I have 1771 observations, with 30% missing data for x1 (Yes:No), and no other missing values from 26 other variables (mix of continuous and factor).
I am using quantile regression in R, with and without imputing values for x1. The parameter estimates for y ~ X1 are similar, but the SEs are actually smaller from the models estimated with the imputed data. This seems true regardless of centile. Have I certainly done something wrong (I am leaning this direction) or can this happen under reasonable circumstances? Happy to provide additional detail. Many thanks.
library(rms) imputes <- aregImpute(formula, data, n.impute = 100, tlinear = FALSE, nk = 5) > qrtest # WITH IMPUTATION Quantile Regression tau: 0.5 fit.mult.impute(formula = y ~ x1, fitter = Rq, xtrans = imputes, data = workDf, tau = 0.5) Coef S.E. t Pr(>|t|) Intercept 3560.0000 21.9590 162.12 <0.0001 x1=Yes -170.0000 29.7172 -5.72 <0.0001 > summary(qrtest2) # NO IMPUTATION Call: rq(formula = y ~ x1, tau = 0.5, data = workDf) tau:  0.5 Coefficients: Value Std. Error t value Pr(>|t|) (Intercept) 3600.00000 27.94167 128.83985 0.00000 x1 -200.00000 36.46074 -5.48535 0.00000
Perhaps a clue, from here
fit.mult.impute warns the user that when a fitting routine is not from rms, then the standard errors and significance tests are based only on the last fitted model
Though there were no such warnings since it's using Rq rather than rq as the fitter. Also, calculating SEs as suggested matches up.
NOTE 2: Using rms::ols with imputation leads to larger SEs, as expected, than ols without imputation.
NOTE 3: It is not the result of using different standard errors.