I've read papers comparing them, but never seen a study that used them together. Is this done? Why or why not? Suppose you use ANCOVA to analyze a reduced sample of matched pairs generated using propensity scores (assuming the propensity scores are estimated from the complete set of confounders X that jointly effect the outcome variable Y and the treatment variable T). Suppose the model has T (considered as a grouping variable for ANCOVA) along with covariate Z predicting the continuous variable Y. Will estimates of the effect size for the treatment and the regression coefficient for Z be biased if Z is included in the set X or if Z and Y are not independent? I would love to find articles that discuss ideas along these lines.

  • $\begingroup$ I don't think that ANCOVA is the tool when you've used matching. It's worth examining whether matching is the best strategy. Have you discarded any data? Is the matching algorithm independent of the order of presentation of the observations? Is the matching fine enough to avoid residual confounding? There are several reasons to entertain covariate adjustment for propensity score instead (e.g., by including in the model a restricted cubic spline function of the logit of propensity). $\endgroup$ – Frank Harrell Aug 24 '11 at 12:33
  • $\begingroup$ What made you do matching, thereby discarding observations and requiring a choice of (1) how you sorted the original dataset and (2) the matching algorithm? $\endgroup$ – Frank Harrell Sep 23 '11 at 14:02

I do no know of a reference that discusses ANCOVA, but the following paper discusses regression modeling applied to matched data:

Ho, Daniel, Kosuke Imai, Gary King, and Elizabeth Stuart. "Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference." Political Analysis 15 (2007): 199-236.

Chapters 9 and (more particularly) 10 of Gelman & Hill also discuss the topic.

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