First you need a hypothesis and then compare the two groups according to your hypothesis with an uncomplicated method for two groups.

Dear Béatrice! I offer help in solving your problem using the method and software tools developed by me

Hello Yanru,

You may compare the regression models for equality of coefficient/s across groups in several ways:

1. Include group and group x IV terms in your model. Significant group x IV term would indicate that the relationship is different for that IV across groups.

Here's two links that walk through the process:

(a) Two groups, via spss: https://psych.unl.edu/psycrs/statpage/rhtest_eg2a.pdf

(b) Three or more groups, via stats: https://stats.oarc.ucla.edu/stata/faq/how-can-i-compare-regression-coefficients-across-3-or-more-groups/

2. Conduct a simultaneous test (equality of all coefficients), such as Pothoff's test. Attached is a simple excel file for comparing two groups for equality of slope and intercept in a bivariate relationship (one IV, one DV), after estimating each group's coefficients independently.

3. Use SEM software to evaluate equality of one or all coefficients by group. You would do this by: (a) estimating an independent model, with each group having unconstrained coefficients; (b) estimating a second model, in which all groups have equal coefficient for a given IV (e.g., a common "b1" term for IV#1, and so on); then (c) comparing the model-data chi-square fit value for change from (a) to (b), relative to the number of coefficients you fixed as being equal.

Good luck with your work.

You could also consider the Chow test to examine whether regression coefficients differ for split data sets. Here is an easy way to carry out a Chow test in SPSS.

An easy way to perform a Chow test. (n.d.). IBM - United States. https://www.ibm.com/support/pages/easy-way-perform-chow-test

Good luck,

Hi David Morse , thank you so much for the detailed explanation!

Hi Mohialdeen Alotumi , thanks for the recommendation!

Canonical correlation (https://en.wikipedia.org/wiki/Canonical_correlation) still better if you apply it on the principal component scores generated by the two variables set computed separatesly so to have a well conditioned model (components are each other independent so you compute canonical correlation with no 'within-variable-set' internal correlations, see atatched file)

Hi,

the construction of an expected label can allow the separation of variables into two groups, of course I'm thinking about lasso regression, I'm following your discussion to know more. Cheers.

Dear Yanru Pan ,

What statistical test should I use? It is often said that the design of a study is more important than the analysis. A badly designed study can never be retrieved, whereas a poorly analyzed study can usually be re-analyzed.

https://blog.statsols.com/types-of-statistical-tests

Regards,

Shafagat

The test statistic t is equal to bj/sbj, the parameter estimate divided by its standard deviation. This value follows a t(n-p-1) distribution when p variables are included in the model.

The F test in multiple regression is used to test the null hypothesis that the coefficient of the multiple determination in the population is equal to zero. The partial F test is used to test the significance of a partial regression coefficient.

Article Introduction to Statistical Tests of Significance

Chapter Statistical Tests

Please consider the above links