# Method to compare variable coefficient in two regression models

I am regressing two butterfly richness variables (summer and winter) against a set of environmental variables separately. (variables with continuous numbers) Environmental variables are identitcal in each model.

In the summer model, the weight rank of coefficients is temp > prec > ndvi.

The weight rank in winter is temp > ndvi > prec.

As it is almost implausible to compare the coefficients directly, pls advise any advanced method other than regression to discriminate such coefficient rank between seasons, such as canonical correlation analysis (unsure if it is suitable here)

The spatial info here richness and environmental variables comprising 2000 grid (continuous distribution) spanning from 100 E to 130 E longitude, 18 to 25 N latitude.

• A few suggestions: 1. Replace acronyms with complete words, 2. Elaborate a little more on what you are trying to achieve statistically. Are you simply trying to determine which regression coefficients are larger or smaller? Aug 16 '10 at 11:45
• Elaine:> what do you want to do? From your question i gather that you want a relative ranking of the coefficient for winter and one for summer. Is this correct, or just an ersatz for something else you have not been able to do. Sep 21 '10 at 6:52

Here is my suggestion. Rerun your model(s) using one single regression. And, the Summer/Winter variable would be simply a single dummy variable (1,0). This way you would have a coefficient for Summer to differentiate it from Winter. And, the regression coefficients for your three other variables would be consistent with one single weight rank.

• Gaetan:> Elane seems to suggest that the slope in the summer are different from the slopes in the winter (not just the intercept). Sep 21 '10 at 6:50
• kwak, you raise an excellent point. I have been told that linear regression can handle that whereby you have dummy variables for the intercepts of the seasons and another one for their respective slope coefficients. Unfortunately, I have not used such a method. So, I can't explain it further. Sep 21 '10 at 15:55
• Gaetan:> yes linear regression can handle slope dummy. Sep 24 '10 at 17:56

One answer is to do a seemingly unrelated regression. Suppose that you only have a single predictor plus an intercept. Create a data set (or data matrix) like

wo 1 wp 0 0
so 0 0  1 sp


where 'wo' is the outcome in the winter season and 'wp' is the winter predictor/"X" value and 'so' is the summer outcome value and 'sp' is the summer predictor. The 1s represent the summer and winter intercept terms. Basically, you have two sets of variables: summer variables and winter variables. In the summer, all the winter variables are set to 0 and vice-versa in the summer.

After you run a regression on the full set of summer and winter variables using the data template above, you get a full covariance matrix that can be used to compare the coefficients for the winter months to the summer months using standard regression procedures.

This is one way of implementing @kwak's suggestion of having different slope coefficients for each season.