## Quasi-likelihood regressions

Occasional Contributor
Posts: 18

# Quasi-likelihood regressions

[ Edited ]

Currently running quasi-likelihood regressions, where the code is PROC GLIMMIX.

Can someone tell me the difference between the following statements:

model y ~ x /link = logit dist = binomial

model y ~ x / link = log solution

When I ran the code with 'link = logit dist = binomial' I was never able to get a value on the coefficients (which is what I'm looking for).

Super User
Posts: 9,867

## Re: Quasi-likelihood regressions

model y ~ x /link = logit dist = binomial :

Like proc logistic .  link function is   log(p/(1-p))      y~binomial distribution

model y ~ x / link = log solution:

link function is    log(y)      y usually is positive value.

Posts: 2,655

## Re: Quasi-likelihood regressions

Logistic regression in GLIMMIX often requires more iterations than the default to reach convergence.  Providing your code and any quotes from the output regarding non-convergence, etc. would be helpful in addressing your problems.

Steve Denham

Valued Guide
Posts: 684

## Re: Quasi-likelihood regressions

You have several issues/problems. With your code with link=log, you are using a normal distribution (the default). This is likely not what you want. Put in the dist= option. Also, your syntax is wrong for GLIMMIX. One does not use "y ~ x". One uses "y=x". Also, you are using pseudo-likelihood, not quasi-likelihood. Quasi-likelihood is when the likelihood is not defined (or definable). If you put in:

random _residual_;

then you would have quasi-likelihood with the binomial. Another way of getting quasi-, is to specify the mean and variance functions directly. Both ways are defining a variance:mean structure that does not correspond to a real probability distribution.

Occasional Contributor
Posts: 18

## Re: Quasi-likelihood regressions

Thanks all for the clarification; I am still running into syntax error codes.

When I include dist = option is says syntax error, expecting one of the foollowing: B, BERNOULLI, BETA, etc.

Below is the code I ran:

proc glimmix data = TEST;
model utility_score = AGE INCOME ... (number of independent variables here) / link = log dist = option;
where utility_score gt 0;
run;

Reason why I'm running quasi-likelihood is because my dependent variable is between 0 and 1; cannot take on the 0 value but can be 1. Also, the dependent variable is skewed (left).

Valued Guide
Posts: 684

## Re: Quasi-likelihood regressions

You missed the point, maybe I wasn't clear. You need to specify a distribution with link=log, otherwise you will get a normal distribution. If you want a binomial, then use dist=binomial or some other distribution (there is no such thing as "dist=option"). If you are using normal distribution (the default), then you are using pseudo-likelihood (the default).
Occasional Contributor
Posts: 18

## Re: Quasi-likelihood regressions

Got it. One (hopefully) last question; I believe that I need dist = beta because my dependent variable is between 0 and 1 (though it cannot take on the value of 0).

But the question I still have remaining is that this dependent variable is left-skewed (skewness: -1.97); is one able to incorporate that in the distribution code anywhere?

If I remember correctly a positively skewed variable would take on a Poisson distribution but I haven't come across how to incorporate a negatively-skewed variable.

Any thoughts would be greatly appreciated.

Valued Guide
Posts: 684

## Re: Quasi-likelihood regressions

Beta does not allow 0 or 1 (defined only between those values). You would get a missing value for any 0s or 1s. This is a challenge when using the beta distribution. Skewness is not a problem. Beta can be very skewed. If you use beta, then you don't need the random _residual_ term I mentioned (there is a scale parameter automatically). If you want beta with 1s, you need to define (in an ad hoc way) a new variable that is always between 0 and 1. Something like yprime = (y-.005)/1.01. Be careful, results will depend on the constants you use.
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