Non-linear diagnostics

[noetsi]

I understand residuals are the best way to spot non-linearity. But the huge amount of data I work with, and my own lack of experience, means that I have a hard time deciding if my regression model show non-linearity.

It has been suggested that you use partial regression plots to spot non-linearity. I generated them and was hoping someone could suggest if they suggest non-linearity (and more generally what to look for). I have no theory to build on, I am actually trying to develop a theory here. My field rarely does statistical analysis.

The only three variables I care about are rate, sum_of_tuition, and inserv. The other variables are dummy variables. My guess is that restriction of range applies to these, but I don't know if the others are non-linear or not.

 

[Dason]

I don't necessarily see anything to suggest non linearity. What do the partial residual plots look like if you log transform the dependent variable though.

 

[hlsmith]

Systematically withhold variables and see if they impact rate. If they don't, then fit a rate only model and look at its QQplot.

 

[spunky]

What's with the groupings in the "Allowed" plots? Do you have a categorical predictor there?

 

[noetsi]

What's with the groupings in the "Allowed" plots? Do you have a categorical predictor there?

Yes spunky. Only inserv, sumoftuition, and rate are interval predictors. But I ran the complete model including dummies, as I think you have to in order to use the partial plots correctly, and did not know how to remove the non-interval predictors. I only am concerned, in terms of linearity, with the interval predictors.

 

[noetsi]

Systematically withhold variables and see if they impact rate. If they don't, then fit a rate only model and look at its QQplot.

I am not sure what you mean by impact rate. Rate is one of the predictors, were you referring to that. Or did you mean see if the impact the dependent variable.

I am confused about the qqplots. I am testing for linearity not normality.

 

[hlsmith]

Yes the Rate variable. What would a qq plot of the residuals for a linear model fit to nonlinear relationship look like?