# Signs of coefficients from NOMREG are reversed from LOGISTIC REGRESSION

## Problem(Abstract)

I have run the same logistic regression model in the LOGISTIC REGRESSION and NOMREG (Multinomial Logistic Regression in the menus) procedures of SPSS. The dependent variable, DV, is binary (0,1), so that I expect to be able to run a model and get identical results for the same data in the two procedures. However, when I compare the unstandardized regression coefficients produced by the 2 procedures, the absolute magnitudes are identical but the signs of the coefficients are reversed. In other words, the NOMREG coefficient for a particular predictor will be (-1)times the coefficient from LOGISTIC REGRESSION. The LOGISTIC REGRESSION coefficients appear to produce the correct probabilities when plugged into a COMPUTE command. Is there a bug in NOMREG?

## Resolving the problem

The reversal in signs of the coefficients is not due to a programming error in NOMREG. It is due to a difference in the dependent variable category which is used as the event to predict. Binary Logistic Regression uses the higher value of the dependent variable as the event to predict, so the lower value is the reference category. By default, Multinomial Logistic Regression (NOMREG) uses the highest (or alphabetically last, in case of a string variable) value of the dependent variable as the reference category. So, for your dependent variable, DV, NOMREG is predicting the 0, whereas Logistic Regression is predicting the 1. Therefore, the signs of the coefficients are reversed. In SPSS versions prior to 11.5, there are no options to change these designations, so you need to recode DV before running NOMREG to have the NOMREG results agree with the LOGISTIC REGRESSION results. In the command below, I recode DV into a new variable, DVREV, leaving DV itself untouched. The 0s are recoded to 2s in the new variable and the 1s are copied over as 1s. If you run NOMREG with DVREV as the dependent variable, the reference category will be 2 and the coefficients should match those of logistic regression in both magnitude and sign.

RECODE dv (0=2) (else = copy) INTO dvrev .
EXECUTE.

In SPSS versions from 11.5 onward, it is possible to specify the reference category for the dependent variable in a NOMREG command. See Technote 1479637 for detailed instructions.

## Historical Number

19555

### Document information

More support for: SPSS Statistics

Software version: Not Applicable

Operating system(s): Platform Independent

Reference #: 1476703

Modified date: 07 September 2016