## quasi-complete separation in logistic regression

Occasional Contributor
Posts: 16

# quasi-complete separation in logistic regression

Hello there,

I am running a logistic regression with my original data and it is ok. But I also groupped them in classes, for example:

age1: 18-25 years old

age2 :25-30 years old

age3: 30+ years old

and now I wanto to run the modell with the groupped variables but when I do I receive the messagem about quasi-complete separation. The problem is, that I don't have a clue about which variable(s) are causing this problem. How should I proceed to fix it?

Thanks!

Posts: 2,655

## Re: quasi-complete separation in logistic regression

Are you using a CLASS statement where the age-related variable has three levels, reflecting what is related, or did you create three binomial age related variables variables and include them in the model somehow?  If the latter is the case, you may have problems doing what I am going to ask next.

If there are three levels of a single variable and the response is binary, it is easy to run PROC FREQ with something like the following:

proc freq;

tables agecat*response:

run;

Take a look at the table and see if all of the observations fall into either the 1 or 0 response category for any of the agecat levels.  If so, that is quasi-separation--for one (or more) of the age groups, all of the responses are identical.

How to solve: collapse the categories so that the group where all of the responses are identical are included with another group.  Make sure that it makes good sense to combine the categories (i.e. don't combine the highest with the lowest, when they are ordered).

Good luck.

Steve Denham

Occasional Contributor
Posts: 16

## Re: quasi-complete separation in logistic regression

I create the variables so :

proc format;

value AVG_DELAY_L24Mgroup  low-0.5 = 'delay1'

0.5-high = 'delay2';run;

PROC FREQ data=score2;

format AVG_DELAY_L24M AVG_DELAY_L24Mgroup.;RUN;

 Category Good Bad delay1 437 376 delay2 40 239

another variable:

proc format;

value DUR_CUST_RELgroup  low-500 = 'dur_cust_rel1'

500 - 1000 = 'dur_cust_rel2'

1000 - 3000 = 'dur_cust_rel3'

3000 - 5000 = 'dur_cust_rel4'

5000 - high = 'dur_cust_rel5'; run;

table:

 Category Good Bad dur_cust_rel1 61 66 dur_cust_rel2 51 108 dur_cust_rel3 142 205 dur_cust_rel4 118 143 dur_cust_rel5 105 93

and in the model I do first wrote the new variables in the dataset:

data test;

set score;

retain AVG_DELAY_L24M_cat DUR_CUST_REL_cat;

AVG_DELAY_L24M_cat = put(AVG_DELAY_L24M,AVG_DELAY_L24Mgroup.);

DUR_CUST_REL_cat = put(DUR_CUST_REL,DUR_CUST_RELgroup.); run;

and the to the model:

proc logistic data = test descending;

class AVG_DELAY_L24M_cat DUR_CUST_REL_cat ;

And for all the other variables the frequency table is just like this two, I don't have any class without observation. I created the classes based on WOE and choose the variables for the model using the IV. I do took a look on the frequencies but I didn't saw anything suspicious.

Could be something else?

Thank you.

Posts: 2,655

## Re: quasi-complete separation in logistic regression

While it might be something else, you do have both variables in the model, and even without the interaction term, there may be a combination of levels that are empty, so I would check that as well  Things may be complete for each variable alone, but together you may be missing something.

It's Friday, and my brain might be fried, but this is the only thing I can think of happening to give quasi-separation right now.

Steve Denham

SAS Super FREQ
Posts: 3,839

## Re: quasi-complete separation in logistic regression

Just a comment: You can save yourself a DATA step if you use the formats in PROC LOGISTIC like you did in PROC FREQ. There is no need to explicitly construct the character variables by using the PUT function.

This is an instance where dynamically linked graphics are helpful. If you have access to JMP or SAS/IML Studio, load the three variables into the product. Create a bar chart of BAD_CLIENT and a mosaic plot of the other two variables. Click on the "Bad" group of clients. Those same observations will be highlighted in the mosaic plot, which will enable you to see which joint levels of classification variables are responsible for the quasi-separation.

SAS Employee
Posts: 308

## Re: quasi-complete separation in logistic regression

Separation occurs if there is a zero count for one of the response levels in any population, where a population is defined as a unique combination of levels of the predictors.  So, you would need to do this to check for zero counts:

proc freq;

tables AVG_DELAY_L24M_cat * DUR_CUST_REL_cat * bad_client;

run;

And then combine populations as needed to remove the zeros.  Alternatively, you may find that just adding the FIRTH option provides an adequate analysis based on a penalized likelihood method.  See this note on the separation issue:

Occasional Contributor
Posts: 16

## Re: quasi-complete separation in logistic regression

Hey StatDave@sas thank you for your suggestions. Unfortunately none of them could help me. I tried everything, firth, forward, stepwise, exact logistic, observation of the estimates and standadr deviation and so on. There is no zero count in any of my categories.

I then built the model inserting one by one and now I know which variables are causing the problem (15 variables) but I dond't understand why. I just can't let all this variables out of my model without a justification.

Can you imagine another solution?

Thanks

Posts: 2,655

## Re: quasi-complete separation in logistic regression

In all combinations of the 15 variables, there is not a single combination with zero count?  And not just at the two-way level, but all the way up to the fifteen-way level (assuming that the variables are all categorical)?  At some point, you are going to have to combine populations/levels in a critical variable to get rid of the zero count cell. At least that way, you will still have all variables accounted for.

Steve Denham

Occasional Contributor
Posts: 16

## Re: quasi-complete separation in logistic regression

Hey Steve,

well I didn't look at all combinations, because when I try to create a table with all the variables SAS tells me "ERROR: The requested table is too large to process." Maybe I don't know how to ask this for SAS. How should I do it?

Posts: 2,655

## Re: quasi-complete separation in logistic regression

Try:

proc freq noprint;

ods output list=list;

tables a*b*c*d*e*f*g*h*i*j*k*l*m*n*o/ list;

run;

where a through o are the variable names.  This would output the results to a dataset ('list') that you can sort on.  If this is what you tried then move to

PROC MEANS or SUMMARY.  I know the syntax better for MEANS, so it is what follows.

proc means noprint nway;

class a b c d e f g h i j k l m n o;

var (response variable goes in here);

output out=datasetname n=/autoname;

run;

Then search datasetname for zeroes.

Steve Denham

Occasional Contributor
Posts: 16

## Re: quasi-complete separation in logistic regression

Hey Steve!

I found it!!! And now, everything is working very well.

Many thanks.

N/A
Posts: 1

## Re: quasi-complete separation in logistic regression

Hi,

Suppose that we are building logit model using few independent variables. Event variable can be dichotomous or multinominal.

Sometimes SAS prompts "Error: Complete Separation" or "Error : Quasi Separation".

Its mean dependent Variable can be fully explain by any one independent Variable (Complete Separation) or  can be fully explain by combinations of few independent variables ( Quasi Separation).

Example 1

Event   Age

1          25

1         45

1         30

0         18

0         24

0          9

0          21

1         40

0         16

1        60

This Shows Complete Separation becaus Event =1 for age > 24

Example 2

Event   Age   Height

 0 16 160 0 18 130 0 24 178 0 21 145 0 45 120 1 38 160 1 55 150 1 30 169 1 40 170 1 25 170

This Shows Quasi Separation because Event =1 for age > 24 and Height>149.

To remove Compete Separation or Quasi Separation, 1) find out variable those were responsible for Separation ( Check the Collinearity Matrix and Classification Matrix between dependent variable and independent  variables)  then 2) remove those variables or classify them in group so that Complete/Quasi separation no more exist.