topic Re: generalized logit model with correlations between the random intercepts for various outcome grou in Statistical Procedures

generalized logit model with correlations between the random intercepts for various outcome groups

Maya1 — Thu, 28 Jul 2016 07:28:26 GMT

Hello,

I want to fit a multilevel model for a multinomial outcome with unordered response categories.

Thus, I face exactly the same problem as described in following post:

https://www.researchgate.net/post/Using_proc_Glimmix_in_SAS_to_fit_a_generalized_logit_model_how_can_I_allow_for_correlations_between_the_random_intercepts_for_various_outcome_groups

It seems like there is no solution to this issue in proc glimmix.

However, I do not have to stick to proc glimmix but could also switch to another procedure. Do you have any hint for me how I could solve the problem in SAS?

Thanks in advance and kind regards,

Re: generalized logit model with correlations between the random intercepts for various outcome grou

Ksharp — Thu, 28 Jul 2016 08:04:13 GMT

I guess you need to take a look at PROC GEE .
There is an alternative way to Generalize Logistic Model.

Re: generalized logit model with correlations between the random intercepts for various outcome grou

SteveDenham — Thu, 28 Jul 2016 14:35:48 GMT

I would definitely consider @Ksharp's suggestion. If you have access to SAS/STAT14.1, take a look at Example 43.6 GEE for Nominal Multinomial Data for a kickstart. If you have additional random effects to consider, it will be easier to port to GLIMMIX once you have done this in GEE.

Now, if the measurements are truly hierarchical and not repeated in nature, the following is a good place to start (especially Example 2, even though that is for ordered responses):

http://support.sas.com/resources/papers/proceedings15/3430-2015.pdf

From there it is a matter of shifting to a generalized logit link, rather than a cumulative logit.

Steve Denham

Re: generalized logit model with correlations between the random intercepts for various outcome grou

Maya1 — Mon, 01 Aug 2016 09:21:19 GMT

Dear Mr Keshan, dear Mr Denham,

thanks for your hints.

I still have not found the best solution to my problem, so I returned to proc glimmix and tried this code for my outcome variable with 3 nominal categories and my binary predictor

proc glimmix data= data method=RSPL ;
class outcome predictor id;
model outcome(ref= first)= predictor/ dist=multinomial link=glogit ;
random predictor /sub=id group=outcome G type=UN;
NLOPTIONS TECH=nrridg;

Thereby I noted, that with ref= first, the G matrix is not positive definite and a wrong G Matrix is estimated:

Effect	predictor	Group	Row	Col1	Col2	Col3	Col4	Col5	Col6
predictor	0	Outcome 0	1	5.25E-8
predictor	1	Outcome 0	2		5.25E-8
predictor	0	Outcome 1	3			0.5991	-0.3839
predictor	1	Outcome 1	4			-0.3839	0.2028
predictor	0	Outcome 2	5					0.9249	0.7053
predictor	1	Outcome 2	6					0.7053	1.2084

However, if I choose ref= last, the error does not occur and the G Matrix has the correct dimension:

Effect	predictor	Group	Row	Col1	Col2	Col3	Col4
predictor	0	Outcome 0	1	0.6886	0.3393
predictor	1	Outcome 0	2	0.3393	0.9590
predictor	0	Outcome 1	3			0.5559	0.1235
predictor	1	Outcome 1	4			0.1235	1.3793

The last category has only 11% of all data, whereas the first category has 40% of all results.

Do you have any idea, why the error occurs and how I can prevent SAS from doing so?

Thanks in advance and kind regards,

Re: generalized logit model with correlations between the random intercepts for various outcome grou

SteveDenham — Mon, 01 Aug 2016 17:43:28 GMT

I would really need to see a cross-tabulation to figure this out. It appears that there is no variability when ref='first' for something. This may be due to a single instance that causes this.

Steve Denham

Re: generalized logit model with correlations between the random intercepts for various outcome grou

Maya1 — Tue, 02 Aug 2016 07:06:31 GMT

If I create a frequency table for the outcome by id and predictor via

proc freq data= raw;
by id;
table predictor* outcome / out= freq;
run;

I find plenty of empty cells both outcome categories, for the first as well as for the last. I have attached the raw data set. Can you figure out the reason?

And another question: Is there any chance to get the estimate of the outcome independent of the predictor within the same model? Since predictor is a dummy coded variable, the intercept is not the mean of both predictor categories, but the estimate of the outcome for predictor=0.

Again, many thanks!

Re: generalized logit model with correlations between the random intercepts for various outcome grou

SteveDenham — Mon, 08 Aug 2016 16:53:24 GMT

I'm still not sure about the main point here. Technical Support may be of a lot more help.

As far as the second question, I am having a spot of confusion in figuring out the question. Surely for all cases, you know what the predictor variable is--I don't think it is ever indeterminate. Thus, you should be able to get a predicted value for each category of the independent variable. Any "mixture" of values will depend on the sample/subpopulation/population ratio. If you had only a single independent variable, your model statement would look like:

model depvar=indvar / solution <other options go here>;

You could get an estimate of the sample value, ignoring the independent variable by fitting:

model depvar= / solution <make sure that the options are identical to the above>;

Steve Denham