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Michael Eisenring

2015-Sep-26 14:46 UTC

[R] How to calculate standard error of estimate (S) for my non-linear regression model?

Dear Peter,
Thank you for your answer.
If I look at my summary I see there a Residual standard error: 1394 on 53
degrees of freedom.
This number is very high (the fit of the curve is pretty bad I know but
still...). Are you sure the residual standard error given in the summary is
the same as the one described on this page:
http://onlinestatbook.com/2/regression/accuracy.html
I am basically just looking for a value that describes the goodness of fit
for my non-linear regression model.


This is probably a pretty obvious question, but I am not a statistician and
as you said the terminology is sometimes pretty confusing.
Thanks mike

-----Urspr?ngliche Nachricht-----
Von: peter dalgaard [mailto:pdalgd at gmail.com] 
Gesendet: Samstag, 26. September 2015 01:43
An: Michael Eisenring <michael.eisenring at gmx.ch>
Cc: r-help at r-project.org
Betreff: Re: [R] How to calculate standard error of estimate (S) for my
non-linear regression model?

This is one area in which terminology in (computational) statistics has gone
a bit crazy. The thing some call "standard error of estimate" is
actually
the residual standard deviation in the regression model, not to be confused
with the standard errors that are associated with parameter estimates. In
summary(nls(...)) (and summary(lm()) for that matter), you'll find it as
"residual standard error",  and even that is a bit of a misnomer.

-pd 
> On 26 Sep 2015, at 07:08 , Michael Eisenring <michael.eisenring at
gmx.ch>
wrote:> 
> Hi all,
> 
> I am looking for something that indicates the goodness of fit for my 
> non linear regression model (since R2 is not very reliable).
> 
> I read that the standard error of estimate (also known as standard 
> error of the regression) is a good alternative.
> 
> 
> 
> The standard error of estimate is described on this page (including 
> the
> formula) http://onlinestatbook.com/2/regression/accuracy.html
> <https://3c.gmx.net/mail/client/dereferrer?redirectUrl=http%3A%2F%2Fon
> linest atbook.com%2F2%2Fregression%2Faccuracy.html>
> 
> Unfortunately however, I have no clue how to programm it in R. Does 
> anyone know and could help me?
> 
> Thank you very much.
> 
> 
> 
> I added an example of my model and a dput() of my data
> 
> #CODE
> 
> dta<-read.csv("Regression_exp2.csv",header=T, sep =
",")
> attach(dta)      # tells R to do the following analyses on this dataset
> head(dta)
> 
> 
> 
> # loading packages: analysis of mixed effect models 
> library(nls2)#model
> 
> #Aim: fit equation to data: y~yo+a*(1-b^x) : Two parameter exp. single 
> rise to the maximum # y =Gossypol (from my data set) x= Damage_cm 
> (from my data set) #The other 3 parameters are unknown: yo=Intercept, 
> a= assymptote ans b=slope
> 
> plot(Gossypol~Damage_cm, 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(Gossypol~y0+a*(1-b^Damage_cm), dta,
>               start=list(y0=0, a=4000, b=.5))
> 
> xval <- seq(0, 10, 0.1)
> lines(xval, predict(dta.nls, data.frame(Damage_cm=xval))) 
> profile(dta.nls, alpha= .05)
> 
> 
> summary(dta.nls)
> 
> 
> 
> 
> 
> 
> 
> #INPUT
> 
> structure(list(Gossypol = c(948.2418407, 1180.171957, 3589.187889, 
> 450.7205451, 349.0864019, 592.3403778, 723.885643, 2005.919344, 
> 720.9785449, 1247.806111, 1079.846532, 1500.863038, 4198.569251, 
> 3618.448997, 4140.242559, 1036.331811, 1013.807628, 2547.326207, 
> 2508.417927, 2874.651764, 1120.955, 1782.864308, 1517.045807, 
> 2287.228752, 4171.427741, 3130.376482, 1504.491931, 6132.876396, 
> 3350.203452, 5113.942098, 1989.576826, 3470.09352, 4576.787021, 
> 4854.985845, 1414.161257, 2608.716056, 910.8879471, 2228.522959, 
> 2952.931863, 5909.068158, 1247.806111, 6982.035521, 2867.610671, 
> 5629.979049, 6039.995102, 3747.076592, 3743.331903, 4274.324792, 
> 3378.151945, 3736.144027, 5654.858696, 5972.926124, 3723.629772, 
> 3322.115942, 3575.043632, 2818.419785), Treatment = structure(c(5L, 
> 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
> 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 
> 3L, 3L, 3L, 2L, 2L, 2L, 4L, 2L, 4L, 4L, 2L, 4L, 2L, 2L, 4L, 4L, 4L, 
> 4L, 4L, 4L, 2L), .Label = c("1c_2d", "1c_7d",
"3c_2d", "9c_2d", "C"),
> class = "factor"), Damage_cm = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0.142, 0.4035, 0.4435, 0.491, 0.4955, 0.578, 0.5895, 0.6925, 0.6965, 
> 0.756, 0.8295, 1.0475, 1.313, 1.516, 1.573, 1.62, 1.8115, 1.8185, 
> 1.8595, 1.989, 2.129, 2.171, 2.3035, 2.411, 2.559, 2.966, 2.974, 
> 3.211, 3.2665, 3.474, 3.51, 3.547, 4.023, 4.409, 4.516, 4.7245, 4.809, 
> 4.9835, 5.568, 5.681, 5.683, 7.272, 8.043, 9.437, 9.7455), 
> Damage_groups = c(0.278, 1.616, 2.501, 3.401, 4.577, 5.644, 7.272, 
> 8.043, 9.591, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), 
> Gossypol_Averaged = c(1783.211, 3244.129, 2866.307, 3991.809, 
> 4468.809, 5121.309, 3723.629772, 3322.115942, 3196.731, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), Groups = c(42006L, 42038L, 
> 42067L, 42099L, 42130L, 42162L, 42193L, 42225L, 42257L, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), .Names = c("Gossypol", 
> "Treatment", "Damage_cm", "Damage_groups",
"Gossypol_Averaged",
> "Groups"), class = "data.frame", row.names = c(NA,
-56L))
> 
> 
> 
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 
> 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.
--
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

