Log-linear Model for Describing the Relationship between Chromosomal Aberrations and Infertility Problems in Holstein-Friesian Cows

Log-linear analysis is widely applied in different scientific research areas, such as its use in veterinary medicine. The objective of this study is to model the relationship between chromosomal aberrations and some diseases in different groups of Holstein-Friesian cows arranged in a contingency table using log linear model. The variables under study were chromosomal aberrations (structural and numerical) and groups of animals with normal (control) and abnormal states. The SPSS statistical package was used for analyzing the data. The results showed that the saturated model significantly fitted the data. The likelihood ratio statistic was 421.023 with a P-value of 0.000, indicating that two-way interactions (group of animals × chromosomal aberrations; group of animals × disease status; and chromosomal aberrations × disease status) have a highly significant effect and are good predictors in the model. The three-way interaction (group of animals, chromosomal aberrations, and disease status) was not significant (P-value = 0.858), so it was eliminated. After backward elimination statistics, it is found that all two-way interactions (group of animals × chromosomal aberrations, group of animals × disease status and chromosomal aberrations × disease status interactions) should not be deleted from the model to avoid model distortion. The total diseased animals compared to total non-diseased ones are both more likely to be grouped where odds ratio = 1.45 with 95% CI (1.549 - 1.360) and be supposed to have chromosomal aberrations. This model was the best fit model because it showed all possible effects, including main effects, interaction effects between each two variables, and interaction effects between the three variables.