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. N. , Onyeagu, S. I. and Osuji, G. A. (2015). On the Estimation of Parameters and Best Model Fits of Log Linear Model for Contingency Table. Open Access Library Journal, 2, e1189. doi: http://dx.doi.org/10.4236/oalib.1101189.
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.
Onder, M. and Adiguzel, E. (2010) Evaluation of Occupational Facilities among
Underground Coal Mine Workers through Log-Linear Models. Industrial
Health, 48,
872-878. http://dx.doi.org/10.2486/indhealth.MS1136
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. http://dx.doi.org/10.1214/aoms/1177731829
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. http://dx.doi.org/10.1080/14786440009463897
Wilks,
S.S. (1938) The Large
Distribution of the Likelihood Ratio for
Testing Composite Hypotheses. Annals of Mathematical Statistics, 9,
60-62. http://dx.doi.org/10.1214/aoms/1177732360
Neyman, J. (1949) Contribution to the Theory of Chi-Square Test. Proceedings of the First Berkeley Symposium
on Mathematical Statistics and Probability, 239-273.
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.