peter dalgaard

2015-Sep-26 15:56 UTC

head link

[R] How to calculate standard error of estimate (S) for my non-linear regression model?

> On 26 Sep 2015, at 16:46 , Michael Eisenring <michael.eisenring at
gmx.ch> wrote:
> 
> Dear Peter,
> Thank you for your answer.
> If I look at my summary I see there a Residual standard error: 1394 on 53
> degrees of freedom.
> This number is very high (the fit of the curve is pretty bad I know but
> still...). Are you sure the residual standard error given in the summary is
> the same as the one described on this page:
> http://onlinestatbook.com/2/regression/accuracy.html
Sure I'm sure (& I did check!)... But notice that unlike R^2, Residual
SE is not dimensionless. Switch from millimeters to meters in your response
measure and the Residual SE instantly turns into 1.394. It's basically
saying that your model claims to be able to predict Y within +/-2800 units. How
good or bad that is, is your judgment.
> I am basically just looking for a value that describes the goodness of fit
> for my non-linear regression model.
> 
> 
> This is probably a pretty obvious question, but I am not a statistician and
> as you said the terminology is sometimes pretty confusing.
> Thanks mike
> 
> -----Urspr?ngliche Nachricht-----
> Von: peter dalgaard [mailto:pdalgd at gmail.com] 
> Gesendet: Samstag, 26. September 2015 01:43
> An: Michael Eisenring <michael.eisenring at gmx.ch>
> Cc: r-help at r-project.org
> Betreff: Re: [R] How to calculate standard error of estimate (S) for my
> non-linear regression model?
> 
> This is one area in which terminology in (computational) statistics has
gone
> a bit crazy. The thing some call "standard error of estimate" is
actually
> the residual standard deviation in the regression model, not to be confused
> with the standard errors that are associated with parameter estimates. In
> summary(nls(...)) (and summary(lm()) for that matter), you'll find it
as
> "residual standard error",  and even that is a bit of a misnomer.
> 
> -pd 
> 
>> On 26 Sep 2015, at 07:08 , Michael Eisenring <michael.eisenring at
gmx.ch>
> wrote:
>> 
>> Hi all,
>> 
>> I am looking for something that indicates the goodness of fit for my 
>> non linear regression model (since R2 is not very reliable).
>> 
>> I read that the standard error of estimate (also known as standard 
>> error of the regression) is a good alternative.
>> 
>> 
>> 
>> The standard error of estimate is described on this page (including 
>> the
>> formula) http://onlinestatbook.com/2/regression/accuracy.html
>>
<https://3c.gmx.net/mail/client/dereferrer?redirectUrl=http%3A%2F%2Fon
>> linest atbook.com%2F2%2Fregression%2Faccuracy.html>
>> 
>> Unfortunately however, I have no clue how to programm it in R. Does 
>> anyone know and could help me?
>> 
>> Thank you very much.
>> 
>> 
>> 
>> I added an example of my model and a dput() of my data
>> 
>> #CODE
>> 
>> dta<-read.csv("Regression_exp2.csv",header=T, sep =
",")
>> attach(dta)      # tells R to do the following analyses on this dataset
>> head(dta)
>> 
>> 
>> 
>> # loading packages: analysis of mixed effect models 
