[R] how to calculate Rsquare

[Spencer Graves]

	  It should be easy to get a separate R^2 from "lm" for each level of a 
factor:  Just split the data and run "lm" once for each level of f. 
I've done this with a "for" loop something like the following:

	dat <- data.frame(x=x, y=y, f=f)
	for(i.f in 1:2){
	   sel <- (f == c("a", "b")[i.f])
	   fit <- lm(y~x, data=dat[sel])
	 ...

	}

where "..." is replaced by appropriate commands to get R^2 from 
summary(fit).  It may also be possible to do with with tapply.

	  Getting an R^2 from glm and lme is harder and controversial:  Some 
people say simply, "Don't do it, because it doesn't mean anything."  For 
those who want to do it anyway, the following papers discuss alternate 
definitions of R^2 outside the standard normal linear model:

	  NagelKerke, N. J. D. (1991) "A note on a general definition of the 
coefficient of determination", Biometrika 78: 691-2.

	  Cox, D. R. and Wermuth, N. (1992) "A comment on the coefficient of 
determination for binary responses", The American Statistician 46:  1-4.

	  Cameron, A. Colin and Windmeijer, F. A. G. (1997) "An R-squared 
measure of goodness of fit for some common nonlinear regression models", 
Journal of Econometrics 77:  329-342.

	  I'd be pleased to hear other comments on this issue.  Hope this 
helps.  spencer graves


Ronaldo Reis Jr. wrote:
> Hi,
> 
> I have something like this:
> 
> 
>>x <- 1:10
>>y2 <- 30+5*x+rnorm(x,sd=3)
>>y <- c(y1,y2)
>>x <- c(x,x)
>>plot(x,y)
>>x <- 1:10
>>y1 <- 1+5*x+rnorm(x,sd=2)
>>y2 <- 30+5*x+rnorm(x,sd=5)
>>y <- c(y1,y2)
>>x <- c(x,x)
>>f <- factor(rep(c("a","b"),c(10,10)))
>>m <- lm(y~x+f)
>>anova(m)
> 
> Analysis of Variance Table
> 
> Response: y
>           Df Sum Sq Mean Sq F value    Pr(>F)    
> x          1 4062.9  4062.9  400.04 2.990e-13 ***
> f          1 4421.5  4421.5  435.35 1.496e-13 ***
> Residuals 17  172.7    10.2                      
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 
> 
>>#rsquare of model
>>(4062.9+4421.5)/(4062.9+4421.5+172.7)
> 
> [1] 0.980051
> 
> In this way I calculate the model rsquare, but how to calculate the rsquare of  
> each levels "a" and "b"?
> 
> This is only an example, the model maybe glm, lme etc.
> 
> Thanks
> Ronaldo