[R] Type III SS and collinearity in R

[Fox, John]

Dear Pamela,

> -----Original Message-----
> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Pamela
> Wong
> Sent: Sunday, July 17, 2016 1:58 AM
> To: r-help at r-project.org
> Subject: [R] Type III SS and collinearity in R
> 
> Hi there
> It appears the Anova() function in the car package cannot compute type
> III SS when there is collinearity in the model. Has anyone else run into
> this problem?

That's right, by default anyway -- when there's *perfect* collinearity -- but in that circumstance what would be the point? That is, the SSs for the collinear terms are 0. You can force Anova() to (arbitrarily) deal with the collinearities

> library(car)
> mod <- lm(prestige ~ income + education + I(income + education), data=Duncan)
> Anova(mod, type="III", singular.ok=TRUE)

Anova Table (Type III tests)

Response: prestige
                      Sum Sq Df F value    Pr(>F)    
(Intercept)            360.2  1  2.0154    0.1631    
income                4474.2  1 25.0331 1.053e-05 ***
education             5516.1  1 30.8626 1.727e-06 ***
I(income + education)         0                      
Residuals             7506.7 42                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' '

But, again, what's the point?

> 
> I would use drop1() to obtain the SS but it does not provide the
> intercept...

Yes, drop1() reports the 0 SSs for all the collinear terms (on 0 df), which is better in a sense -- e.g.,

> drop1(mod)
Single term deletions

Model:
prestige ~ income + education + I(income + education)
                      Df Sum of Sq    RSS    AIC
<none>                             7506.7 236.26
income                 0         0 7506.7 236.26
education              0         0 7506.7 236.26
I(income + education)  0         0 7506.7 236.26


Why would it be interesting in this circumstance to know whether the intercept is 0? As you can see, Anova() reports the test; you can also get it from linearHypothesis():

> linearHypothesis(mod, "(Intercept)", singular.ok=TRUE)
Linear hypothesis test

Hypothesis:
(Intercept) = 0

Model 1: restricted model
Model 2: prestige ~ income + education + I(income + education)

  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     43 7866.9                           
2     42 7506.7  1    360.22 2.0154 0.1631

I suspect that there's a statistical issue lurking here that's not addressed by showing you how to get the tests you're asking for.

Best,
 John

--------------------------------------
John Fox, Professor
McMaster University
Hamilton, Ontario, Canada
Web: socserv.mcmaster.ca/jfox



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