The Hazards of Transforming Infant Mortality with Logs: The General Pattern of 20th Century Infant Mortality Decline in 22 Countries

David Bishai, Johns Hopkins University
Marjorie Opuni-Akuamoa, Johns Hopkins University

Statisticians since Preston have approached the task of exploring factors associated with Infant Mortality Rate (IMR) decline by first applying a logarithmic transformation to IMR. This paper assesses how correct the log transform is by nesting the log transform within the more general Box Cox transformation. If lambda=1 the Box Cox transform amounts to a simple linear model. As lambda approaches 0 Box Cox converges to a logarithmic specification. Studying 22 country’s IMR time series for periods that typically stretch from late 1870 to late 1988 revealed the log transform is the best fit to IMR in only 4 of 22 countries. The assumption of linearity is best for 2 of 22. Further analysis shows that the logarithmic assumption can lead to substantial biases in estimating the coefficient of IMR on covariates like GDP per capita. Log-IMR is not generally the best transformation for the analysis of IMR.