>> library(nls2)#model
>> 
>> #Aim: fit equation to data: y~yo+a*(1-b^x) : Two parameter exp. single 
>> rise to the maximum # y =Gossypol (from my data set) x= Damage_cm 
>> (from my data set) #The other 3 parameters are unknown: yo=Intercept, 
>> a= assymptote ans b=slope
>> 
>> plot(Gossypol~Damage_cm, 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(Gossypol~y0+a*(1-b^Damage_cm), dta,
>>              start=list(y0=0, a=4000, b=.5))
>> 
>> xval <- seq(0, 10, 0.1)
>> lines(xval, predict(dta.nls, data.frame(Damage_cm=xval))) 
>> profile(dta.nls, alpha= .05)
>> 
>> 
>> summary(dta.nls)
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> #INPUT
>> 
>> structure(list(Gossypol = c(948.2418407, 1180.171957, 3589.187889, 
>> 450.7205451, 349.0864019, 592.3403778, 723.885643, 2005.919344, 
>> 720.9785449, 1247.806111, 1079.846532, 1500.863038, 4198.569251, 
>> 3618.448997, 4140.242559, 1036.331811, 1013.807628, 2547.326207, 
>> 2508.417927, 2874.651764, 1120.955, 1782.864308, 1517.045807, 
>> 2287.228752, 4171.427741, 3130.376482, 1504.491931, 6132.876396, 
>> 3350.203452, 5113.942098, 1989.576826, 3470.09352, 4576.787021, 
>> 4854.985845, 1414.161257, 2608.716056, 910.8879471, 2228.522959, 
>> 2952.931863, 5909.068158, 1247.806111, 6982.035521, 2867.610671, 
>> 5629.979049, 6039.995102, 3747.076592, 3743.331903, 4274.324792, 
>> 3378.151945, 3736.144027, 5654.858696, 5972.926124, 3723.629772, 
>> 3322.115942, 3575.043632, 2818.419785), Treatment = structure(c(5L, 
>> 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
>> 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 
>> 3L, 3L, 3L, 2L, 2L, 2L, 4L, 2L, 4L, 4L, 2L, 4L, 2L, 2L, 4L, 4L, 4L, 
>> 4L, 4L, 4L, 2L), .Label = c("1c_2d", "1c_7d",
"3c_2d", "9c_2d", "C"),
>> class = "factor"), Damage_cm = c(0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,
>> 0.142, 0.4035, 0.4435, 0.491, 0.4955, 0.578, 0.5895, 0.6925, 0.6965, 
>> 0.756, 0.8295, 1.0475, 1.313, 1.516, 1.573, 1.62, 1.8115, 1.8185, 
>> 1.8595, 1.989, 2.129, 2.171, 2.3035, 2.411, 2.559, 2.966, 2.974, 
>> 3.211, 3.2665, 3.474, 3.51, 3.547, 4.023, 4.409, 4.516, 4.7245, 4.809, 
>> 4.9835, 5.568, 5.681, 5.683, 7.272, 8.043, 9.437, 9.7455), 
>> Damage_groups = c(0.278, 1.616, 2.501, 3.401, 4.577, 5.644, 7.272, 
>> 8.043, 9.591, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), 
>> Gossypol_Averaged = c(1783.211, 3244.129, 2866.307, 3991.809, 
>> 4468.809, 5121.309, 3723.629772, 3322.115942, 3196.731, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), Groups = c(42006L, 42038L, 
>> 42067L, 42099L, 42130L, 42162L, 42193L, 42225L, 42257L, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), .Names =
c("Gossypol",
>> "Treatment", "Damage_cm",
"Damage_groups", "Gossypol_Averaged",
>> "Groups"), class = "data.frame", row.names = c(NA,
-56L))
>> 
>> 
>> 
>> 
>> 	[[alternative HTML version deleted]]
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see 
>> 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.
> 
> --
> 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
> 
> 
> 
> 
> 
> 
> 
> 
-- 
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

