Estimating log models: to transform or not to transform?

Abstract

Health economists often use log models to deal with skewed outcomes, such as health utilization or health expenditures. The literature provides a number of alternative estimation approaches for log models, including ordinary least-squares on ln(y) and generalized linear models. This study examines how well the alternative estimators behave econometrically in terms of bias and precision when the data are skewed or have other common data problems (heteroscedasticity, heavy tails, etc.). No single alternative is best under all conditions examined. The paper provides a straightforward algorithm for choosing among the alternative estimators. Even if the estimators considered are consistent, there can be major losses in precision from selecting a less appropriate estimator.

Association Between Modifiable Risk Factors and Pharmaceutical Expenditures Among Adults With Atherosclerotic Cardiovascular Disease in the United States: 2012–2013 Medical Expenditures Panel Survey

“…The 2‐part model consists of (1) a binary choice model fit for the probability of observing a positive‐versus‐zero annual expenditure on medications using the probit command and (2), contingent on having >$0 annual pharmaceutical expenditure, a generalized linear model (with γ distribution and a log link) was fitted for the >$0 expenditure to estimate the effect of MRFs on pharmaceutical expenditures 23, 24. To determine the appropriate distribution of the generalized linear model in the 2‐part model, we used the modified Park test 25. We used the margins postestimation command to determine the marginal and absolute pharmaceutical expenditures associated with the predictor variables in the 2‐part model.…”

Impact of morbid obesity on medical expenditures in adults

“…18 In the first part of the model, we used logistic regression to predict the probability of incurring any healthcare expenditure in 2000. For the second part, we used the algorithm of Manning and Mullahy 19 to identify the most appropriate model specifications to predict health expenditures for adults who incurred any healthcare expenditures in 2000. Expenditures were logtransformed to estimate an ordinary least squares equation and address the substantial kurtosis (43) exhibited in the residuals.…”

“…Heteroskedasticity was not evident, so expenditures were retransformed using the Duan nonparametric procedure to obtain predictions expressed in dollars. 18,19 We calculated overall annual per capita expenditures by multiplying each individual's probability of incurring any expense by his or her predicted expenditure. Using these same methods, we also calculated annual per capita expenditures for office-based visits, outpatient hospital visits, in-patient hospital visits, and prescription drugs.…”

A population‐based estimate of the economic burden of influenza in Peru, 2009–2010

“…The Kruskal–Wallis and Wilcoxon–Mann–Whitney tests were used as appropriate to determine group differences in the median direct, indirect, and total costs and number of days lost. We used generalized linear models with gamma family, log link, and cluster adjustment by participant to evaluate the association between costs and the aforementioned variable as previously described 18, 19. Variables that were significant ( P  < 0·05) in bivariate analysis were included in the multivariable analysis.…”