in principle I agree with Rod.
However, I think in using MI one should be aware, that
measure for the predictive accuracy like R-squared should be handeled with greater care
than regression parameter estimates.
The reason for this is, that measures of predictive accuracy are more sensitive to the choice of the
model we use (implicitely) in generating the imputations than regression parameters. If we apply
MI to regression models (with missing values in the covariates) many people use procedures, which
assume that the regression model is correctly specified (and negelecting the general advice, that
the model we using to generate the MIs should be more general than the model we would like to
analyse). So it will happen frequently, that if we have for example in reality a quadratic model,
we draw imputations still in a way assuming a linear model. This is no big problem, as long
as we look on the regression parameters, as one does not introduce bias in the estimation this
way (although confidence intervals will be too optimistic). However, with respect to measures of
predictive accuracy we will introduce a bias, because the imputations make the data as looking
like the model.
So whenever one would like to use MI to measure predictive accuracy, I recommend to base the generation
of the MIs on models, which are much more general than the regression model to be analysed, e.g.
including quadratic terms and interactions and perhaps heterogeneous variances.
Best
Werner
Rod Little schrieb:
Jonathan: R-squared is just another estimand, and the correct MI procedure is to simply average the values from each MI data set. Rod LittleOn Mon, 24 Nov 2003, Jonathan Mohr wrote:I am in the midst of using multiple imputation with multiple regression. The literature I've seen focuses on combining regression coefficients and corresponding standard errors. However, I've seen nothing on combining the estimates of R-squared. I would appreciate any guidance or leads that list members can offer. Best, Jon __________________________________ Jonathan Mohr, Ph.D. Assistant Professor Department of Psychology Loyola College 4501 North Charles Street Baltimore, MD 21210-2699 E-mail: [EMAIL PROTECTED] Phone: 410-617-2452 Fax: 410-617-5341 _____________________________________________________________________________________________________________________ Roderick Little Richard D. Remington Collegiate Professor (734) 936-1003 Department of Biostatistics Fax: (734) 763-2215 U-M School of Public Health M4045 SPH II [EMAIL PROTECTED] 1420 Washington Hgts http://www.sph.umich.edu/~rlittle/ Ann Arbor, MI 48109-2029
