Specifying the VC matrix with MCMC

[GDistiller]

Hi
I need some help on how to go about specifying the VC matric when fitting a random effects model using the MCMC estimation option.

I have read the help files and have an idea of how the different pieces fit together but am a bit unsure about the notation used to specify correlations. I understand that one uses "rho(x)" to specify a particular correlation that one wants to estimate in the off-diagonal of the matrix but am unsure what exactly the x is referring to. I have found the following but it is still not clear to me: "The correlation parameter is specified as rho(x), where x takes on the value 1, 2, ... to correspond to the number of hyperdistribution parameters. The notation corresponds to the means (mu(1), mu(2), ...) and standard deviations (sigma(1), sigma(2), ...) of the hyperdistributions. " The last statement I find particularly confusing - if one specifies a correlation between 2 different hyperdbns, say rho(2), how can the 2 here refer to a particular mean or SD since that relates only to one of the distributions?

In the example given (under help with MCMC VCmatrix) to model the correlation between sets of paramers (the example with 3 banding periods and 2 hyperdbns - one for the 2 survival rates and one for the 3 recovery rates), rho(1) is used to specify the correlation between S1 and f1 and S2 and f2, does this mean that there is only one correlation estimate? This makes sense to me ie that one is "drawing" an estimate for survival and recovery at each time period from a particular bivariate dbn with a certain covariance between the parameters. But if this is correct, how does this relate to the statement above about the 1 corresponding to the mean mu(1) and std deviation sigma(1)?

Any help to clear this up would be much appreciated - I cannot seem to find much documentation at all on how to use the various GUI's to setup a random effects model...

Thanks a lot

Greg

[cooch]

Hi
Any help to clear this up would be much appreciated - I cannot seem to find much documentation at all on how to use the various GUI's to setup a random effects model...

Greg

Thats because it (documentation) isn't finished yet.

I'm traveling at the moment, and will leave it to Gary to answer the question(s) about mechanics.

[gwhite]

Greg:

"if one specifies a correlation between 2 different hyperdbns, say rho(2), how can the 2 here refer to a particular mean or SD since that relates only to one of the distributions?"

The position of the rho(x) parameter within the VC matrix determines which parameters are being modeled.

"In the example given (under help with MCMC VCmatrix) to model the correlation between sets of parameters (the example with 3 banding periods and 2 hyperdbns - one for the 2 survival rates and one for the 3 recovery rates), rho(1) is used to specify the correlation between S1 and f1 and S2 and f2, does this mean that there is only one correlation estimate? This makes sense to me ie that one is "drawing" an estimate for survival and recovery at each time period from a particular bivariate dbn with a certain covariance between the parameters. But if this is correct, how does this relate to the statement above about the 1 corresponding to the mean mu(1) and std deviation sigma(1)?"

Because in this example, every place that there is a row and column intersection of a sigma(1) that corresponds to the survival distribution, and a sigma(2) that corresponds to the recovery distribution, there is a rho(1) in the VC matrix, i.e., the correlation of the survival and recovery parameters. The help screen unfortunately doesn't stay properly formatted on all monitors, so you may have to rearrange it a bit to see that rho(1) entries line up on the sigma(1) rows over the sigma(2) columns. The matrix is assumed to be symmetric, so you don't have to enter the below diagonal portion.

Gary

[GDistiller]

Thanks very much for the quick replies!

Ok I understand how the position in the matrix determines what is being correlated with what. I am still a little unsure as to how the indexing of the x in rho(x) works. Is the number x simply an index in that it specifies the number of rho parameters being estimated? If the x number is simply indexing the number of rho parameters that one wants to estimate, what does this mean from the help file: "The notation corresponds to the means (mu(1), mu(2), ...) and standard deviations (sigma(1), sigma(2), ...) of the hyperdistributions"

My confusion stems from trying to understand in the example given how rho(1) links to mu(1) and sigma(1) from the first hyperdistribution (or not?). Would it make any difference if it was specified as rho(2)...or rho(8)?

Thanks again...

Greg

[gwhite]

Greg:
The indexing is totally artificial. rho(1) has no relationship to sigma(1) -- just the location in the VC matrix determines the relationship. Although you should start with an index of 1, I don't think it is absolutely necessary (but I haven't checked this and its been a few years since I programmed all of this).

Gary

[GDistiller]

OK cool, thanks again for the input...that makes sense...

[GDistiller]

One more quick question: I ran a MCMC model and it took a little over 24 hours to run. When it finished it popped up with the results in a text file which I scanned through. Unfortunately I then closed the file without saving it, not being aware that the results were not automatically stored in the results browser like other models.

I have looked in the help file and have read that one should save the results to a permanent file. Does this mean that I have lost the results and have to rerun the model? I know there is a MCMC bin file that contains the samples but I am not sure how to extract the info that I need.

Any advice would be greatly appreciated....

Thanks!

Greg

[cooch]

One more quick question: I ran a MCMC model and it took a little over 24 hours to run. When it finished it popped up with the results in a text file which I scanned through. Unfortunately I then closed the file without saving it, not being aware that the results were not automatically stored in the results browser like other models.

I have looked in the help file and have read that one should save the results to a permanent file. Does this mean that I have lost the results and have to rerun the model? I know there is a MCMC bin file that contains the samples but I am not sure how to extract the info that I need.

Any advice would be greatly appreciated....

Thanks!

Greg

Running it again isn't a big deal, if it only takes a day (it is not uncommon for complex random effects models to take days -> weeks to run. Only a day is not a major hurdle).

Extracting information from MCMC.BIN using either SAS or R is documented in the helpfile.

[GDistiller]

Ok thanks...found the R code you mentioned so will first try that...

Thanks again for the help...

[gwhite]

Greg:
if you closed MARK, then, yes, the temporary file has been deleted, and you lost it. Good experience -- run simple models until you understand what you are doing, rather than"learning" on the real stuff.

Gary