Re: [R] physical constraint with gam

[Dominik Schneider]

Thanks for the clarification!

On Sat, May 14, 2016 at 1:24 AM, Simon Wood  wrote:

> On 12/05/16 02:29, Dominik Schneider wrote:
>
> Hi again,
> I'm looking for some clarification on 2 things.
> 1. On that last note, I realize that s(x1,x2) would be the other obvious
> interaction to compare with - and I see that you recommend te(x1,x2) if
> they are not on the same scale.
>
> - yes that's right, s(x1,x2) gives an isotropic smooth, which is usually
> only appropriate if x1 and x2 are naturally on the same scale.
>
> 2. If s(x1,by=x1) gives you a "parameter" value similar to a GLM when you
> plot s(x1):x1, why does my function above return the same yhat as
> predict(mdl,type='response') ?  Shouldn't each of the terms need to be
> multiplied by the variable value before applying
> rowSums()+attr(sterms,'constant') ??
>
> predict returns s(x1)*x1 (plot.gam just plots s(x1), because in general
> s(x1,by=x2) is not smooth). If you want to get s(x1) on its own you need to
> do something like this:
>
> x2 <- x1 ## copy x1
> m <- gam(y~s(x1,by=x2)) ## model implementing s(x1,by=x1) using copy of x1
> predict(m,data.frame(x1=x1,x2=rep(1,length(x2))),type="terms") ## now
> predicted s(x1)*x2 = s(x1)
>
> best,
> Simon
>
>
> Thanks again
> Dominik
>
> On Wed, May 11, 2016 at 10:11 AM, Dominik Schneider <
> dominik.schnei...@colorado.edu> wrote:
>
>> Hi Simon, Thanks for this explanation.
>> To make sure I understand, another way of explaining the y axis in my
>> original example is that it is the contribution to snowdepth relative to
>> the other variables (the example only had fsca, but my actual case has a
>> couple others). i.e. a negative s(fsca) of -0.5 simply means snowdepth 0.5
>> units below the intercept+s(x_i), where s(x_i) could also be negative in
>> the case where total snowdepth is less than the intercept value.
>>
>> The use of by=fsca is really useful for interpreting the marginal impact
>> of the different variables. With my actual data, the term s(fsca):fsca is
>> never negative, which is much more intuitive. Is it appropriate to compare
>> magnitudes of e.g. s(x2):x2 / mean(x2) and s(x2):x2 / mean(x2)  where
>> mean(x_i) are the mean of the actual data?
>>
>> Lastly, how would these two differ: s(x1,by=x2); or
>> s(x1,by=x1)*s(x2,by=x2) since interactions are surely present and i'm not
>> sure if a linear combination is enough.
>>
>> Thanks!
>> Dominik
>>
>>
>> On Wed, May 11, 2016 at 3:11 AM, Simon Wood < 
>> simon.w...@bath.edu> wrote:
>>
>>> The spline having a positive value is not the same as a glm coefficient
>>> having a positive value. When you plot a smooth, say s(x), that is
>>> equivalent to plotting the line 'beta * x' in a GLM. It is not equivalent
>>> to plotting 'beta'. The smooths in a gam are (usually) subject to
>>> `sum-to-zero' identifiability constraints to avoid confounding via the
>>> intercept, so they are bound to be negative over some part of the covariate
>>> range. For example, if I have a model y ~ s(x) + s(z), I can't estimate the
>>> mean level for s(x) and the mean level for s(z) as they are completely
>>> confounded, and confounded with the model intercept term.
>>>
>>> I suppose that if you want to interpret the smooths as glm parameters
>>> varying with the covariate they relate to then you can do, by setting the
>>> model up as a varying coefficient model, using the `by' argument to 's'...
>>>
>>> gam(snowdepth~s(fsca,by=fsca),data=dat)
>>>
>>>
>>> this model is `snowdepth_i = f(fsca_i) * fsca_i + e_i' . s(fsca,by=fsca)
>>> is not confounded with the intercept, so no constraint is needed or
>>> applied, and you can now interpret the smooth like a local GLM coefficient.
>>>
>>> best,
>>> Simon
>>>
>>>
>>>
>>>
>>> On 11/05/16 01:30, Dominik Schneider wrote:
>>>
 Hi,
 Just getting into using GAM using the mgcv package. I've generated some
 models and extracted the splines for each of the variables and started
 visualizing them. I'm noticing that one of my variables is physically
 unrealistic.

