fixed effects correlated with the intercept
Is'nt this what might be expected. Center the covariate about its mean and, depending on the detailed variance-covariance structure, the correlation may well reduce to zero. Check this out with a model created using lm(), where it is easier to follow the detail. If you write the model y = a + b(x - mean(x)), the estimates of a and b are uncorrelated. If x is not centered, then you have y = a - b mean(x))] + bx = adash + bx. Then adash = a - b mean(x) involves b, and is clearly correlated with b. By making mean(x) large enough or small enough, the correlation can be made arbitrarily close to -1 or 1, respectively. What do you mean when you say "I have two covariates that I consider to be controls in my model." Do you mean that these code for observations that you are treating as controls? Or what? John Maindonald email: john.maindonald at anu.edu.au phone : +61 2 (6125)3473 fax : +61 2(6125)5549 Centre for Mathematics & Its Applications, Room 1194, John Dedman Mathematical Sciences Building (Building 27) Australian National University, Canberra ACT 0200.
On 24 Mar 2007, at 6:07 AM, Austin Frank wrote:
And hello again! I'm getting a result that is very confusing to me and I'm hoping for some advice or clarification. I have two covariates that I consider to be controls in my model. When I include either in the model, the fixed effect shows a strong correlation ( > .85 ) with the intercept. The result of including these factors is that the estimated intercept is much lower than I would expect. Is there any conclusion to be drawn from these correlations? Normally when I see correlations among fixed effects I worry about collinearity. I'm absolutely confused about what it would mean for a covariate to be collinear with the estimated population mean. Any help is appreciated in clearing this up. It's possible that the appropriate conclusion is that I'm overfitting. I'm not sure this is the case. The degrees of freedom in the model is still relatively low compared to the number of data points (12 df on ~2500 observations). Is overfitting still the most likely culprit? One attempt at dealing with the above problem was to remove the intercept from the model. This causes lmer to estimate a coefficient for each of the levels in the first factor in the model. I think that this treatment did not resolve whatever problem there is with these two covariates-- now instead of being correlated with the intercept, they are correlated with both levels of the split factor. While this approach didn't resolve my original issue, it did bring up a few others. First of all, the coef() method fails on a model with no intercept for the fixed effects, giving the error "unable to align random and fixed effects". Is this a known issue? Is there a workaround? Second, while the estimates for both levels of the split factor are shown to be significantly different from zero using mcmcsamp, I'm still interested in whether there is a difference between the two levels. What's the appropriate test to check the null hypothesis that the difference between the two parameter estimates is zero? Thanks again, /au -- Austin Frank http://aufrank.net GPG Public Key (D7398C2F): http://aufrank.net/personal.asc
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