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Why does adding a covariate of age cause the variance of random slope (log time) to increase? Isn't it supposed to decrease when a covariate is added?

Firstly, there is only $log(time)$ in the model with random intercept and random slope.

$Y=(b_0+e_{b0})+(b_1+e_{b1})*log(time)+e$

Then I add age as covariate:(also with random intercept and random slope)

$Y=(b_0+e_{b0})+(b_1+e_{b1})*log(time)+b_2*age+e$

I found that the variance of the random slope in the first model is even smaller than it is in the 2nd model.

I am very confused, is it necessarily true that adding a covariate into the model will lead to smaller variance of random slope?

Is there any possible explanation?

jonsca
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user1421972
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  • Can you say more about your situation, your data, your model & your goals? I'm not sure if this question is answerable in its current form. – gung - Reinstate Monica Sep 05 '12 at 22:48
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    Age and time can often be fairly correlated, so you might be running into a multicollinearity issue, which will cause the error error to go up. This happens because you have very little independent variation in log(time). – dimitriy Sep 05 '12 at 23:21
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    I doubt that this is a general phenomena. It probably is just a consequence of the given data set. – Michael R. Chernick Sep 05 '12 at 23:30
  • I know of no reason why this should be required.

    What are age and time? As @DimitriyV.Masterov said, they could be collinear.

     – Peter Flom Sep 05 '12 at 23:36

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