 In the example below, my interpretation of the following plot is that
 the
 y-axis is basically the equivalent of a "parameter" value of a GLM; in
 GAM
 this value can change as the functional relationship changes between x
 and
 y. In my case, I am predicting snowdepth based on the fractional snow
 covered area. In no case will snowdepth realistically decrease for a
 unit
 increase in fsca so my question is: *Is there a way to constrain the
 spline
 to positive values? *

 Thanks
 Dominik

 library(mgcv)
 library(dplyr)
 library(ggplot2)
 extract_splines=function(mdl){
sterms=predict(mdl,type='terms')
datplot=cbind(sterms,mdl$model) %>% tbl_df
datplot$intercept=attr(sterms,'constant')
datplot$yhat=rowSums(sterms)+attr(sterms,'constant')
return(datplot)
 }

Re: [R] physical constraint with gam

[Simon Wood]

On 12/05/16 02:29, Dominik Schneider wrote:
> Hi again,
> I'm looking for some clarification on 2 things.
> 1. On that last note, I realize that s(x1,x2) would be the other 
> obvious interaction to compare with - and I see that you recommend 
> te(x1,x2) if they are not on the same scale.
- yes that's right, s(x1,x2) gives an isotropic smooth, which is usually 
only appropriate if x1 and x2 are naturally on the same scale.

> 2. If s(x1,by=x1) gives you a "parameter" value similar to a GLM when 
> you plot s(x1):x1, why does my function above return the same yhat as 
> predict(mdl,type='response') ? Shouldn't each of the terms need to be 
> multiplied by the variable value before applying 
> rowSums()+attr(sterms,'constant') ??
predict returns s(x1)*x1 (plot.gam just plots s(x1), because in general 
s(x1,by=x2) is not smooth). If you want to get s(x1) on its own you need 
to do something like this:

x2 <- x1 ## copy x1
m <- gam(y~s(x1,by=x2)) ## model implementing s(x1,by=x1) using copy of x1
predict(m,data.frame(x1=x1,x2=rep(1,length(x2))),type="terms") ## now 
predicted s(x1)*x2 = s(x1)

best,
Simon

> Thanks again
> Dominik
>
> On Wed, May 11, 2016 at 10:11 AM, Dominik Schneider 
>  > wrote:
>
> Hi Simon, Thanks for this explanation.
> To make sure I understand, another way of explaining the y axis in
> my original example is that it is the contribution to snowdepth
> relative to the other variables (the example only had fsca, but my
> actual case has a couple others). i.e. a negative s(fsca) of -0.5
> simply means snowdepth 0.5 units below the intercept+s(x_i), where
> s(x_i) could also be negative in the case where total snowdepth is
> less than the intercept value.
>
> The use of by=fsca is really useful for interpreting the marginal
> impact of the different variables. With my actual data, the term
> s(fsca):fsca is never negative, which is much more intuitive. Is
> it appropriate to compare magnitudes of e.g. s(x2):x2 / mean(x2)
> and s(x2):x2 / mean(x2)  where mean(x_i) are the mean of the
> actual data?
>
> Lastly, how would these two differ: s(x1,by=x2); or
> s(x1,by=x1)*s(x2,by=x2) since interactions are surely present and
> i'm not sure if a linear combination is enough.
>
> Thanks!
> Dominik
>
>
> On Wed, May 11, 2016 at 3:11 AM, Simon Wood  > wrote:
>
> The spline having a positive value is not the same as a glm
> coefficient having a positive value. When you plot a smooth,
> say s(x), that is equivalent to plotting the line 'beta * x'
> in a GLM. It is not equivalent to plotting 'beta'. The smooths
> in a gam are (usually) subject to `sum-to-zero'
> identifiability constraints to avoid confounding via the
> intercept, so they are bound to be negative over some part of
> the covariate range. For example, if I have a model y ~ s(x) +
> s(z), I can't estimate the mean level for s(x) and the mean
> level for s(z) as they are completely confounded, and
> confounded with the model intercept term.
>
> I suppose that if you want to interpret the smooths as glm
> parameters varying with the covariate they relate to then you
> can do, by setting the model up as a varying coefficient
> model, using the `by' argument to 's'...
>
> gam(snowdepth~s(fsca,by=fsca),data=dat)
>
>
> this model is `snowdepth_i = f(fsca_i) * fsca_i + e_i' .
> s(fsca,by=fsca) is not confounded with the intercept, so no
> constraint is needed or applied, and you can now interpret the
> smooth like a local GLM coefficient.
>
> best,
> Simon
>
>
>
>
> On 11/05/16 01:30, Dominik Schneider wrote:
>
> Hi,
> Just getting into using GAM using the mgcv package. I've
> generated some
> models and extracted the splines for each of the variables
> and started
> visualizing them. I'm noticing that one of my variables is
> physically
> unrealistic.
>
> In the example below, my interpretation of the following
> plot is that the
> y-axis is basically the equivalent of a "parameter" value
> of a GLM; in GAM
> this value can change as the functional relationship
> changes between x and
> y. In my case, I am predicting snowdepth based on the
> fractional snow
> covered area. In no case will snowdepth realistically
> decrease for a unit
> increase in fsca so my question is: *Is there a way to
> constrain the spline
> to positive values? *
>
> Thanks
> Dominik
>
> library(mgcv)
>   

