Comparison of Probit and Logit Models for Binary Response Variable with Applications to Birth Data in South-Western, Nigeria

摘要

Logit and Probit models are members of generalized linear models that are widely used to estimate the functional relationship between binary response variable and predictors. Comparison of regression models for binary response variable could be complicated by the choice of link function. The focus of this study is to determine which of the models will perform better in fitting birth data. The second focus of this study is to also make a comparative study between Yoruba women in Igbo-Ora known for high rate of multiple births and Yoruba women in Ogbomoso with sparse record of multiple birth, with the aim of determining factors that are responsible for the high rate of multiple births among the Igbo-Ora women in South-Western Nigeria. Theoretical derivations of the two models were given. Binomial regression model was fitted to the birth data with logit and probit links which resulted into logit and probit regression models respectively. The pchisq value of both the logit and the probit models were in excess of 0.05, an indication that the models fitted the birth data well. Due to simplicity of interpretation of results for Logit model, it was focused on for interpretation. The predictors considered in the models were age, religion, parity, tribe and the interaction term between age and religion of women. The results showed that the logit of having multiple births was positively related to tribe and the interaction term age*religion , but was found to be negatively related to women’s age, religion and their parity . It was also discovered that the odds of having multiple births by Yoruba women in Igbo-Ora is about three times higher than Yoruba women in Ogbomoso. The marked difference between the odds of having multiple births by women in Igbo-Ora and women in Ogbomoso is an indication that an inherent factor was responsible for the high rate of multiple births in Igbo-Ora. The high rate of multiple births could be ascribed to their regular consumption of Ilasa and Amala or due to a hereditary factor peculiar to Igbo-Ora women. Religion of women was only marginally significant, in the presence of other predictors. Graphical and numerical diagnostic evaluations of the models conducted revealed that the models were good summary of the birth data. Criterion-based variable selection procedure was also considered in selecting predictors that produce the most parsimonious models for both logit and probit models. Based on the AIC values, the final logit and the final probit regression models contained only tribe variable as the predictor for the most parsimonious model. It was difficult to distinguish between the logit and the probit models on the Receiver Operating Characteristic (ROC) curve, showing that the two models are quite similar, though the logit appeared to yield better performance than the probit model. This is an indication that the logit model has slight better prediction than the probit model. The choice of link function between logit and probit therefore depends on the data generating the process; and largely the choice is subjective.