Doubly robust estimation of multivariate fractional outcome means with multivalued treatments

Abstract.: This article suggests a doubly robust method of estimating potential outcome means for multivariate fractional outcomes when the treatment of interest is unconfounded and can take more than two values. The method involves maximizing a propensity score weighted multinomial quasi-log-likelihood function with a multinomial logit conditional mean. We show that this estimator, which we call weighted multivariate fractional logit (wmflogit), consistently estimates the potential outcome means if either the propensity score model or the conditional mean model is misspecified. Our simulations demonstrate this double robustness property for the case of shares generated using a Dirichlet distribution. Finally, we advocate for the use of wmflogit by applying it to estimate time-use shares of women participating in the Mexican conditional cash transfer program, Progresa, using Stata’s fmlogit command developed by Buis.