R help - Sep 2015 - Calculate Total CORRECTED SS for non linear regression

Hello

I started to work on nonlinear regressions recently,

I want to compare a set of models and would like to use an equivalent of R2
for  nonlinear regression models.

I learned that a good alternative is to calculate the following corrected
formula:

 

 1 - (Residual SS/Total Corrected SS)

 

This provides a measure of how well the model fits versus just the overall
mean for the response variable.

 

With some help I could program the formula for my model and , but I am not
quite sure if it is correct and what exactly the total CORRECTED SS is
(compared to the Total SS)

Can anyone tell me how to calculate the Total Corrected SS in R and how it
can be implemented in my code?

 

CODE and INPUT:

 

 


# REGRESSION NON-LINEAR REGRESSION MODEL
FIT------------------------------------
dta<-read.csv("input.csv",header=T, sep = ",")
dput(dta)
head(dta)

 

# loading packages: analysis of mixed effect models
library(nls2)#model

 

 


#EQUATION 1: y~yo+a*(1-b^x)
#Aim: fit equation to data: y~yo+a*(1-b^x)
# y =Compound (from my data set) x= Damage (from my data set)
#The other 3 parameters are unknown: yo=Intercept, a= assymptote ans b=slope

plot(Compound~Damage, dta)
# Looking at the plot, 0 is a plausible estimate for y0:
# a+y0 is the asymptote, so estimate about 4000;
# b is between 0 and 1, so estimate .5
dta.nls <- nls(Compound~y0+a*(1-b^Damage), dta,
               start=list(y0=0, a=4000, b=.5))

xval <- seq(0, 10, 0.1)
lines(xval, predict(dta.nls, data.frame(Damage=xval)))
profile(dta.nls, alpha= .05)


summary(dta.nls)


#Calculation R2 Variation expl: total Variation--> Is deviance(dta.nls) the
same as Total Corrected SS???
CompoundSS <- sum((dta$Compound - mean(dta$Compound))^2)
R2 <- deviance(dta.nls)/CompoundSS
R2
#R2=0.5723023

 

 

 

structure(list(Treatment = structure(c(1L, 2L, 3L, 1L, 2L, 3L, 
4L, 1L, 2L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 
1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 
1L, 2L, 3L, 4L, 1L, 2L, 4L), .Label = c("1_2d", "3_2d",
"9_2d",
"C"), class = "factor"), Compound = c(1036.331811,
4171.427741,
6039.995102, 4140.242559, 4854.985845, 6982.035521, 948.2418407, 
3618.448997, 3130.376482, 1180.171957, 1500.863038, 4576.787021, 
5629.979049, 3589.187889, 2508.417927, 1989.576826, 5972.926124, 
450.7205451, 1120.955, 3470.09352, 3575.043632, 349.0864019, 
1013.807628, 910.8879471, 3743.331903, 592.3403778, 1517.045807, 
1504.491931, 3736.144027, 723.885643, 1782.864308, 1414.161257, 
3723.629772, 2005.919344, 4198.569251, 2228.522959, 3322.115942, 
720.9785449, 2874.651764, 2287.228752, 5654.858696, 1247.806111, 
2547.326207, 2608.716056, 1079.846532), Damage = c(0.4955, 1.516, 
4.409, 0.491, 2.3035, 3.51, 0, 0.4435, 1.573, 0, 0.142, 2.171, 
4.023, 0, 0.6925, 1.989, 5.683, 0, 0.756, 2.129, 9.437, 0, 0.578, 
2.966, 4.7245, 0, 1.0475, 1.62, 5.568, 0, 0.8295, 2.411, 7.272, 
0, 0.4035, 2.974, 8.043, 0, 0.6965, 1.313, 5.681, 0, 0.5895, 
2.559, 0)), .Names = c("Treatment", "Compound",
"Damage"), class "data.frame", row.names = c(NA,
-45L))

 

 

 


	[[alternative HTML version deleted]]

> On 30 Sep 2015, at 02:08 , Michael Eisenring <michael.eisenring at
gmx.ch> wrote:
> 
> Can anyone tell me how to calculate the Total Corrected SS in R and how it
> can be implemented in my code?
It is just sum((y-mean(y))^2).

Beware that a fair amount of (somewhat silly) contention is going on in this
area, though. In particular, the formula can give negative values, which is
unfortunate if you try calling it "R^2".
 
-pd

-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

Some workers consider it bad practise to compute what is called
R-squared for a nonlinear model. I find it useful for nonlinear models
as a signpost of how good a fit has been found. But just as signposts
can be turned around by vandals, nonlinear models can give a misleading
indication. With linear models, sum((y - model(y))^2) must be smaller
than sum((y - mean(y))^2). That is not necessary for nonlinear models.
Also for linear models there are many equivalent formulas due to the
many identities that go with the linear algebra. Those are not in force
for nonlinear models. So what in linear models is "R-squared" is just
a
comparison to the model that is the mean of the predicted variable,
i.e., the best single number model.

JN

On 15-09-30 04:09 AM, peter dalgaard wrote:
> 
>> On 30 Sep 2015, at 02:08 , Michael Eisenring <michael.eisenring at
gmx.ch> wrote:
>>
>> Can anyone tell me how to calculate the Total Corrected SS in R and how
it
>> can be implemented in my code?
> 
> It is just sum((y-mean(y))^2).
> 
> Beware that a fair amount of (somewhat silly) contention is going on in
this area, though. In particular, the formula can give negative values, which is
unfortunate if you try calling it "R^2".
>  
> -pd
>

Hi Peter,
Thanks for your answer.
I am still a bit confused- So that means that the calculation of the "
R2"
for my non-linear model is in fact the formula I used in my eample:

CompoundSS <- sum((dta$Compound - mean(dta$Compound))^2)
R2 <- deviance(dta.nls)/CompoundSS
R2


What's then the difference to the normally calculated R2 used for linear
regression? To me it looks the same.



-----Urspr?ngliche Nachricht-----
Von: peter dalgaard [mailto:pdalgd at gmail.com] 
Gesendet: Mittwoch, 30. September 2015 01:09
An: Michael Eisenring <michael.eisenring at gmx.ch>
Cc: r-help at r-project.org
Betreff: Re: [R] Calculate Total CORRECTED SS for non linear regression

> On 30 Sep 2015, at 02:08 , Michael Eisenring <michael.eisenring at
gmx.ch>
wrote:
> 
> Can anyone tell me how to calculate the Total Corrected SS in R and 
> how it can be implemented in my code?
It is just sum((y-mean(y))^2).

Beware that a fair amount of (somewhat silly) contention is going on in this
area, though. In particular, the formula can give negative values, which is
unfortunate if you try calling it "R^2".
 
-pd

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000
Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com