Bert Gunter

2015-Sep-26 16:20 UTC

head link

[R] How to calculate standard error of estimate (S) for my non-linear regression model?

Michael:

You appear to be laboring under the illusion that a single numeric
summary (**any summary**)is a useful measure of model adequacy. It is
not; for details about why not, consult any applied statistics text
(e.g. on regression) and/or post on a statistics site, like
stats.stackexchange.com. Better yet, consult a local statistician.

Incidentally, this is even more the case for NON-linear models. Again,
consult appropriate statistical resources. Even googling on "R^2
inadequate for nonlinear models" brought up some interesting
resources, among them:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2892436/

Cheers,
Bert

Bert Gunter

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
   -- Clifford Stoll


On Sat, Sep 26, 2015 at 8:56 AM, peter dalgaard <pdalgd at gmail.com>
wrote:>
>> On 26 Sep 2015, at 16:46 , Michael Eisenring <michael.eisenring at
gmx.ch> wrote:
>>
>> Dear Peter,
>> Thank you for your answer.
>> If I look at my summary I see there a Residual standard error: 1394 on
53
>> degrees of freedom.
>> This number is very high (the fit of the curve is pretty bad I know but
>> still...). Are you sure the residual standard error given in the
summary is
>> the same as the one described on this page:
>> http://onlinestatbook.com/2/regression/accuracy.html
>
> Sure I'm sure (& I did check!)... But notice that unlike R^2,
Residual SE is not dimensionless. Switch from millimeters to meters in your
response measure and the Residual SE instantly turns into 1.394. It's
basically saying that your model claims to be able to predict Y within +/-2800
units. How good or bad that is, is your judgment.
>
>> I am basically just looking for a value that describes the goodness of
fit
>> for my non-linear regression model.
>>
>>
>> This is probably a pretty obvious question, but I am not a statistician
and
>> as you said the terminology is sometimes pretty confusing.
>> Thanks mike
>>
>> -----Urspr?ngliche Nachricht-----
>> Von: peter dalgaard [mailto:pdalgd at gmail.com]
>> Gesendet: Samstag, 26. September 2015 01:43
>> An: Michael Eisenring <michael.eisenring at gmx.ch>
>> Cc: r-help at r-project.org
>> Betreff: Re: [R] How to calculate standard error of estimate (S) for my
>> non-linear regression model?
>>
>> This is one area in which terminology in (computational) statistics has
gone
>> a bit crazy. The thing some call "standard error of estimate"
is actually
>> the residual standard deviation in the regression model, not to be
confused
>> with the standard errors that are associated with parameter estimates.
In
>> summary(nls(...)) (and summary(lm()) for that matter), you'll find
it as
>> "residual standard error",  and even that is a bit of a
misnomer.
>>
>> -pd
>>
>>> On 26 Sep 2015, at 07:08 , Michael Eisenring <michael.eisenring
at gmx.ch>
>> wrote:
>>>
>>> Hi all,
>>>
>>> I am looking for something that indicates the goodness of fit for
my
>>> non linear regression model (since R2 is not very reliable).
>>>
>>> I read that the standard error of estimate (also known as standard
>>> error of the regression) is a good alternative.
>>>
>>>
>>>
>>> The standard error of estimate is described on this page (including
>>> the
>>> formula) http://onlinestatbook.com/2/regression/accuracy.html
>>>
<https://3c.gmx.net/mail/client/dereferrer?redirectUrl=http%3A%2F%2Fon
>>> linest atbook.com%2F2%2Fregression%2Faccuracy.html>
>>>
>>> Unfortunately however, I have no clue how to programm it in R. Does
