Comparison of linear and exponential multivariate models for explaining national infant and child mortality

Product form multivariate regression models (multiplicative exponential) were developed with infant and child mortality as outcomes, and national economic, health, nutrition, education, and demographic statistics as predictor variables. The models were applied to data from 129 countries, resulting in R-square values for the product form models of infants and child mortality of 0.77 and 0.80. For comparison purposes, more conventional sum form models (additive linear) were also estimated, and yielded R-square values (0.22, 0.29) markedly lower than the product form models. The product form models also had a much more uniform distribution of residuals and provided improved model fit across the different categories of nations. An inherent advantage to the product form models is that they did not predict negative mortality rates, in contrast to the sum form models which did predict negative mortalities for some of the more developed nations. Using a product form model, the correlation between physicians per capita and infant mortality was shown to be negative rather than positive--thus correcting for an anomaly seen in previous studies which showed a positive correlation between physicians per capita and infant mortality.