## How to impute a two-level model with repeated measures

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TiagoVPereira
Posts: 4
Joined: Fri Feb 17, 2017 3:00 am

### How to impute a two-level model with repeated measures

Dear all,

My question is how to organize data in order to impute a two-level model with 5 repeated measures.

To sum up: We have been using Stata and RealComImpute. Level 1 = patient id, Level 2 = month.

Month is a repeated measure taken from the same patient at month 0 (baseline), 1, ..., 4.

Letting i denote the i-th month (i = 0,...,4) and j = 1,...,n participants, our model is like:

y_ij = β_0 + β_1month_ij + β_2gender_j + ....+ u_0j + u_1j month_ ij + e_ ij

We have missing data for i = 3 and i = 4 only (~10% and 90% respectively). Data for the remaining months are complete.

y from month 2 is highly correlated with y from month 3 (r>0.90), y from month 2 is also highly correlated with y from month 4 (apparently - with r>0.70).

So, we would like to use y from month 2 as one of the predictors for y month 3 and 4.

In order to use y from month 2 as predictor, I created (in Stata) an additional column called pred_2, which contains y from month 2 for every subject.

In Stata, the final dataset would look like this:

*/------------------- start -----------------------------
clear
set seed 12345
set obs 1000
gene id = _n
gene age = round(runiform()*30)+20
gene gender = round(runiform())
gene covariate1 = runiform()
gene covariate2 = runiform()
forvalues i = 0/4 {
gene y`i' = round(rnormal(100,20))
}
replace y3 = . if runiform()<0.10
replace y4 = . if runiform()<0.90
gene pred_2 = y2
reshape long y, i(id) j(month)
gene cons = 1
sort month id
order id month y pred_2
realcomImpute y age gender covariate1 covariate2 pred_2 using mydata , numresponses(1) cons(cons) level2id(month)
*/------------------- end -----------------------------

Is this the correct set up for the two-level imputation?

Look forward to hearing from you.

Tiago
Harvey Goldstein
Posts: 49
Joined: Sun Sep 06, 2009 5:30 pm

### Re: How to impute a two-level model with repeated measures

As I understand it, your model is a repeated measures model where you have some responses missing for some individuals at some occasions (months). If you just set this up as a 2-level model then there is typically no problem since the level 2 units (individuals) just have different numbers of level 1 measures. Any multilevel software that can handlerandom coefficients will fit this. Imputation only arises if one or more predictors has missing data, or if you happen to be using a standard MANOVA or SEM design that requires balance.
Harvey Goldstein
TiagoVPereira
Posts: 4
Joined: Fri Feb 17, 2017 3:00 am

### Re: How to impute a two-level model with repeated measures

Thanks, Dr. Goldstein.

So, apparently there is no point in imputing responses in that repeated measure analysis? No gain in terms of standard errors?

Tiago
TiagoVPereira
Posts: 4
Joined: Fri Feb 17, 2017 3:00 am

### Re: How to impute a two-level model with repeated measures

It took me some minutes only: Journal of Clinical Epidemiology 66 (2013) 1022e1028
Multiple imputation of missing values was not necessary before
performing a longitudinal mixed-model analysis
Jos Twisk a,b, *, Michiel de Boer b , Wieke de Vente c , Martijn Heymans a,b
TiagoVPereira
Posts: 4
Joined: Fri Feb 17, 2017 3:00 am

### Re: How to impute a two-level model with repeated measures

Dear all,

After some days of reading, I've decided that I would like to see if MI will provide different results for my data. Assuming that I want to impute response variables (repeated measures), is the approach I pointed out above OK?
rajveervyas
Posts: 1
Joined: Sat May 12, 2018 12:54 pm

### Re: How to impute a two-level model with repeated measures

Thanks for sharing this information.