TITLE:
On the Estimation of Parameters and Best Model Fits of Log Linear Model for Contingency Table
AUTHORS:
Cecilia N. Okoli, Sidney I. Onyeagu, George A. Osuji
KEYWORDS:
Hierarchical Log Linear Models, Categorical Data, Contingency Table, Likelihood Ratio Test Statistic, AIC, BIC, Interaction
JOURNAL NAME:
Open Access Library Journal,
Vol.2 No.1,
January
14,
2015
ABSTRACT:
In this paper, we proposed the generalized method and algorithms developed for estimation of parameters and best model fits of log linear model for n-dimensional contingency table. For purpose of this work, the method was used to provide parameter estimates of log-linear model for three-dimensional contingency table. In estimating parameter estimates and best model fit, computer programs in R were developed for the implementation of the algorithms. The iterative proportional fitting procedure was used to find the parameter estimates and goodness of fits of the log linear model. Akaike information criteria (AIC) and Bayesian information criteria (BIC) were used to check the adequacy of the model of the best fit. Secondary data were used for illustration and the result obtained showed that the best model fit for three-dimensional contingency table had a generating class: [CA, AB]. This showed that the best model fit had sufficient evidence to fit the data without loss of information. This model also revealed that breed was independent of chick loss given age. The best model in harmony with the hierarchy principle isLogmijk＝μ＋μC(i)＋ μA(j)＋ μB(k)＋ μCA(ij)＋ μAB(jk).