# [R] multiple imputation of anova tables

Leo Gürtler leog at anicca-vijja.de
Fri Nov 25 11:00:50 CET 2005

```Dear list members,

how can multiple imputation realized for anova tables in R? Concretely,
how to combine

F-values and R^2, R^2_adjusted from multiple imputations in R?

Of course, the point estimates can be averaged, but how to get
standarderrors for F-values/R^2 etc. in R?
For linear models, lm.mids() works well, but according to Rubins rules,
standard errors have to be used together with the estimates to get
unbiased estimates. The same is needed for lme models. For the
regression coefficients of lme, it is no problem, because s.e.'s are
present. But how to combine AIC/ BIC,loglik and especially how to
proceed with the random effects in lme's? I assume there is a general
rule which can be applied to all these cases, but I do not get it right.

e.g.

> anova(limo1)
Analysis of Variance Table

Response: lverb.ona
Df Sum Sq Mean Sq F value  Pr(>F)
klasse      6  301.6    50.3  2.0985 0.05514 .
Residuals 193 4623.3    24.0
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

or (from the manpage of lme)

>      summary(fm2)
Linear mixed-effects model fit by REML
Data: Orthodont
AIC      BIC    logLik
447.5125 460.7823 -218.7563

Random effects:
Formula: ~1 | Subject
(Intercept) Residual
StdDev:    1.807425 1.431592

Fixed effects: distance ~ age + Sex
Value Std.Error DF   t-value p-value
(Intercept) 17.706713 0.8339225 80 21.233044  0.0000
age          0.660185 0.0616059 80 10.716263  0.0000
SexFemale   -2.321023 0.7614168 25 -3.048294  0.0054
Correlation:
(Intr) age
age       -0.813
SexFemale -0.372  0.000

Standardized Within-Group Residuals:
Min          Q1         Med          Q3         Max
-3.74889609 -0.55034466 -0.02516628  0.45341781  3.65746539

Number of Observations: 108
Number of Groups: 27
>

and the ANOVA of the lme:

> anova(fm2)
numDF denDF  F-value p-value
(Intercept)     1    80 4123.156  <.0001
age             1    80  114.838  <.0001
Sex             1    25    9.292  0.0054

I am confused about that and I did not find any hint in norm,
mice/pan/mix or Hmisc.

Any help and hints are appreciated,

best regards

Leo Gürtler / Germany

```