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Log-linear modeling using conditional log-linear structures

DSpace at IIT Bombay

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Title Log-linear modeling using conditional log-linear structures
 
Creator VELLAISAMY, P
VIJAY, V
 
Subject contingency-tables
categorical data
conditional log-linear model
graphical model
hierarchical model
interaction factor
log-linear model
mobius inversion
model combining
 
Description Analysis of large dimensional contingency tables is rather difficult. Fienberg and Kim (1999, Journal of American Statistical Association, 94, 229-239) studied the problem of combining conditional (on single variable) log-linear structures for graphical models to obtain partial information about the full graphical log-linear model. In this paper, we consider the general log-linear models and obtain explicit representation for the log-linear parameters of the full model based on that of conditional structures. As a consequence, we give conditions under which a particular log-linear parameter is present or not in the full model. Some of the main results of Fienberg and Kim follow from our results. The explicit relationships between full model and the conditional structures are also presented. The connections between conditional structures and the layer structures are pointed out. We investigate also the hierarchical nature of the full model, based on conditional structures. Kim (2006, Computational Statistics and Data Analysis, 50, 2044-2064) analyzed graphical log-linear models based on conditional log-linear structures, when a set of variables is conditioned. For this case, we employ the Mobius inversion technique to obtain the interaction parameters of the full log-linear model, and discuss their properties. The hierarchical nature of the full model is also studied based on conditional structures. This result could be effectively used for the model selection also. As applications of our results, we have discussed several typical examples, including a real-life example.
 
Publisher SPRINGER HEIDELBERG
 
Date 2011-08-30T04:53:47Z
2011-12-26T12:58:46Z
2011-12-27T05:49:16Z
2011-08-30T04:53:47Z
2011-12-26T12:58:46Z
2011-12-27T05:49:16Z
2009
 
Type Article
 
Identifier ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 61(2), 309-329
0020-3157
http://dx.doi.org/10.1007/s10463-007-0153-1
http://dspace.library.iitb.ac.in/xmlui/handle/10054/12198
http://hdl.handle.net/10054/12198
 
Language en