Confidence intervals for variance function

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jrachele
Posts: 2
Joined: Thu Apr 12, 2018 3:51 am

Confidence intervals for variance function

Post by jrachele »

Hi there,

I've estimated some random coefficient models in mlwin, and used the variance function window to estimate level 2 variance for a binary independent variable, and so have a result and result se for when my independent variable is 0 or 1.

My question is, can I calculate a confidence interval from this standard error? If so, can I assume that it follows a normal distribution?

Thanks,
Jerome
billb
Posts: 132
Joined: Fri May 21, 2010 1:21 pm

Re: Confidence intervals for variance function

Post by billb »

Hi Jerome,
It's not usually the case that variances follow normal distributions but you would get an approximate interval using the SE. If you used MCMC estimation then you could get a chain of variance functions and thus an empirical credible interval for the 2 variances. Don't know if that is helpful?
Best wishes,
Bill.
jrachele
Posts: 2
Joined: Thu Apr 12, 2018 3:51 am

Re: Confidence intervals for variance function

Post by jrachele »

Hi Bill,

Thanks for much for your prompt reply. Yes, I used MCMC estimation, and I'm able to get a credible interval for the variance function for when X=0 (i.e., variance of cons), which I can get from the MCMC diagnostics window, or from the results table of the stored model.

However, I'm trying to get a confidence (or credible) interval for when X=1. I can't see any MCMC diagnostics in the trajectories window for this coefficient as it wasn't specified in the model. Rather, I'm estimating the variance function for when X=1 from the variance function window. The variance function window gives me estimates (and standard errors) for when X = both 0 and 1, and the standard error for when X=0 is the same as the MCMC diagnostics.

Do you know how I can obtain the confidence (or credible) intervals for when X=1, or, do you know how the standard error is calculated for when X=1 in the variance function window?

Thanks again,
Jerome
billb
Posts: 132
Joined: Fri May 21, 2010 1:21 pm

Re: Confidence intervals for variance function

Post by billb »

Hi Jerome,
If you look at my MCMC book then in section 4.9 I describe how one works out estimates and confidence intervals for functions of parameters - in this case a VPC and so you could do something similar. Perhaps an even easier solution is to to reparameterise your model so that you don't have CONS and X=1 at level 2 but instead have X=1 and X=0 at level 2 (i.e. construct a variable that is 1-X for this) and then you can see the 2 parameters directly.
Best wishes,
Bill.
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