>>> anyone know and could help me?
>>>
>>> Thank you very much.
>>>
>>>
>>>
>>> I added an example of my model and a dput() of my data
>>>
>>> #CODE
>>>
>>> dta<-read.csv("Regression_exp2.csv",header=T, sep =
",")
>>> attach(dta)      # tells R to do the following analyses on this
dataset
>>> head(dta)
>>>
>>>
>>>
>>> # loading packages: analysis of mixed effect models
>>> library(nls2)#model
>>>
>>> #Aim: fit equation to data: y~yo+a*(1-b^x) : Two parameter exp.
single
>>> rise to the maximum # y =Gossypol (from my data set) x= Damage_cm
>>> (from my data set) #The other 3 parameters are unknown:
yo=Intercept,
>>> a= assymptote ans b=slope
>>>
>>> plot(Gossypol~Damage_cm, 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(Gossypol~y0+a*(1-b^Damage_cm),
dta,
>>>              start=list(y0=0, a=4000, b=.5))
>>>
>>> xval <- seq(0, 10, 0.1)
>>> lines(xval, predict(dta.nls, data.frame(Damage_cm=xval)))
>>> profile(dta.nls, alpha= .05)
>>>
>>>
>>> summary(dta.nls)
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>> #INPUT
>>>
>>> structure(list(Gossypol = c(948.2418407, 1180.171957, 3589.187889,
>>> 450.7205451, 349.0864019, 592.3403778, 723.885643, 2005.919344,
>>> 720.9785449, 1247.806111, 1079.846532, 1500.863038, 4198.569251,
>>> 3618.448997, 4140.242559, 1036.331811, 1013.807628, 2547.326207,
>>> 2508.417927, 2874.651764, 1120.955, 1782.864308, 1517.045807,
>>> 2287.228752, 4171.427741, 3130.376482, 1504.491931, 6132.876396,
>>> 3350.203452, 5113.942098, 1989.576826, 3470.09352, 4576.787021,
>>> 4854.985845, 1414.161257, 2608.716056, 910.8879471, 2228.522959,
>>> 2952.931863, 5909.068158, 1247.806111, 6982.035521, 2867.610671,
>>> 5629.979049, 6039.995102, 3747.076592, 3743.331903, 4274.324792,
>>> 3378.151945, 3736.144027, 5654.858696, 5972.926124, 3723.629772,
>>> 3322.115942, 3575.043632, 2818.419785), Treatment = structure(c(5L,
>>> 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>>> 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
>>> 3L, 3L, 3L, 2L, 2L, 2L, 4L, 2L, 4L, 4L, 2L, 4L, 2L, 2L, 4L, 4L, 4L,
>>> 4L, 4L, 4L, 2L), .Label = c("1c_2d", "1c_7d",
"3c_2d", "9c_2d", "C"),
>>> class = "factor"), Damage_cm = c(0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0,
>>> 0.142, 0.4035, 0.4435, 0.491, 0.4955, 0.578, 0.5895, 0.6925,
0.6965,
>>> 0.756, 0.8295, 1.0475, 1.313, 1.516, 1.573, 1.62, 1.8115, 1.8185,
>>> 1.8595, 1.989, 2.129, 2.171, 2.3035, 2.411, 2.559, 2.966, 2.974,
>>> 3.211, 3.2665, 3.474, 3.51, 3.547, 4.023, 4.409, 4.516, 4.7245,
4.809,
>>> 4.9835, 5.568, 5.681, 5.683, 7.272, 8.043, 9.437, 9.7455),
>>> Damage_groups = c(0.278, 1.616, 2.501, 3.401, 4.577, 5.644, 7.272,
>>> 8.043, 9.591, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),
>>> Gossypol_Averaged = c(1783.211, 3244.129, 2866.307, 3991.809,
>>> 4468.809, 5121.309, 3723.629772, 3322.115942, 3196.731, NA, NA, NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), Groups = c(42006L, 42038L,
>>> 42067L, 42099L, 42130L, 42162L, 42193L, 42225L, 42257L, NA, NA, NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), .Names =
c("Gossypol",
>>> "Treatment", "Damage_cm",
"Damage_groups", "Gossypol_Averaged",
>>> "Groups"), class = "data.frame", row.names =
c(NA, -56L))
>>>
>>>
>>>
>>>
>>>      [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
>>> 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.
>>
>> --
>> 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
>>
>>
>>
>>
>>
>>
>>
>>
>
> --
> 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
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.

