Woodbury and Manton (1982), Swartz et al. (1987), Davidson et al. (1988)), and to the study of health status of the elderly by Berkman, Singer and Manton (1988). However, the model lacks full theoretical justification. Singer (1989) was one of the first investigators to lay the theoretical foundation for the GOM model. In this thesis, the theoretical attributes of the GOM model are more fully investigated.
520 $a The conceptual foundations of the GOM model are given by defining crisp and fuzzy classifications, and showing that the GOM model is a fuzzy classification model. Maximum likelihood estimation of the conditional likelihood of this model is obtained with the EM algorithm, and an alternative parameterization of the GOM score is suggested. The unconditional likelihood estimation is also examined. By specifying a form of parametric density function for the GOM score, it is shown that a set of moments from the unconditional likelihood determines this GOM score density function uniquely. With a 2 x 2 contingency table under the condition of extreme admissible profile, the two maximum likelihood estimation methods are compared by the Kullback-Leibler information measure. A goodness of fit test for the marginal probability distribution is developed via the Monte Carlo method. To calculate appropriate degrees of freedom for the test, the approach of Blackman and Tukey (1958), who introduced the concept of the "equivalent number of degrees of freedom", is used. The equivalent number of degrees of freedom are obtained using the Monte Carlo method.
590 $a School code: 0265.
650 4 $a Biology, Biostatistics. $3 1018416
650 4 $a Engineering, Biomedical. $3 1017684
650 4 $a Statistics. $3 517247
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710 2 0 $a Yale University. $3 515640
773 0 $t Dissertation Abstracts International $g 51-08B.
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791 $a Ph.D.
792 $a 1990
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9101271