[R] Question about mars() -function

[Tiina Hakanen]

Hi!

I have some questions about MARS model's coefficient of determination.  
I use the MARS method in my master's thesis and I have noticed some  
problems with
the MARS model's R^2.

You can see the following example that the MARS model's R^2 is too big  
when i have used mars() -function for MARS model building, and when I  
have made MARS-model using a linear regression, it gives much smaller  
R^2.

So can you please tell me some information about why the MARS model  
R^2 is so big? How can I get the MARS model´s correct R^2 in  
R-projector some another way than in the following example or by  
calculating it myself using R^2-formula?

I hope you can reply soon.

Best regards,

Tiina Hakanen


library(ElemStatLearn)
library(mda)
data<-ozone
m<-mars(data[,-1], data[,1], nk=4)
m$factor[m$s,]
m$cuts[m$s,]
m$coef
marsmodel<-lm(data[,1]~m$x-1)
summary(marsmodel)

Call:
lm(formula = data[, 1] ~ m$x - 1)

Residuals:
     Min      1Q  Median      3Q     Max
-36.264 -15.993  -2.351   9.993 122.793

Coefficients:
      Estimate Std. Error t value Pr(>|t|)
m$x1  52.9783     3.8894  13.621  < 2e-16 ***
m$x2   4.7383     0.9599   4.936 2.92e-06 ***
m$x3  -1.9428     0.3084  -6.300 6.61e-09 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Residual standard error: 23.38 on 108 degrees of freedom
Multiple R-squared: 0.8147,     Adjusted R-squared: 0.8095
F-statistic: 158.2 on 3 and 108 DF,  p-value: < 2.2e-16

knot1 <- function (x,k) ifelse(x > k, x-k, 0)
knot2 <- function(x, k) ifelse(x < k, k-x, 0)
reg <- lm(ozone ~knot1(temperature,85)+knot2(temperature,85),data=data)

summary(reg)

Call:
lm(formula = ozone ~ knot1(temperature, 85) + knot2(temperature,
     85), data = data)

Residuals:
     Min      1Q  Median      3Q     Max
-36.264 -15.993  -2.351   9.993 122.793

Coefficients:
                        Estimate Std. Error t value Pr(>|t|)
(Intercept)             52.9783     3.8894  13.621  < 2e-16 ***
knot1(temperature, 85)   4.7383     0.9599   4.936 2.92e-06 ***
knot2(temperature, 85)  -1.9428     0.3084  -6.300 6.61e-09 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Residual standard error: 23.38 on 108 degrees of freedom
Multiple R-squared: 0.5153,     Adjusted R-squared: 0.5064
F-statistic: 57.42 on 2 and 108 DF,  p-value: < 2.2e-16