Jeff Newmiller

2015-Sep-26 20:26 UTC

head link

[R] How to calculate standard error of estimate (S) for my non-linear regression model?

You may not be a statistician, but you should at least learn about the 
calculations you are making. You cannot expect to convince others that 
your calculations are right just because "Peter on the internet said they 
were right".

To give you a gentle push in this direction, I have reproduced the 
calculations on that reference web page using R, so you can get a head 
start on understanding how to perform them on your data. (Hint: about all 
you should need to do is give your dta.nls to predict and use your 
column names instead of X and Y.) Once you have convinced yourself that
the pre-defined functions are doing what you expect, then you can omit the 
do-it-yourself option with confidence in the results.

Please note that no use of attach is included here... that usually ends in 
unhappiness at some point, so prefer to use the data argument instead.

###
dta <- data.frame( X=c(1,2,3,4,5), Y=c(1,2,1.3,3.75,2.25) )
nrow( dta )
# linear regression
y.lm <- lm( Y~X, data=dta )
# compute predictions from original data
## Be aware that you can also "predict" using a nonlinear regression
fit
## Also be aware that you can compute estimates using different data if you
## specify the "newdata" argument... see the help for predict.lm
## ?predict.lm
dta$Yprime <- predict( y.lm )
# ?with
dta$YlessYprime <- with( dta, Y - Yprime )
dta$YlessYprime2 <- with( dta, YlessYprime^2 )

# confirm sums
# ?sum
sum( dta$X )
sum( dta$Y )
sum( dta$Yprime )
sum( dta$YlessYprime )
sum( dta$YlessYprime2 )

# standard error of the estimate for population data
sigma.est <- sqrt( sum( dta$YlessYprime2 ) / nrow( dta ) )
sigma.est
# sd function assumes sample standard deviation, can correct the result if 
# you want
# ?sd
# ?all.equal
all.equal( sigma.est, sd( dta$YlessYprime ) * sqrt( ( nrow( dta ) - 1 ) / 
nrow( dta ) ) )

# alternate formulation
SSY <- sum( ( dta$Y - mean( dta$Y ) )^2 )
rho <- with( dta, cor( Y, X ) )
all.equal( sigma.est, sqrt( (1-rho^2)*SSY/nrow(dta) ) )

