Frequency tables are examined in which some cells are not distinguishable. log-linear models are proposed for these tables which lead to likelihood equations closely related to those associated with log-linear models ...
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Frequency tables are examined in which some cells are not distinguishable. log-linear models are proposed for these tables which lead to likelihood equations closely related to those associated with log-linear models for conventional frequency tables. Just as in conventional tables, the maximum likelihood equations are shown to be the same under Poisson or multinomial sampling. Applications are made to the problem of estimation of gene frequencies from observed phenotype frequencies.
Estimation methods are proposed for the row, column and interaction effects in two-way contingency tables, the one-way table being treated as a special case. The methods are appropriate when the parameters are thought...
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Estimation methods are proposed for the row, column and interaction effects in two-way contingency tables, the one-way table being treated as a special case. The methods are appropriate when the parameters are thought a priori to be related to each other. The posterior estimates have the practical effects of smoothing the contingency table, and are valid even if some of the cell frequencies are zero. The main case treated is where particular assumptions of exchangeability are reasonable a priori for the unknown parameters. Some possible relaxations of the exchangeability assumptions are discussed. The methods are used to provide a numerical analysis of a mobility table originally due to Karl Pearson, and to measure the association between the occupations of fathers and sons in this table.
A general model is proposed for analysis of frequency tables. This model includes conventional log-linear models for complete and incomplete factorial tables and logit models for quantal response analysis. By use of c...
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A general model is proposed for analysis of frequency tables. This model includes conventional log-linear models for complete and incomplete factorial tables and logit models for quantal response analysis. By use of coordinate-free methods of linear algebra and differential calculus, complete minimal sufficient statistics and likelihood equations for the maximum likelihood estimate are derived. The maximum likelihood estimate is shown to be unique if it exists, and necessary and sufficient conditions are given for its existence.
log-linear models are extensively used to analyse categorical and “stimulus-response” data. This paper gives an iterative procedure for obtaining maximum likelihood estimates of cell frequencies and of the parameter...
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log-linear models are extensively used to analyse categorical and “stimulus-response” data. This paper gives an iterative procedure for obtaining maximum likelihood estimates of cell frequencies and of the parameters of a log-linear model in a multinomial experiment.
Raw language data dealing with frequency of letters, phonemes, words and categories were transformed to determine the goodness of fit of such obtained data to several Zipf‐type distributions: log percentage‐log rank...
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We derive Neyman's locally asymptotically most powerful test criterion to test a linear hypothesis, and in particular, obtain such criteria to test linear hypotheses in binomial and multinomial experiments. We als...
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We derive Neyman's locally asymptotically most powerful test criterion to test a linear hypothesis, and in particular, obtain such criteria to test linear hypotheses in binomial and multinomial experiments. We also discuss testing log-linear hypotheses in the parameters of a multinomial experiment, and give a simple criterion for testing the hypothesis of no second order interaction in ap×q×r(p, q, r, > 2) contingency table. Asymptotic tests of the hypotheses mentioned above are available in the literature, but the tests proposed in this paper are simple and are based on explicit optimality consideration.
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