# How to compare coefficients in different models?

I used a binary logit regression with three different dependent variables in order to end up with three models. The dependent variables are configured with 0=no/1=yes. I use a variety of different independent variables (binary and continuous) but the same independent variables for each model of course. Now I would like to compare the independent variables of model 2 and 3 with each other in order to see if the coefficients significantly differ from each other? For example I would like to see if the variable age has a bigger effect on the dependent variable of model 2 then on the dependent variable of model 3. How can I do that? I will be using SPSS.

## 1 Answer

Essentially, what you want is an hypothesis test. This test needs to take into account that the alternative hypothesis is not a single value but a distribution.

Thus, you could test $H_0:\hat{\beta}_{1,1}=\hat{\beta}_{1,2}$ against $H_A:\hat{\beta}_{1,1}\neq\hat{\beta}_{1,2}$ where the second digit stands for the model from which the coefficient $\beta_1$ comes from.

The statistic in that case is: $(\hat{\beta}_{1,1}-\hat{\beta}_{1,2})/\sqrt{s.e.(\hat{\beta}_{1,1})^2+s.e.(\hat{\beta}_{1,2})^2}$ and, if errors are distributed Normally, is a regular t-test.

However, this test is valid for Normally distributed errors. I do not know what is the equivalent for Logistic regressions (or even if there is a difference.)

• You should not formulate your hypothesis about estimated values, but population parameters! Could you give a reference for the test statistic? Products of standard errors look fairly uncommon to me. – Christoph Hanck Jan 8 '16 at 8:50
• I edited the formula. This was not a multiplication of the standard errors as I thought, but the square root of the sum of squared standard errors. – user89073 Jan 11 '16 at 8:48
• The test is given is this article: psycnet.apa.org/psycinfo/1995-27766-001, cited by udel.edu/soc/faculty/parker/SOCI836_S08_files/… – user89073 Jan 11 '16 at 8:51