Re: [R] physical constraint with gam

[Simon Wood]

On 11/05/16 17:11, Dominik Schneider wrote:
> Hi Simon, Thanks for this explanation.
> To make sure I understand, another way of explaining the y axis in my 
> original example is that it is the contribution to snowdepth relative 
> to the other variables (the example only had fsca, but my actual case 
> has a couple others). i.e. a negative s(fsca) of -0.5 simply means 
> snowdepth 0.5 units below the intercept+s(x_i), where s(x_i) could 
> also be negative in the case where total snowdepth is less than the 
> intercept value.
>
- Yes, this looks right.

> The use of by=fsca is really useful for interpreting the marginal 
> impact of the different variables. With my actual data, the term 
> s(fsca):fsca is never negative, which is much more intuitive. Is it 
> appropriate to compare magnitudes of e.g. s(x2):x2 / mean(x2) and 
> s(x2):x2 / mean(x2)  where mean(x_i) are the mean of the actual data?
>
- I guess so (similarly to lm/glm).

> Lastly, how would these two differ: s(x1,by=x2); or 
> s(x1,by=x1)*s(x2,by=x2) since interactions are surely present and i'm 
> not sure if a linear combination is enough.
>
- you'd probably use te(x1,x2) unless x1 and x2 are really on the same 
scale, in which case s(x1,x2) might be appropriate. The `by' variable 
trick is probably not going to work so well for interactions, however 
(it's not so clear what the by variable should be).


-- 
Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
+44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190


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Re: [R] physical constraint with gam

[Dominik Schneider]

Hi again,
I'm looking for some clarification on 2 things.
1. On that last note, I realize that s(x1,x2) would be the other obvious
interaction to compare with - and I see that you recommend te(x1,x2) if
they are not on the same scale.
2. If s(x1,by=x1) gives you a "parameter" value similar to a GLM when you
plot s(x1):x1, why does my function above return the same yhat as
predict(mdl,type='response') ?  Shouldn't each of the terms need to be
multiplied by the variable value before applying
rowSums()+attr(sterms,'constant') ??
Thanks again
Dominik

On Wed, May 11, 2016 at 10:11 AM, Dominik Schneider <
dominik.schnei...@colorado.edu> wrote:

