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Extensions of the Penalized Spline of Propensity Prediction Method of Imputation
Author(s) -
Zhang Guangyu,
Little Roderick
Publication year - 2009
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2008.01155.x
Subject(s) - imputation (statistics) , computer science , spline (mechanical) , data mining , statistics , econometrics , mathematics , machine learning , missing data , engineering , structural engineering
Summary Little and An (2004, Statistica Sinica 14 , 949–968) proposed a penalized spline of propensity prediction (PSPP) method of imputation of missing values that yields robust model‐based inference under the missing at random assumption. The propensity score for a missing variable is estimated and a regression model is fitted that includes the spline of the estimated logit propensity score as a covariate. The predicted unconditional mean of the missing variable has a double robustness (DR) property under misspecification of the imputation model. We show that a simplified version of PSPP, which does not center other regressors prior to including them in the prediction model, also has the DR property. We also propose two extensions of PSPP, namely, stratified PSPP and bivariate PSPP, that extend the DR property to inferences about conditional means. These extended PSPP methods are compared with the PSPP method and simple alternatives in a simulation study and applied to an online weight loss study conducted by Kaiser Permanente.