# when working with a sample...
s.est <- sqrt( sum( dta$YlessYprime2 ) / ( nrow( dta ) - 2 ) )
s.est

####> dta <- data.frame( X=c(1,2,3,4,5), Y=c(1,2,1.3,3.75,2.25) )
> nrow( dta )
[1] 5> # linear regression
> y.lm <- lm( Y~X, data=dta )
> # compute predictions from original data
> ## Be aware that you can also "predict" using a nonlinear
regression fit
> ## Also be aware that you can compute estimates using different data if you
> ## specify the "newdata" argument... see the help for predict.lm
> ## ?predict.lm
> dta$Yprime <- predict( y.lm )
> # ?with
> dta$YlessYprime <- with( dta, Y - Yprime )
> dta$YlessYprime2 <- with( dta, YlessYprime^2 )
>
> # confirm sums
> # ?sum
> sum( dta$X )
[1] 15> sum( dta$Y )
[1] 10.3> sum( dta$Yprime )
[1] 10.3> sum( dta$YlessYprime )
[1] 2.220446e-16> sum( dta$YlessYprime2 )
[1] 2.79075>
> # standard error of the estimate for population data
> sigma.est <- sqrt( sum( dta$YlessYprime2 ) / nrow( dta ) )
> sigma.est
[1] 0.7470944> # sd function assumes sample standard deviation, can correct the result 
> # if you want
> # ?sd
> # ?all.equal
> all.equal( sigma.est, sd( dta$YlessYprime ) * sqrt( ( nrow( dta ) - 1 ) / nrow( dta ) ) )
[1] TRUE>
> # alternate formulation
> SSY <- sum( ( dta$Y - mean( dta$Y ) )^2 )
> rho <- with( dta, cor( Y, X ) )
> all.equal( sigma.est, sqrt( (1-rho^2)*SSY/nrow(dta) ) )
[1] TRUE>
> # when working with a sample...
> s.est <- sqrt( sum( dta$YlessYprime2 ) / ( nrow( dta ) - 2 ) )
> s.est
[1] 0.9644947>

