Dear community,
I am conducting a multiple linear regression with three metric and multiple control variables. The latter are ordinate and dummy variables. How do I assess the model assumptions (normal distribution, homoscedasticity, linearity and no multicollinearity) with the non-metric variables? Is there any literature to cite on this issue?
Hello Merina,
The presumptions about regression that specifically attach to the IVs are: (a) not excessively collinear (as you mention in your query) and (b) the form of the relationship with Y is linear (since Pearson correlations are the metric). As Mehmet Sinan Iyisoy 's reply correctly notes, the principal assumptions (normality, homoscedasticity, independence) apply to the model residuals (as estimates of error).
So, the recasting of nominal variables having three or more levels into sets of dichotomous dummy variates isn't really an issue. Go ahead with the usual checks on model residuals. The usual indicators for collinearity will be satisfactory (if you wanted to know, how does the set of dummy variates carrying the information for a categorical/nominal variable correspond to the remaining IVs, you could run a canonical correlation. The model Wilks lambda will tell you the proportion of unique variance that is not shared, akin to tolerance).
Good luck with your work.
Merina -
Yes, I often suggest a "graphical residual analysis" and "cross-validation" for checking model fit, and the possibility of overfitting to your particular sample, respectively. A graphical residual analysis will often show heteroscedasticity, which is actually a feature to generally be expected, not a bug, and one that can be handled by using regression weights. (See https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression.)
Cheers - Jim
Thank you!
Apart from the graphic residual inspection, if I am doing the analytical tests in SPSS (Kolmogorov-Smirnov, Shapiro-Wilk, Breusch-Pagan, Durbin-Watson) to test these conditions, should I also include the Dummy variables and the ordinal variable or can those tests only be performed with continuous variables?
Mehmet Sinan Iyisoy Sure not, you are right. But still, when conducting these tests in SPSS, I have to enter the respective variables into SPSS to get those test outputs. Thats where my question is aiming at.
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