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

## Confidence intervals for variance function

### Re: Confidence intervals for variance function

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.

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.

### Re: Confidence intervals for variance function

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

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

### Re: Confidence intervals for variance function

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.

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.