> Hi Simon, Thanks for this explanation.
> To make sure I understand, another way of explaining the y axis in my
> original example is that it is the contribution to snowdepth relative to
> the other variables (the example only had fsca, but my actual case has a
> couple others). i.e. a negative s(fsca) of -0.5 simply means snowdepth 0.5
> units below the intercept+s(x_i), where s(x_i) could also be negative in
> the case where total snowdepth is less than the intercept value.
>
> The use of by=fsca is really useful for interpreting the marginal impact
> of the different variables. With my actual data, the term s(fsca):fsca is
> never negative, which is much more intuitive. Is it appropriate to compare
> magnitudes of e.g. s(x2):x2 / mean(x2) and s(x2):x2 / mean(x2)  where
> mean(x_i) are the mean of the actual data?
>
> Lastly, how would these two differ: s(x1,by=x2); or
> s(x1,by=x1)*s(x2,by=x2) since interactions are surely present and i'm not
> sure if a linear combination is enough.
>
> Thanks!
> Dominik
>
>
> On Wed, May 11, 2016 at 3:11 AM, Simon Wood  wrote:
>
>> The spline having a positive value is not the same as a glm coefficient
>> having a positive value. When you plot a smooth, say s(x), that is
>> equivalent to plotting the line 'beta * x' in a GLM. It is not equivalent
>> to plotting 'beta'. The smooths in a gam are (usually) subject to
>> `sum-to-zero' identifiability constraints to avoid confounding via the
>> intercept, so they are bound to be negative over some part of the covariate
>> range. For example, if I have a model y ~ s(x) + s(z), I can't estimate the
>> mean level for s(x) and the mean level for s(z) as they are completely
>> confounded, and confounded with the model intercept term.
>>
>> I suppose that if you want to interpret the smooths as glm parameters
>> varying with the covariate they relate to then you can do, by setting the
>> model up as a varying coefficient model, using the `by' argument to 's'...
>>
>> gam(snowdepth~s(fsca,by=fsca),data=dat)
>>
>>
>> this model is `snowdepth_i = f(fsca_i) * fsca_i + e_i' . s(fsca,by=fsca)
>> is not confounded with the intercept, so no constraint is needed or
>> applied, and you can now interpret the smooth like a local GLM coefficient.
>>
>> best,
>> Simon
>>
>>
>>
>>
>> On 11/05/16 01:30, Dominik Schneider wrote:
>>
>>> Hi,
>>> Just getting into using GAM using the mgcv package. I've generated some
>>> models and extracted the splines for each of the variables and started
>>> visualizing them. I'm noticing that one of my variables is physically
>>> unrealistic.
>>>
>>> In the example below, my interpretation of the following plot is that the
>>> y-axis is basically the equivalent of a "parameter" value of a GLM; in
>>> GAM
>>> this value can change as the functional relationship changes between x
>>> and
>>> y. In my case, I am predicting snowdepth based on the fractional snow
>>> covered area. In no case will snowdepth realistically decrease for a unit
>>> increase in fsca so my question is: *Is there a way to constrain the
>>> spline
>>> to positive values? *
>>>
>>> Thanks
>>> Dominik
>>>
>>> library(mgcv)
>>> library(dplyr)
>>> library(ggplot2)
>>> extract_splines=function(mdl){
>>>sterms=predict(mdl,type='terms')
>>>datplot=cbind(sterms,mdl$model) %>% tbl_df
>>>datplot$intercept=attr(sterms,'constant')
>>>datplot$yhat=rowSums(sterms)+attr(sterms,'constant')
>>>return(datplot)
>>> }
>>> dat=data_frame(snowdepth=runif(100,min =
>>> 0.001,max=6.7),fsca=runif(100,0.01,.99))
>>> mdl=gam(snowdepth~s(fsca),data=dat)
>>> termdF=extract_splines(mdl)
>>> ggplot(termdF)+
>>>geom_line(aes(x=fsca,y=`s(fsca)`))
>>>
>>> [[alternative HTML version deleted]]
>>>
>>> __
>>> R-help@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.
>>>
>>
>>
>> --
>> Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
>> +44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190
>>
>>
>

[[alternative HTML version deleted]]

__
R-help@r-project.org 

Re: [R] physical constraint with gam

[Dominik Schneider]

Hi Simon, Thanks for this explanation.
To make sure I understand, another way of explaining the y axis in my
original example is that it is the contribution to snowdepth relative to
the other variables (the example only had fsca, but my actual case has a
couple others). i.e. a negative s(fsca) of -0.5 simply means snowdepth 0.5
units below the intercept+s(x_i), where s(x_i) could also be negative in
the case where total snowdepth is less than the intercept value.

The use of by=fsca is really useful for interpreting the marginal impact of
the different variables. With my actual data, the term s(fsca):fsca is
never negative, which is much more intuitive. Is it appropriate to compare
magnitudes of e.g. s(x2):x2 / mean(x2) and s(x2):x2 / mean(x2)  where
mean(x_i) are the mean of the actual data?

Lastly, how would these two differ: s(x1,by=x2); or s(x1,by=x1)*s(x2,by=x2)
since interactions are surely present and i'm not sure if a linear
combination is enough.

