Hello,
I have conducted a multiple regression with two predictor variables and would like to find out whether the difference between the standardized regression coefficients is significant. Which test shall I use and how can I conduct the test in SPSS?
Thank you
Petra
Dear Petra,
actually you should not do that and focus on the comparison of the UNstandardized effects. Standardized effects will differ between the groups even if the true effects are equal but the groups differ in their variances.
When you want to compare the unstandardized effects, there are two options:
a) setting up the regression model as a SEM and using equality constraints (EQ). In this approach to have a multi-group model and you specify an EQ that restricts the algorithm to find the optimal *common* estimate for both groups. If both groups, however, differ in their effects, the model chi-square test (its significance) will tell you that. Going one step further, you can set EQs also for the variance of the IV and you finally get what you want (i.e., the combination of equally set variances AND significantly different effects imply a difference in the standardized effects (for whatever reasons ....)
b) Using a simple formula involving the group's effects and SEs:
Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for the equality of regression coefficients. Criminology, 36(4), 859-866.
HTH
Holger
I think this website is very useful to find the answer to your question.
https://stats.idre.ucla.edu/spss/faq/how-can-i-compare-regression-coefficients-between-two-groups/
Best
Sevilay
Hello Petra,
Here's a link (see example/method 4 and the alternatives listed thereafter) that walks through the kind of comparison you seek: https://andrewpwheeler.com/2016/10/19/testing-the-equality-of-two-regression-coefficients/
Good luck with your work.
Dear Petra,
actually you should not do that and focus on the comparison of the UNstandardized effects. Standardized effects will differ between the groups even if the true effects are equal but the groups differ in their variances.
When you want to compare the unstandardized effects, there are two options:
a) setting up the regression model as a SEM and using equality constraints (EQ). In this approach to have a multi-group model and you specify an EQ that restricts the algorithm to find the optimal *common* estimate for both groups. If both groups, however, differ in their effects, the model chi-square test (its significance) will tell you that. Going one step further, you can set EQs also for the variance of the IV and you finally get what you want (i.e., the combination of equally set variances AND significantly different effects imply a difference in the standardized effects (for whatever reasons ....)
b) Using a simple formula involving the group's effects and SEs:
Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for the equality of regression coefficients. Criminology, 36(4), 859-866.
HTH
Holger
If your focus on differ group in variances and have more than one response variables you can use manova
I'm not an expert my no means, but have studied linear statistical models as a one semester long module. If I was looking at multiple regression, I would do a model comparison, maybe even learn how to use R-studio to work out the anova table. Since I'm only a student there are a lot of approaches I'm willing to research and explore, but I would have refer to my lecture notes.
Dear Petra,
Check out this instructional video: https://www.youtube.com/watch?v=qKnpiGwNDMk
It might fit to your purpose.
Best regards,
Robin
I'll do this with the raw betas, but you can standardize everything if you like (and I'll assume just three predictors). The H0: beta_1 = beta_2 can be evaluated by comparing
m1
Hi Daniel,
I did not know that. Great.
With regard to the comparison of standardized betas, I would have some problems to give it a go as betas can differ solely because of differences in the variances while the effect itself is identical. Correct?
Best,
Holger
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