Hello all,
I want to assess the effect of one categorical independent variable along with a few confounders on one continuous outcome variable, I fitted a multiple regression and see the adjusted R square is negative like -0.002.
I added a few interactions and just increase from -0.002 to -.02, I believe linear regression is not a good model here.
All the figures for this variable is not positive to fit gamma regression or b/n zero and one to fit beta regression, I am not sure what to do in this case?
there is also no multicollinearity
Sample size=200
One independent variable
Two confounder
Any input appreciated.
A negative adjusted R2 means that a horizontal line fits the data better than your model, implying OLS regression doesn't really work at all. Did you check the distribution of the residuals? If they're no good you could try a generalized additive model (GAM) or some non-parametric models, or maybe there is nothing going on between your variables (no relationship is still a result)
Thanks for your answer,
The residual plot is not good, like a right-skewed, and has no constant variance; I removed a few outliers, which are influential points and see that residual plots look better and the Adjusted R square increases from -0.006 to 0.0041. I was wondering if I could report this one, as it's still too low?
I think if I add a few interactions, it might increase a little bit
I fitted univariate analysis for each confounder and independent variable and see no significance between them and the dependent variable; based on this, do you still suggest GAM?
The adjusted R2 means that less than 1% of the outcome variance can be explained by the model, meaning that the predictors don't really have much exploratory power.
If the confounders (and IV) show no significant effects even in a simple linear model, a GAM might not drastically improve the fit, but it really doesn't hurt to try it (if there's a non-linear relationship)
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