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Estimating random effect when there exist none (simulation)

[ Edited ]

Hi all,

I am trying to run simulation for a mixed model. For one of the variable (xij) I do not add random effect (non-varying) at the data generation process but try to estimate the random effect during the estimation process. The expectation is that estimated variance component should be zero but it is not. This is the case even group-mean centering the variable. Is there an obvious explanation for this? I am not familiar with the estimation procedure of the PROC MIXED. The data generating mechanism and the model is below

``````* 	Level-1 Model
*   	yij = beta0j + beta1j*xij + .50*vij + rij
* 	Level-2 Model
*   	beta0j = gamma00 + gamma01*tj + u0j
*   	beta1j = gamma10 + gamma11*tj``````

I am trying to estimate random term for xij with PROC MIXED as

``````proc mixed data=SimData2 covtest NOCLPRINT method = REML;
class SchID;
model yij = xij  / ddfm = BW solution;
random INTERCEPT xij /subject = SchID  type=UN g gcorr;
ods output CovParms=CovParms1 SolutionF=SolutionF1;
by SampleID;
run;quit;``````

Thanks

Accepted Solutions
Solution
‎02-07-2018 05:58 PM
Posts: 3,054

Re: Estimating random effect when there exist none (simulation)

[ Edited ]

But the average doesn't have to be zero, no matter how many runs you make (unless you can do an infinite number of runs).

The real test is as I described, that the values are not statistically different than zero, 95% of the time.

--
Paige Miller

All Replies
Posts: 3,054

Re: Estimating random effect when there exist none (simulation)

[ Edited ]

Perhaps this is just a difference in wording, but I would not agree with this statement:

The expectation is that estimated variance component should be zero but it is not

I would say there that the estimated variance component should not be statistically different than zero, 95% of the time (assuming you do the test with alpha = 0.05 and the errors are iid normal)

But in an individual run a non-zero estimated variance component does not bother me.

--
Paige Miller
Contributor
Posts: 46

Re: Estimating random effect when there exist none (simulation)

There are cases where it is zero or very close to zero but running over 5000 replications the average is different from zero (not statistically). I wanted to get the average value as close to zero as possible, which is the true value.

Solution
‎02-07-2018 05:58 PM
Posts: 3,054

Re: Estimating random effect when there exist none (simulation)

[ Edited ]

But the average doesn't have to be zero, no matter how many runs you make (unless you can do an infinite number of runs).

The real test is as I described, that the values are not statistically different than zero, 95% of the time.

--
Paige Miller
Contributor
Posts: 46