Non-linear diagnostics

noetsi

Fortran must die
#1
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.
 

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Dason

Ambassador to the humans
#2
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

Less is more. Stay pure. Stay poor.
#3
Systematically withhold variables and see if they impact rate. If they don't, then fit a rate only model and look at its QQplot.
 

noetsi

Fortran must die
#5
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

Fortran must die
#6
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

Less is more. Stay pure. Stay poor.
#7
Yes the Rate variable. What would a qq plot of the residuals for a linear model fit to nonlinear relationship look like?