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LINEAR MODELS ANALYSIS OF INCOMPLETE MULTIVARIATE CATEGORICAL DATA
, 1972
"... This research deals with experiments or surveys producing multivariate categorical data which is incomplete, in the sense that not all variables of interest are measured on every subject or element of the sample. For the most part, incompleteness is taken to arise by design, rather than by random fa ..."
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This research deals with experiments or surveys producing multivariate categorical data which is incomplete, in the sense that not all variables of interest are measured on every subject or element of the sample. For the most part, incompleteness is taken to arise by design, rather than by random failure of the measurement process. In these circumstances, one can often assume that counts derived from appropriate disjoint subsets of the data arise from independent multinomial distributions with linearly related parameters. Best asymptotically normal oJ estimates of these parameters may be determined by maximizing the likelihood of the observations or by minimizing Pearson'sx 2, Neyman's X~,
The Admissibility Of The Maximum Likelihood Estimator For Decomposable LogLinear Interaction Models For Contingency Tables
, 1998
"... It is well known that for certain loglinear interaction models for contingency tables, i.e. those that are decomposable, the maximum likelihood estimator can be found explicitly. In this note we will show that in such cases this estimator is admissible. The proof is based on a stepwise Bayes argume ..."
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It is well known that for certain loglinear interaction models for contingency tables, i.e. those that are decomposable, the maximum likelihood estimator can be found explicitly. In this note we will show that in such cases this estimator is admissible. The proof is based on a stepwise Bayes argument and is a generalization of a proof of the admissibility of the maximum likelihood estimator for the usual unconstrained multinomial model. It is then shown that this result is a special case of a result for discrete exponential families. 1. INTRODUCTION In loglinear models for contingency tables maximum likelihood is the standard method of estimation. For certain hierarchical models, called decomposable models, (see Goodman (1970, 1971) and Andersen (1974)) it was shown in Haberman (1974) that the maximum likelihood estimator could be found explicitly. Darroch, Lauritzen and Speed (1980) considered a certain class of graphical models which contains the family of hierarchical models. T...
Office: GriffinFloyd 204
"... reserve for this course at the Science library) This course surveys methods for the analysis of categorical response variables. The main subject areas covered are descriptive and inferential statistics for twoway and threeway contingency tables, generalized linear models for discrete responses, bi ..."
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reserve for this course at the Science library) This course surveys methods for the analysis of categorical response variables. The main subject areas covered are descriptive and inferential statistics for twoway and threeway contingency tables, generalized linear models for discrete responses, binary regression models (emphasizing logistic regression), models for multicategory responses, loglinear models for contingency tables, matched pairs, and maximum likelihood inference for categorical response data.
ESTIMATED PARAMETERS FROM CONTINGENCY TABLE LOGLINEAR MODELS
"... This paper presents a matrix formulation for loglinear model analysis of contingency tables. Both weighted least squares estimators and maximum likelihood estimators are considered in this fr~ework with results being given for their corresponding covariance matrix atructures. Moreover, a general an ..."
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This paper presents a matrix formulation for loglinear model analysis of contingency tables. Both weighted least squares estimators and maximum likelihood estimators are considered in this fr~ework with results being given for their corresponding covariance matrix atructures. Moreover, a general analytical strategy is presented for the simultaneous use of these two estimation procedures in a manner which emphasizes their respective strengths. Four examples illustrating the application of this methodology are then provided.
Supplemented Margins Including Applications to Mixed Models.
, 1970
"... The general linear model approach for the analysis of categorical data is extended to the case of supplemental data. In the usual case, each individual i ~ classified according to each of the d dimensions of the corresponding contingency table. With supplementation, there is additional information o ..."
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The general linear model approach for the analysis of categorical data is extended to the case of supplemental data. In the usual case, each individual i ~ classified according to each of the d dimensions of the corresponding contingency table. With supplementation, there is additional information on d ' < d dimensions for a random sample selected from the same homogeneous population. This situation might arise if there was special interest in only certain of the responses and/or possibly for reasons of economy and is distinctly different from the empty cell problem. Starting with the simplest case, maximum likelihood and iterated weighted least squares estimates are obtained for the basic parameters for 2 x 2 tables with one margin supplemented. The maximum likelihood estimates are unbiased and have the same asymptotic covariance matrix
SURVIVAL ANALYSIS \H'l1I
, 1982
"... by K. L.Q. READ · r • R.R. HARRIS"', A.A. NOURA t and DENNIS GILLINGS';'i' SUMMARY A general approach to the analysis of survival data is developed, based on the fitting of loglinear and similar models to multidimensional contingency tables formed from such data by suitable categorisation of the ti ..."
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by K. L.Q. READ · r • R.R. HARRIS"', A.A. NOURA t and DENNIS GILLINGS';'i' SUMMARY A general approach to the analysis of survival data is developed, based on the fitting of loglinear and similar models to multidimensional contingency tables formed from such data by suitable categorisation of the time domain and the covariates (including treatment). Consideration is given to nonproportional hazards, timedependent or sequentially realised covariates, alternative transformations of the survivor function and subsets of the parameters which may be involved nonlinearly. The work is presented in terms of weighted least squares estimation, though this is not necessary to the underlying formulation and other methods, of fitting may be adopted. Some keywonds: Survival analysis, categorical data, loglinear models, conplementary loglog transforn~tion, timerelated covariates, weiehted least squares. p 'I
Exam Date
"... Topics: This course surveys methods for the analysis of categorical response variables, from the maximum likelihood (frequentist) perspective. The main subject areas covered are descriptive and inferential statistics for twoway and threeway contingency tables, generalized linear models for discret ..."
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Topics: This course surveys methods for the analysis of categorical response variables, from the maximum likelihood (frequentist) perspective. The main subject areas covered are descriptive and inferential statistics for twoway and threeway contingency tables, generalized linear models for discrete responses, binary regression models (emphasizing logistic regression), multicategory logit models for nominal and ordinal responses, loglinear models for contingency tables, and matched pairs. Instructor: Alan Agresti (I am an emeritus faculty member at UF but I am teaching here parttime during spring semester 2010.) Office: GriffinFloyd 204
“British, American, and BritishAmerican Social Mobility: Intergenerational Occupational Change Among Migrants and NonMigrants in the Late 19th Century”
, 2010
"... The occupational mobility experienced by immigrants in the nineteenth century has been difficult to assess because of a lack of both information on their premigration occupations and information on a comparable group of individuals who were observed at the same origin but did not migrate. We take a ..."
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The occupational mobility experienced by immigrants in the nineteenth century has been difficult to assess because of a lack of both information on their premigration occupations and information on a comparable group of individuals who were observed at the same origin but did not migrate. We take advantage of new samples of Americans linked 18601880 & 18801900, British linked 186181 & 18811901, and BritishAmerican migrants linked 18611880 & 18811900 to compare the experience of migrants from Britain to the U.S. to both those who remained in Britain and those who were always located in the U.S. We assess the selectivity of migration and explore several of the mechanisms through which the intergenerational mobility of migrants exceeded that of both those they left behind in Britain and those they joined in the U.S.