All entries for Monday 08 August 2005
August 08, 2005
Note about IPW
(1) There is an example of how to use IPW in the notes from introduction-to-missing-data course. But the missing variable is a covariate, not a dependent variable. We can follow this example. Notice that the same variables are used in both the structure model and the missing-data model. Must check what Wooldridge has to say about this. Also, the coefficient of the missing covariate is still significant and of the same magnitude even though we delete some observations due to the missingness in this variable. However, the missingness of this covariate does affect the coefficient of other covariates such as "gender". This is quite unexpected.
(2) Tell Mark about the limitation of Heckman's approach which is that it wroks only with some special case of non-linear model (exponential). This is noted by Wooldridge (2002). However, nonparametric version of Heckman's approach may be intended as an relaxation of this limitation.
(3) Consider the IPW estimator in the light of Mark's comment. The model of Y given X can be non-linear as in the nonlinear LS case. The distribution of X has to satisfy certain conditions but we dont have to specify it ( again as in nonlinear LS case; look in Wooldridge (2002)). However, we have to model R and make MAR Assumption. Note that although the model of R has to be known, nonparamatric modelling is possible. Wooldridge suggests us to read the paper of Hirano, Imbens..