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Association-marginal modeling of multivariate categorical responses: A maximum likelihood approach

Association-marginal modeling of multivariate categorical responses: A maximum likelihood approach
Association-marginal modeling of multivariate categorical responses: A maximum likelihood approach
Generalized log-linear models can be used to describe the association structure and marginal distribution using association-marginal (AM) models, which are specially formulated generalized log-linear models that combine two models: an association (A) model, which describes the association among all responses; and a marginal (M) model, which describes the marginal distributions of the responses. Because the model's composite link function is nor required to be invertible, a large class of models can be entertained and model specification is typically straightforward.
We proposed a "mixed freedom/constraint" parameterization that exploits the special structure of an AM model. Using this parameterization, maximum likehood fitting is straightforward and typically feasible for large , sparse tables. When a parsimonious association model is used , the size of the fitting problem is substantially reduced, and some of the problems associated with sampling 0's are avoided. We compare the asymptotic behavior of AM model parameter estimators assuming product-multinomial and Poisson variances. We propose a conditional score atatistic for AM model assessment. The proposed maximum likelihhood methods are illustrated through an analysis of marijuana use data from five waves of the National Youth Service.
association model, composite link function, conditional score statistic, correlated responses, generalized loglinear model, marginal model, partitioning of chi-square
0162-1459
1161-1171
Lang, Joseph B.
851ea9d3-24dc-4d2c-8571-49271b9a1c0a
McDonald, John W.
9adae16e-e1e1-4ddf-bf4c-7231ee8c1c8e
Smith, Peter W.F.
961a01a3-bf4c-43ca-9599-5be4fd5d3940
Lang, Joseph B.
851ea9d3-24dc-4d2c-8571-49271b9a1c0a
McDonald, John W.
9adae16e-e1e1-4ddf-bf4c-7231ee8c1c8e
Smith, Peter W.F.
961a01a3-bf4c-43ca-9599-5be4fd5d3940

Lang, Joseph B., McDonald, John W. and Smith, Peter W.F. (1999) Association-marginal modeling of multivariate categorical responses: A maximum likelihood approach. Journal of the American Statistical Association, 94, 1161-1171.

Record type: Article

Abstract

Generalized log-linear models can be used to describe the association structure and marginal distribution using association-marginal (AM) models, which are specially formulated generalized log-linear models that combine two models: an association (A) model, which describes the association among all responses; and a marginal (M) model, which describes the marginal distributions of the responses. Because the model's composite link function is nor required to be invertible, a large class of models can be entertained and model specification is typically straightforward.
We proposed a "mixed freedom/constraint" parameterization that exploits the special structure of an AM model. Using this parameterization, maximum likehood fitting is straightforward and typically feasible for large , sparse tables. When a parsimonious association model is used , the size of the fitting problem is substantially reduced, and some of the problems associated with sampling 0's are avoided. We compare the asymptotic behavior of AM model parameter estimators assuming product-multinomial and Poisson variances. We propose a conditional score atatistic for AM model assessment. The proposed maximum likelihhood methods are illustrated through an analysis of marijuana use data from five waves of the National Youth Service.

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More information

Published date: 1999
Keywords: association model, composite link function, conditional score statistic, correlated responses, generalized loglinear model, marginal model, partitioning of chi-square

Identifiers

Local EPrints ID: 34317
URI: http://eprints.soton.ac.uk/id/eprint/34317
ISSN: 0162-1459
PURE UUID: 34ad5f47-343d-4a68-b04a-57d5b0e38944
ORCID for Peter W.F. Smith: ORCID iD orcid.org/0000-0003-4423-5410

Catalogue record

Date deposited: 02 Aug 2006
Last modified: 07 Oct 2020 01:34

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