OALibJ  Vol.2 No.1 , January 2015
On the Estimation of Parameters and Best Model Fits of Log Linear Model for Contingency Table
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 is Logmijk=μ+μC(i)+ μA(j)+ μB(k)+ μCA(ij)+ μAB(jk).
Cite this paper: Okoli, C. , Onyeagu, S. and Osuji, G. (2015) On the Estimation of Parameters and Best Model Fits of Log Linear Model for Contingency Table. Open Access Library Journal, 2, 1-11. doi: 10.4236/oalib.1101189.

[1]   Agresti, A. (2002) Categorical Data Analysis. 2nd Edition, John Wiley & Sons, Inc., New York, 320-332.

[2]   Knoke, D. and Burke, P.J. (1980) Log-Linear Models. Sage Publications, Inc., New Jersey, 8-17.

[3]   Akaike, H. (1987) Factor Analysis and AIC. Psychometrika, 52, 317-332.

[4]   Anderson, A.H. (1974) Multidimensional Contingency Tables. Scandinavean Journal of Statistics, 1, 115-127.

[5]   Green, J.A. (1988) Bayesian Model Comparison for the Order Restricted RC Association Model. Psychometrica, 74, 561-587.

[6]   Marascuilo, L. (1987) Log Linear Models: A Way to Study Main Effects and Interactions for Multidimensional with Categorical Data. Journal of America Psychological Associations, 34, 443-445.

[7]   Onder, M. and Adiguzel, E. (2010) Evaluation of Occupational Facilities among Underground Coal Mine Workers through Log-Linear Models. Industrial Health, 48, 872-878.

[8]   Olmus, H. (2012) Analysis of Traffic Accidents Caused by Drivers Using Log-Linear Models. Promet—Traffic & Transportation, 24, 495-504.

[9]   Shaffer, J.P. (1973) Defining and Testing Hypothesis in Three-Dimensional Contingency Tables. Psychological Bulletin, 79, 127-141.

[10]   Deming, W.E. and Stephen, F.F. (1940) On Least Square Adjustment of a Frequency Tables When the Expected Marginal Totals Are Known. Annals of Mathematical Statistics, 11, 427-444.

[11]   Pearson, K. (1990) On a Criterion That a Given System of Derivations from Probable in the Case of a Corrected System of Variables Is Such That It Can Be Reasonably Supposed to Have Arisen from a Random Sampling. Philosophical Magazine, 50, 157-175.

[12]   Wilks, S.S. (1938) The Large Distribution of the Likelihood Ratio for Testing Composite Hypotheses. Annals of Mathematical Statistics, 9, 60-62.

[13]   Kullback, S. (1959) Information Theory and Statistics. Wiley, New York.

[14]   Neyman, J. (1949) Contribution to the Theory of Chi-Square Test. Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability, 239-273.

[15]   Bishop, Y.M.M., et al. (1975) Discrete Multivariate Analysis: Theory and Practice. Mass MIT Press, Cambridge, 18-37.

[16]   Lawal, H.B. (2003) Categorical Data Analysis with SAS and SPSS Applications. Lawrence Erlbaum Associates, Inc., New Jersey, 83-128.

[17]   Raftery, A.E. (1986) A Note on Bayesian Factors for Log-Linear Contingency Table Models with Vague Prior Information. Journal of the Royal Statistical Society, Series B, 48, 249-250.