Regression and LRT: Please help

[Salma Aboelmaaty]

I have two dependant variables (Satisfaction and Motivation). Both have the same scale and similar means and they are 0.6 correlated. When I conduct regression, can I merge them as one dependant variable even though i treated them in the correlation matrix separately (are there rules for that?) or do I just do a multi-variate model?

Also, i did a Likelihood ratio test between two models to test which is better. The LRT chi square came back 46 with pvale < 0 .. Does that mean that the second model (the one that had more variables) is better? I can't seem to understand that value or what it means. I am still learning.

One more thing, in order to avoid collinearity of independent variables, is correlation (0.3 - 0.4) okay ? I also conducted VIF and they all came back as below. Is it okay?

Variable VIF 1/VIF

VALUESOCIETY 1.32 0.754852
PSMTOTAL 1.28 0.782972
PAYSATISFIED 1.22 0.821911

Mean VIF 1.27


Thanks alot

[Weiwen Ng]

I think of likelihood ratio tests as trying to see if two models explain the data about equally well (p > 0.05), or if one explains the data better (p < 0.05). If both explain the data about equally well, then there’s a case to prefer the simpler model.

for the question about satisfaction and motivation as dependent variables, I would not try to merge them. They are theoretically distinct things. Conducting two separate regressions would be perfectly acceptable. There are more complex techniques you can learn, like structural equation modeling, but those are complex to teach.

as to independent variables, we very often have some collinearity. If an independent variable is theoretically important, you can include it regardless of its correlation to other variables (well, unless it is completely or very strongly correlated).