R help - Jan 2013 - How to fit a linear model to data by minimizing the mean absolute percent error?

Hi All,

I wonder if you can help me with an aparently simple task.  I have been
searching examples for this without any luck:

#Assume
x<-1:10  #x ranges from 1 to 10.
y<-x*runif(10)+ 1.5*x  #y is a linear function of x with some error. Add
uniform error that is scaled to be larger as x values also become larger

#error is proportional to x size, this should cause heterocedasticity.


#I know there are many methods to deal with heterocedasticity, but in my
specific case, I want to use percent regression to minimize the mean absolute 
#percentual error as opposed to regular regression that deals with the square of
the errors.

#Question, how to fit a linear model to minimize this error on the data y ~ x
above?
#Please do not use model<-lm(y ~ x....) as this will minimize the square of
the errors, not the mean absolute percent error

Best regards, André Cesta

	[[alternative HTML version deleted]]

Hi All, I wonder if you can help me with an aparently simple task. ?I have been
searching examples for this without any luck: #Assume
x<-1:10 ?#x ranges from 1 to 10.
y<-x*runif(10)+ 1.5*x ?#y is a linear function of x with some error. Add
uniform error that is scaled to be larger as x values also become larger #error
is proportional to x size, this should cause heterocedasticity. #I know there
are many methods to deal with heterocedasticity, but in my specific case,?I want
to use percent regression to minimize the mean absolute?
#percentual error as opposed to regular regression that deals with the square of
the errors. #Question, how to fit a linear model to minimize this error on the
data y ~ x above?
#Please do not use model<-lm(y ~ x....) as this will minimize the square of
the errors, not the mean absolute percent error Best regards, Andr? Cesta

Take the logs of both side and minimize the absolute error on the log
scale, then transform your results back. The quantreg package does L1
regression.

If you want to know **why**, this works, consult a local statistician
or post to a statistical list like stats.stackexchange.com.  This is
not an R question.

--- Bert

On Mon, Jan 14, 2013 at 4:22 AM, Andre Cesta <aacesta at yahoo.com>
wrote:
>
>
> Hi All,
>
> I wonder if you can help me with an aparently simple task.  I have been
searching examples for this without any luck:
>
> #Assume
> x<-1:10  #x ranges from 1 to 10.
> y<-x*runif(10)+ 1.5*x  #y is a linear function of x with some error. Add
uniform error that is scaled to be larger as x values also become larger
>
> #error is proportional to x size, this should cause heterocedasticity.
>
>
> #I know there are many methods to deal with heterocedasticity, but in my
specific case, I want to use percent regression to minimize the mean absolute
> #percentual error as opposed to regular regression that deals with the
square of the errors.
>
> #Question, how to fit a linear model to minimize this error on the data y ~
x above?
> #Please do not use model<-lm(y ~ x....) as this will minimize the square
of the errors, not the mean absolute percent error
>
> Best regards, Andr? Cesta
>
>         [[alternative HTML version deleted]]
>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm

Hi Bert,

Thanks for your reply.

Your recommendation seems to minimize the error transformed with log, but not
the percent error, that is, the model error divided by the observed value (for
each observation).

I need to minimize the percent error.

With log, there could be a very large observation, with a very large error and
even with log it would be larger than other errors and have more influence in
the regression. ?But if I take the percent error to minimize, this observation
with large error would not have a larger influence.

Best regards, Andr?

________________________________
From: Bert Gunter <gunter.berton at gene.com>
To: Andre Cesta <aacesta at yahoo.com> 
Cc: "r-help at r-project.org" <r-help at r-project.org> 
Sent: Monday, 14 January 2013, 13:34
Subject: Re: [R] How to fit a linear model to data by minimizing the mean
absolute percent error?

Take the logs of both side and minimize the absolute error on the log
scale, then transform your results back. The quantreg package does L1
regression.

If you want to know **why**, this works, consult a local statistician
or post to a statistical list like stats.stackexchange.com.? This is
not an R question.

--- Bert

On Mon, Jan 14, 2013 at 4:22 AM, Andre Cesta <aacesta at yahoo.com>
wrote:
>
>
> Hi All,
>
> I wonder if you can help me with an aparently simple task.? I have been
searching examples for this without any luck:
>
> #Assume
> x<-1:10? #x ranges from 1 to 10.
> y<-x*runif(10)+ 1.5*x? #y is a linear function of x with some error. Add
uniform error that is scaled to be larger as x values also become larger
>
> #error is proportional to x size, this should cause heterocedasticity.
>
>
> #I know there are many methods to deal with heterocedasticity, but in my
specific case, I want to use percent regression to minimize the mean absolute
> #percentual error as opposed to regular regression that deals with the
square of the errors.
>
> #Question, how to fit a linear model to minimize this error on the data y ~
x above?
> #Please do not use model<-lm(y ~ x....) as this will minimize the square
of the errors, not the mean absolute percent error
>
> Best regards, Andr? Cesta
>
>? ? ? ???[[alternative HTML version deleted]]
>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website:
http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm