In this article, we proposed generalized method and developed algorithms for estimation of parameters and best model fit of log linear model for dimensional contingency tables. For purpose of this work, the method was used to provide estimates of parameters of log –linear model for four- dimensional contingency table. Parameters of higher dimensional tables can in like manner be estimated. In estimating these parameters and best model fit, computer programs in R were developed for the implementation of the algorithms. The iterative proportional fitting was used to estimate the parameters and goodness of fits of models of the log linear model. A real life data was used for illustration and the result obtained showed the best model fit for four dimensional contingency table is [BSG, BGA]. This showed that the best model fit must have sufficient evidence to fit the data without loss of information and must have the highest p-value and least likelihood ratio estimate.
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