Can I pool parameter estimates of multiple imputed data obtained through10-fold cross-validation？

[shenlan17]

I performed 10-fold cross-validation on mice，using 'ignore' parameter in mice package, 5 datasets were obtained each time, and a total of 50 imputed datasets were obtained. I want to do linear regression using these 50 datasets .

Can I use Rubin's Rules to directly combine the effect estimates(β) of 50 datasets and then derive confidence intervals and p-values? or only every 5 datasets ( imputed by the same training set and test set ) can be combined?

Thank you,
Liu.

[gerkovink]

@paulinavonstackelberg Could you shine your light on this, perhaps with a reference to code?

[paulinavonstackelberg]

Hi Liu,
could you elaborate a bit more on your goal? E.g., what are you interested in, and what is your evaluation measure?

[gerkovink]

This is a good remark. Depending on the aim, there could be different approaches to pooling the predictions, parameter estimates, etc.

[shenlan17]

Sorry for the confusion in the message.
 
Actually, I split my whole dataset into two parts: the training dataset (80% observations) and the testing dataset (the other 20% observations). Now, I would like to use mice package to impute the missing value in the training dataset, and then use the same model to impute the missing values in the test dataset. The ignore option in mice function was used, and 5 sets of data were imputed.

#The dataset has 100 observations and 20 variables #
ig<-c(rep(FALSE,80),rep(TRUE,20))
imp <- mice(data, m=5, maxit=10, seed=1234, ignore=ig)
imp.data=complete(imp,'all')

Subsequently, I perform multiple linear regression in the imputed training dataset and testing dataset (i.e, with the same variables but different observations), respectively.
 

for (i in 1:5){                         #5 imputed data
     training.data=imp.data[[ i ]][1:80,]
     training.data=imp.data[[ i ]][81:100,]
     lm(y~.，data=training.data)
}

Here, I am just wondering that could I direct use the Rubin's Rules to combine the effect estimates (i.e., beta coefficients) and derive the p values in the 5 training datasets, 5 testing datasets or 10 datasets (including all training and testing datasets)? In other words, if the observations of two datasets (here, training and testing) are different, could I use Rubin's Rules to combine the effect estimates?
 
 
Second question, following the first question, I also want to split the whole observations 10 times, i.e., random sample 80% observations as training dataset and the other 20% as testing dataset in each time. After imputation, I totally obtain 50 training dataset and 50 testing datasets. I combine each training dataset with the corresponding testing dataset, and then get 50 imputed whole datasets. Subsequently, linear regression is performed in each of these 50 imputed whole datasets. I am wondering could I use Rubin's Rules to combine the effect estimates in these 50 imputed whole datasets.

set.seed(1234)
folds<-createFolds(1:dim(data)[1],k=10)
for(ff in 1:length(folds)){
         testindex <- folds[[ff]]
         ig<-rep(FALSE,dim(data)[1])
         ig[testindex]<-TRUE 
         imp <- mice(data1,m=5,seed = 1,maxit=5,ignore = ig)
  }

Thank you