[R] ANOVA Table for Full Linear Model?

[Frank E Harrell Jr]

Peter Dalgaard wrote:
> Jason R. Finley wrote:
>> Hello,
>> I have spent a good deal of time searching for an answer to this but  
>> have come up empty-handed; I apologize if I missed something that is  
>> common knowledge.
>>
>> I am trying to figure out how to get an ANOVA table that shows the  
>> sum of squares. degrees of freedom, etc, for the full model versus  
>> the error (aka residuals).
>>
>> Here is an example of the kind of table I'd like to get:
>>
>> Analysis of Variance
>> Source       DF          SS          MS         F        P
>> Regression    1      8654.7      8654.7    102.35    0.000
>> Error        75      6342.1        84.6
>> Total        76     14996.8
>>
>> This kind of table is prevalent throughout my statistics textbook,  
>> and can apparently be easily obtained in other statistical software  
>> tools.  I'm not saying this as a gripe, but just as evidence that I'm  
>> not trying to do something obviously bizarre.
>>
>>
>> Here is an example of the only kind of ANOVA table for a single  
>> linear model that I've been able to get using R:
>>
>>  > regression9 <- lm(y ~ x1 + x2 + x3, data=data9)
>>  > anova.lm(regression9)
>> Analysis of Variance Table
>>
>> Response: y
>>            Df Sum Sq Mean Sq F value    Pr(>F)
>> x1         1 8275.4  8275.4 81.8026 2.059e-11 ***
>> x2         1  480.9   480.9  4.7539   0.03489 *
>> x3         1  364.2   364.2  3.5997   0.06468 .
>> Residuals 42 4248.8   101.2
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>
>>
>> Is there a way to get an ANOVA table with the full linear regression  
>> model considered as a whole rather than broken down into each  
>> additional predictor variable?  In other words, is there a way to get  
>> the former kind of table?
>>   
> The logical thing to do would be (please avoid calling methods like 
> anova.lm directly)
> 
> # following example(anova.lm):
> 
>> anova(update(fit,~1),fit)
> 
> Analysis of Variance Table
> 
> Model 1: sr ~ 1
> 
> Model 2: sr ~ pop15 + pop75 + dpi + ddpi
> 
>   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
> 
> 1     49 983.63                                  
> 
> 2     45 650.71  4    332.92 5.7557 0.0007904 ***
> 
> 
> If you really want the column of MS, you have a little extra work to do. 
> Notice also that the F test is part of the standard summary(fit)
> 
> 
>> Again, apologies if I'm missing something basic.
>> thanks very much,
>> ~jason

You can also do

library(Design)   # which also requires the Hmisc package
f <- ols( . . .)
anova(f)          # also includes many interesting composite hypothesis 
tests  involving linearity, pooling main effects with interactions, etc.

Frank Harrell
>>
>>
>> PS - I am on Mac OSX 10.4.8 using R 2.4.1 GUI 1.18 (4038)
>>
>> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>> Jason R. Finley
>> Graduate Student, Department of Psychology
>> Cognitive Division
>> University of Illinois, Urbana-Champaign
>>
>> uniace at mac.com
>> jrfinley at uiuc.edu
>> http://www.jasonfinley.com/
>> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~