Suppose a two-way experiment with interaction. Is it correct to estimate the missing values by OLS, input those values in the data (fill the blanks) and now perform a polynomial (or any kind of) regression? Do you have some literature to suggest about this subject?
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$\begingroup$ Why is the data missing? Is it random, or is there a underlying pattern? $\endgroup$– RepmatCommented Jul 5, 2015 at 15:00
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$\begingroup$ Let's consider them MCAR $\endgroup$– WalterCommented Jul 5, 2015 at 15:15
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$\begingroup$ See cran.r-project.org/web/packages/StatMatch/index.html $\endgroup$– user227710Commented Jul 5, 2015 at 19:12
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Imputation of multiple data sets is better. The approach you suggest would only provide a single data set whose imputed values would be strongly determined by the particular data sample you have. Multiple imputation (also see this page) stochastically generates a number of separate complete data sets, which are then analyzed separately by the method of interest, like polynomial regression as you suggest. The R package mice is one source of the necessary tools, including a wide variety of ways to structure the imputations.
