Programming the statistical procedures from SAS

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

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Contributor
Posts: 24

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

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...

 

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,

M

Grand Advisor
Posts: 9,457

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

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


Respected Advisor
Posts: 2,655

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

[ Edited ]

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

Contributor
Posts: 24

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

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,

M

Respected Advisor
Posts: 2,655

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

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

Contributor
Posts: 24

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

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!

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Respected Advisor
Posts: 2,655

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

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

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