Specifying t-distribution in multivariate mixed effect model

[Jascalla]

Dear All,
I have 3 continuous outcome variables and I am fitting level 2 multivariate regression model.
The outcome variables were approximately normal using histogram and they are z-scores generated with about 95% negative z-scores values and no log transformation can apply.
After fitting the model and extracting the level 2 and 1 residuals, there was a departure from the normality assumption using Q-Q plots.
Is it possible to specify t-distribution for this model as against the default normal distribution?
Secondly, is there any other way to go about the residuals departure from the normality assumption?
Any help will be highly appreciated.
Many thanks.
Jascalla

[GeorgeLeckie]

Hi Jascalla,

If the outcome variables are approximately normal then you would expect 50% of the standardised outcome (i.e., z-scores) to be negative. So I am not sure why you have about 95% negative z-scores, it would suggest to me that the outcomes are rather positively skewed. Note that standardizing an outcome only shifts its location and scale, it does not make the outcome "more normal". So standardizing the outcomes will not make your Q-Q plots look better. Some researchers normalize the outcome to make it approximately normally distributed.

No you can only specify a multivariate normal distribution for the random effects in MLwiN.

If you want to specify a multivariate t distribution specify the model with a multivariate normal distribution, then you could use the WinBUGS software. If you chose to go down this route, you could output the nearest equivilent MLwiN model as a set of WinBUGS files, modify the model statement text file to specify a multivariate t distribution and fit the resulting model in WinBUGS

I hope that helps

George

[Jascalla]

Hi George,
Many thanks for this helpful response.
The World Health Organization developed models for computing the Z-scores for measuring children nutritional status which uses Box-Cox Exponential distribution for the underlying population with relevant age and sex so is not the same as the usual Z-scores we do compute directly from our data hence the huge number of negative scores but plausible.
The Z scores are heavy tailed (both ends) and will need such distributions and one that readily came to my mind is the t-distribution because I tried using the t-distribution to check for the normality of the residual I computed from the normal distribution and it worked well so I wish to try fitting the model with t and see how it goes.
Winbugs is something I am new with so I will give it ago and see how it goes and any readily available syntax will be helpful.
Thank you so much George.
-Jascalla

[GeorgeLeckie]

Dear Jascalla,

You wrote...

"Winbugs is something I am new with so I will give it ago and see how it goes and any readily available syntax will be helpful."

Example with changing a univariate normal distribution to a univariate t-distribution is found at

http://www.bristol.ac.uk/cmm/media/runm ... n_MLwiN.do

Best wishes

George

[Jascalla]

Hi George,
This is so helpful.
I will give it ago.
Many thanks and I wish you happy weekend in advance.
-Jascalla

[Jascalla]

Hi George,
I am back just to inform you that I am smoothly running the models in WinBugs now with success based on your earlier suggestion.
Many thanks and I am very grateful for this.
Cheers.
-Jascalla

[GeorgeLeckie]

That is fabulous, getting into WinBUGS can be a steep learning curve so well done for making the transition
George