On Sat, 26 Sep 2015, Michael Eisenring wrote:
> Dear Peter,
> Thank you for your answer.
> If I look at my summary I see there a Residual standard error: 1394 on 53
> degrees of freedom.
> This number is very high (the fit of the curve is pretty bad I know but
> still...). Are you sure the residual standard error given in the summary is
> the same as the one described on this page:
> http://onlinestatbook.com/2/regression/accuracy.html
> I am basically just looking for a value that describes the goodness of fit
> for my non-linear regression model.
>
>
> This is probably a pretty obvious question, but I am not a statistician and
> as you said the terminology is sometimes pretty confusing.
> Thanks mike
>
> -----Urspr?ngliche Nachricht-----
> Von: peter dalgaard [mailto:pdalgd at gmail.com]
> Gesendet: Samstag, 26. September 2015 01:43
> An: Michael Eisenring <michael.eisenring at gmx.ch>
> Cc: r-help at r-project.org
> Betreff: Re: [R] How to calculate standard error of estimate (S) for my
> non-linear regression model?
>
> This is one area in which terminology in (computational) statistics has
gone
> a bit crazy. The thing some call "standard error of estimate" is
actually
> the residual standard deviation in the regression model, not to be confused
> with the standard errors that are associated with parameter estimates. In
> summary(nls(...)) (and summary(lm()) for that matter), you'll find it
as
> "residual standard error",  and even that is a bit of a misnomer.
>
> -pd
>
>> On 26 Sep 2015, at 07:08 , Michael Eisenring <michael.eisenring at
gmx.ch>
> wrote:
>>
>> Hi all,
>>
>> I am looking for something that indicates the goodness of fit for my
>> non linear regression model (since R2 is not very reliable).
>>
>> I read that the standard error of estimate (also known as standard
>> error of the regression) is a good alternative.
>>
>>
>>
>> The standard error of estimate is described on this page (including
>> the
>> formula) http://onlinestatbook.com/2/regression/accuracy.html
>>
<https://3c.gmx.net/mail/client/dereferrer?redirectUrl=http%3A%2F%2Fon
>> linest atbook.com%2F2%2Fregression%2Faccuracy.html>
>>
>> Unfortunately however, I have no clue how to programm it in R. Does
>> anyone know and could help me?
>>
>> Thank you very much.
>>
>>
>>
>> I added an example of my model and a dput() of my data
>>
>> #CODE
>>
>> dta<-read.csv("Regression_exp2.csv",header=T, sep =
",")
>> attach(dta)      # tells R to do the following analyses on this dataset
>> head(dta)
>>
>>
>>
>> # loading packages: analysis of mixed effect models
>> library(nls2)#model
>>
>> #Aim: fit equation to data: y~yo+a*(1-b^x) : Two parameter exp. single
>> rise to the maximum # y =Gossypol (from my data set) x= Damage_cm
>> (from my data set) #The other 3 parameters are unknown: yo=Intercept,
>> a= assymptote ans b=slope
>>
>> plot(Gossypol~Damage_cm, 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(Gossypol~y0+a*(1-b^Damage_cm), dta,
>>               start=list(y0=0, a=4000, b=.5))
>>
>> xval <- seq(0, 10, 0.1)
>> lines(xval, predict(dta.nls, data.frame(Damage_cm=xval)))
>> profile(dta.nls, alpha= .05)
>>
>>
>> summary(dta.nls)
>>
>>
>>
>>
>>
>>
>>
>> #INPUT
>>
>> structure(list(Gossypol = c(948.2418407, 1180.171957, 3589.187889,
>> 450.7205451, 349.0864019, 592.3403778, 723.885643, 2005.919344,
>> 720.9785449, 1247.806111, 1079.846532, 1500.863038, 4198.569251,
>> 3618.448997, 4140.242559, 1036.331811, 1013.807628, 2547.326207,
>> 2508.417927, 2874.651764, 1120.955, 1782.864308, 1517.045807,
>> 2287.228752, 4171.427741, 3130.376482, 1504.491931, 6132.876396,
>> 3350.203452, 5113.942098, 1989.576826, 3470.09352, 4576.787021,
>> 4854.985845, 1414.161257, 2608.716056, 910.8879471, 2228.522959,
>> 2952.931863, 5909.068158, 1247.806111, 6982.035521, 2867.610671,
>> 5629.979049, 6039.995102, 3747.076592, 3743.331903, 4274.324792,
>> 3378.151945, 3736.144027, 5654.858696, 5972.926124, 3723.629772,
>> 3322.115942, 3575.043632, 2818.419785), Treatment = structure(c(5L,
>> 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
>> 1L, 1L, 1L, 1L, 1L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
>> 3L, 3L, 3L, 2L, 2L, 2L, 4L, 2L, 4L, 4L, 2L, 4L, 2L, 2L, 4L, 4L, 4L,
>> 4L, 4L, 4L, 2L), .Label = c("1c_2d", "1c_7d",
"3c_2d", "9c_2d", "C"),
>> class = "factor"), Damage_cm = c(0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0,
>> 0.142, 0.4035, 0.4435, 0.491, 0.4955, 0.578, 0.5895, 0.6925, 0.6965,
>> 0.756, 0.8295, 1.0475, 1.313, 1.516, 1.573, 1.62, 1.8115, 1.8185,
>> 1.8595, 1.989, 2.129, 2.171, 2.3035, 2.411, 2.559, 2.966, 2.974,
>> 3.211, 3.2665, 3.474, 3.51, 3.547, 4.023, 4.409, 4.516, 4.7245, 4.809,
>> 4.9835, 5.568, 5.681, 5.683, 7.272, 8.043, 9.437, 9.7455),
>> Damage_groups = c(0.278, 1.616, 2.501, 3.401, 4.577, 5.644, 7.272,
>> 8.043, 9.591, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),
>> Gossypol_Averaged = c(1783.211, 3244.129, 2866.307, 3991.809,
>> 4468.809, 5121.309, 3723.629772, 3322.115942, 3196.731, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA), Groups = c(42006L, 42038L,
>> 42067L, 42099L, 42130L, 42162L, 42193L, 42225L, 42257L, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
>> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), .Names =
c("Gossypol",
>> "Treatment", "Damage_cm",
"Damage_groups", "Gossypol_Averaged",
>> "Groups"), class = "data.frame", row.names = c(NA,
-56L))
>>
>>
>>
>>
>> 	[[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> 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.
>
> --
> 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
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.
>
---------------------------------------------------------------------------
Jeff Newmiller                        The     .....       .....  Go Live...
DCN:<jdnewmil at dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live
Go...
                                       Live:   OO#.. Dead: OO#..  Playing
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R help - Sep 2015 - How to calculate standard error of estimate (S) for my non-linear regression model?

[R] How to calculate standard error of estimate (S) for my non-linear regression model?

[R] How to calculate standard error of estimate (S) for my non-linear regression model?

[R] How to calculate standard error of estimate (S) for my non-linear regression model?

[R] How to calculate standard error of estimate (S) for my non-linear regression model?