Thanks!
Dominik


On Wed, May 11, 2016 at 3:11 AM, Simon Wood  wrote:

> The spline having a positive value is not the same as a glm coefficient
> having a positive value. When you plot a smooth, say s(x), that is
> equivalent to plotting the line 'beta * x' in a GLM. It is not equivalent
> to plotting 'beta'. The smooths in a gam are (usually) subject to
> `sum-to-zero' identifiability constraints to avoid confounding via the
> intercept, so they are bound to be negative over some part of the covariate
> range. For example, if I have a model y ~ s(x) + s(z), I can't estimate the
> mean level for s(x) and the mean level for s(z) as they are completely
> confounded, and confounded with the model intercept term.
>
> I suppose that if you want to interpret the smooths as glm parameters
> varying with the covariate they relate to then you can do, by setting the
> model up as a varying coefficient model, using the `by' argument to 's'...
>
> gam(snowdepth~s(fsca,by=fsca),data=dat)
>
>
> this model is `snowdepth_i = f(fsca_i) * fsca_i + e_i' . s(fsca,by=fsca)
> is not confounded with the intercept, so no constraint is needed or
> applied, and you can now interpret the smooth like a local GLM coefficient.
>
> best,
> Simon
>
>
>
>
> On 11/05/16 01:30, Dominik Schneider wrote:
>
>> Hi,
>> Just getting into using GAM using the mgcv package. I've generated some
>> models and extracted the splines for each of the variables and started
>> visualizing them. I'm noticing that one of my variables is physically
>> unrealistic.
>>
>> In the example below, my interpretation of the following plot is that the
>> y-axis is basically the equivalent of a "parameter" value of a GLM; in GAM
>> this value can change as the functional relationship changes between x and
>> y. In my case, I am predicting snowdepth based on the fractional snow
>> covered area. In no case will snowdepth realistically decrease for a unit
>> increase in fsca so my question is: *Is there a way to constrain the
>> spline
>> to positive values? *
>>
>> Thanks
>> Dominik
>>
>> library(mgcv)
>> library(dplyr)
>> library(ggplot2)
>> extract_splines=function(mdl){
>>sterms=predict(mdl,type='terms')
>>datplot=cbind(sterms,mdl$model) %>% tbl_df
>>datplot$intercept=attr(sterms,'constant')
>>datplot$yhat=rowSums(sterms)+attr(sterms,'constant')
>>return(datplot)
>> }
>> dat=data_frame(snowdepth=runif(100,min =
>> 0.001,max=6.7),fsca=runif(100,0.01,.99))
>> mdl=gam(snowdepth~s(fsca),data=dat)
>> termdF=extract_splines(mdl)
>> ggplot(termdF)+
>>geom_line(aes(x=fsca,y=`s(fsca)`))
>>
>> [[alternative HTML version deleted]]
>>
>> __
>> R-help@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.
>>
>
>
> --
> Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
> +44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190
>
>

[[alternative HTML version deleted]]

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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Re: [R] physical constraint with gam

[Simon Wood]

The spline having a positive value is not the same as a glm coefficient 
having a positive value. When you plot a smooth, say s(x), that is 
equivalent to plotting the line 'beta * x' in a GLM. It is not 
equivalent to plotting 'beta'. The smooths in a gam are (usually) 
subject to `sum-to-zero' identifiability constraints to avoid 
confounding via the intercept, so they are bound to be negative over 
some part of the covariate range. For example, if I have a model y ~ 
s(x) + s(z), I can't estimate the mean level for s(x) and the mean level 
for s(z) as they are completely confounded, and confounded with the 
model intercept term.


I suppose that if you want to interpret the smooths as glm parameters 
varying with the covariate they relate to then you can do, by setting 
the model up as a varying coefficient model, using the `by' argument to 
's'...


gam(snowdepth~s(fsca,by=fsca),data=dat)


this model is `snowdepth_i = f(fsca_i) * fsca_i + e_i' . s(fsca,by=fsca) 
is not confounded with the intercept, so no constraint is needed or 
applied, and you can now interpret the smooth like a local GLM coefficient.


best,
Simon




On 11/05/16 01:30, Dominik Schneider wrote:

Hi,
Just getting into using GAM using the mgcv package. I've generated some
models and extracted the splines for each of the variables and started
visualizing them. I'm noticing that one of my variables is physically
unrealistic.

