Doubly robust estimation of multivariate fractional outcome means with multivalued treatments
提出一种双重稳健方法估计多值处理下多元分数结果（如时间分配份额）的潜在结果均值，通过加权多元分数Logit模型实现，即使倾向得分或条件均值模型之一设定错误仍能一致估计。
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.