Relationships Between Full and Layer Models with Applications to Level Merging
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"Relationships Between Full and Laye..." refers background in this paper
...It is well known, from (4.9), that (see Bishop et al., 1975) 12 1 j = ln p 1 j − 1 I ∑ i ln p i j − 1 J ∑ r ln p 1 r + 1 IJ ∑ i r ln p i r (4.10) and similarly, 12 2 j = ln p 2 j − 1 I ∑ i ln p i j − 1 J ∑ r ln p 2 r + 1 IJ ∑ i r ln p i r (4.11) Using (4.10) and (4.11), 12 1 j = 12 2 j implies ln p…...
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...When, for example, Z = 1 r , the interaction parameter Z satisfies the following zero-sum property (for more details, see Bishop et al., 1975; Vellaisamy and Vijay, 2007):∑ ij Z iZ = 0 for all j ∈ 1 r (2.2) Similarly, let the log-linear model for the (n− 1)-dimensional table corresponding to Xn =…...
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1,817 citations
"Relationships Between Full and Laye..." refers background or methods in this paper
...The reduction depends on whether the direction and/or strength of interaction among the factors remains the same for both the full table and the reduced table (Simpson, 1951). For log-linear models, Whittemore (1978) and Vellaisamy and Vijay (2007) discussed this concept of collapsibility. If this reduction is not possible, that is, if Simpson’s paradox occurs, then we need to analyze the full (large) contingency table. When reduction of dimension is not possible, that is, when collapsibility conditions do not hold, and the number of levels of variables is large, then merging of levels also may reduce the analysis. Although, the merging of factor levels does not lead to reduction of dimension, it reduces the number of factor levels. Wermuth and Cox (1998) discussed factor level merging for ordinal variables based on interaction parameters of a new parametrization. For nominal data, Dellaportas and Tarantola (2005) extended their results for graphical log-linear models....
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...The reduction depends on whether the direction and/or strength of interaction among the factors remains the same for both the full table and the reduced table (Simpson, 1951). For log-linear models, Whittemore (1978) and Vellaisamy and Vijay (2007) discussed this concept of collapsibility....
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...The reduction depends on whether the direction and/or strength of interaction among the factors remains the same for both the full table and the reduced table (Simpson, 1951)....
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...The reduction depends on whether the direction and/or strength of interaction among the factors remains the same for both the full table and the reduced table (Simpson, 1951). For log-linear models, Whittemore (1978) and Vellaisamy and Vijay (2007) discussed this concept of collapsibility. If this reduction is not possible, that is, if Simpson’s paradox occurs, then we need to analyze the full (large) contingency table. When reduction of dimension is not possible, that is, when collapsibility conditions do not hold, and the number of levels of variables is large, then merging of levels also may reduce the analysis. Although, the merging of factor levels does not lead to reduction of dimension, it reduces the number of factor levels. Wermuth and Cox (1998) discussed factor level merging for ordinal variables based on interaction parameters of a new parametrization....
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...The reduction depends on whether the direction and/or strength of interaction among the factors remains the same for both the full table and the reduced table (Simpson, 1951). For log-linear models, Whittemore (1978) and Vellaisamy and Vijay (2007) discussed this concept of collapsibility. If this reduction is not possible, that is, if Simpson’s paradox occurs, then we need to analyze the full (large) contingency table. When reduction of dimension is not possible, that is, when collapsibility conditions do not hold, and the number of levels of variables is large, then merging of levels also may reduce the analysis. Although, the merging of factor levels does not lead to reduction of dimension, it reduces the number of factor levels. Wermuth and Cox (1998) discussed factor level merging for ordinal variables based on interaction parameters of a new parametrization. For nominal data, Dellaportas and Tarantola (2005) extended their results for graphical log-linear models. The results are again based on the same parametrization. We first note that the results obtained by Wermuth and Cox (1998) are valid for nominal variables if the chain independence condition is satisfied....
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1,717 citations
257 citations
"Relationships Between Full and Laye..." refers background in this paper
...Secondly, these are useful to interpret various hierarchical log-linear models (Santner and Duffy, 1989, p. 154)....
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154 citations
"Relationships Between Full and Laye..." refers methods in this paper
...For log-linear models, Whittemore (1978) and Vellaisamy and Vijay (2007) discussed this concept of collapsibility....
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