In the example below, my interpretation of the following plot is that the
y-axis is basically the equivalent of a "parameter" value of a GLM; in GAM
this value can change as the functional relationship changes between x and
y. In my case, I am predicting snowdepth based on the fractional snow
covered area. In no case will snowdepth realistically decrease for a unit
increase in fsca so my question is: *Is there a way to constrain the spline
to positive values? *

Thanks
Dominik

library(mgcv)
library(dplyr)
library(ggplot2)
extract_splines=function(mdl){
   sterms=predict(mdl,type='terms')
   datplot=cbind(sterms,mdl$model) %>% tbl_df
   datplot$intercept=attr(sterms,'constant')
   datplot$yhat=rowSums(sterms)+attr(sterms,'constant')
   return(datplot)
}
dat=data_frame(snowdepth=runif(100,min =
0.001,max=6.7),fsca=runif(100,0.01,.99))
mdl=gam(snowdepth~s(fsca),data=dat)
termdF=extract_splines(mdl)
ggplot(termdF)+
   geom_line(aes(x=fsca,y=`s(fsca)`))

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--
Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK
+44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190

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and provide commented, minimal, self-contained, reproducible code.

Re: [R] physical constraint with gam

[David Winsemius]

> On May 10, 2016, at 5:30 PM, Dominik Schneider 
>  wrote:
> 
> Hi,
> Just getting into using GAM using the mgcv package. I've generated some
> models and extracted the splines for each of the variables and started
> visualizing them. I'm noticing that one of my variables is physically
> unrealistic.
> 
> In the example below, my interpretation of the following plot is that the
> y-axis is basically the equivalent of a "parameter" value of a GLM; in GAM
> this value can change as the functional relationship changes between x and
> y. In my case, I am predicting snowdepth based on the fractional snow
> covered area. In no case will snowdepth realistically decrease for a unit
> increase in fsca so my question is: *Is there a way to constrain the spline
> to positive values? *
> 

I would think that the mass or volume of snow might not realistically decrease 
with increase in area but I see no reason why increasing the area might not be 
associated with an decrease in mean depth. Depth would be "orthogonal" to area.



> Thanks
> Dominik
> 
> library(mgcv)
> library(dplyr)
> library(ggplot2)
> extract_splines=function(mdl){
>  sterms=predict(mdl,type='terms')
>  datplot=cbind(sterms,mdl$model) %>% tbl_df
>  datplot$intercept=attr(sterms,'constant')
>  datplot$yhat=rowSums(sterms)+attr(sterms,'constant')
>  return(datplot)
> }
> dat=data_frame(snowdepth=runif(100,min =
> 0.001,max=6.7),fsca=runif(100,0.01,.99))
> mdl=gam(snowdepth~s(fsca),data=dat)
> termdF=extract_splines(mdl)
> ggplot(termdF)+
>  geom_line(aes(x=fsca,y=`s(fsca)`))
> 
>   [[alternative HTML version deleted]]
> 
> __
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius
Alameda, CA, USA

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[R] physical constraint with gam

[Dominik Schneider]

Hi,
Just getting into using GAM using the mgcv package. I've generated some
models and extracted the splines for each of the variables and started
visualizing them. I'm noticing that one of my variables is physically
unrealistic.

In the example below, my interpretation of the following plot is that the
y-axis is basically the equivalent of a "parameter" value of a GLM; in GAM
this value can change as the functional relationship changes between x and
y. In my case, I am predicting snowdepth based on the fractional snow
covered area. In no case will snowdepth realistically decrease for a unit
increase in fsca so my question is: *Is there a way to constrain the spline
to positive values? *

Thanks
Dominik

library(mgcv)
library(dplyr)
library(ggplot2)
extract_splines=function(mdl){
  sterms=predict(mdl,type='terms')
  datplot=cbind(sterms,mdl$model) %>% tbl_df
  datplot$intercept=attr(sterms,'constant')
  datplot$yhat=rowSums(sterms)+attr(sterms,'constant')
  return(datplot)
}
dat=data_frame(snowdepth=runif(100,min =
0.001,max=6.7),fsca=runif(100,0.01,.99))
mdl=gam(snowdepth~s(fsca),data=dat)
termdF=extract_splines(mdl)
ggplot(termdF)+
  geom_line(aes(x=fsca,y=`s(fsca)`))

[[alternative HTML version deleted]]

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and provide commented, minimal, self-contained, reproducible code.