[R] Interactions in a nls model

[Gabor Grothendieck]

On Tue, Feb 8, 2011 at 11:43 PM, Gabor Grothendieck
<ggrothendieck at gmail.com> wrote:
> On Tue, Feb 8, 2011 at 4:12 PM, Anthony Lawrence Nguy-Robertson
> <anthony.robertson at huskers.unl.edu> wrote:
>> I am interested in testing two similar nls models to determine if the lines
>> are statistically different when fitted with two different data sets; one
>> corn, another soybean. I know I can do this in linear models by testing for
>> interactions. See Introductory Statistics with R by Dallgaard p212-218 for
>> an example. I have two different data sets I am comparing to lai. ci.re
>> should have very little difference between corn and soybean, while ci.gr,
>> there should be a difference. If I use the simplistic form described in
>> Dallgaard (see example in code below) it does not work correctly. What do I
>> need to do to test for this interaction? Thank you!
>>
>> My data is located here: ftp://snrftp.unl.edu/Outgoing/example/
>>
>> Here is my example code:
>>
>> ###load data###
>> data <- read.csv("example.csv", header=TRUE)
>> eq <- function(x,a,b,c) {a+b*exp(x^c)}
>>
>> ##create non-linear models##
>> nls.ci.re <- nls(lai~eq(ci.re,a,b,c),data=data, start=c(a=1,b=1,c=1))
>> nls.ci.gr <- nls(lai~eq(ci.gr,a,b,c),data=data, start=c(a=1,b=1,c=1))
>>
>> #create non-linear models for corn#
>> nls.ci.re.corn <- nls(lai~eq(ci.re,a,b,c),data=subset(data,crop=="corn"),
>> start=c(a=1,b=1,c=1))
>> nls.ci.gr.corn <- nls(lai~eq(ci.gr,a,b,c),data=subset(data,crop=="corn"),
>> start=c(a=1,b=1,c=1))
>>
>> #create non-linear models for soybean#
>> nls.ci.re.soybean <-
>> nls(lai~eq(ci.re,a,b,c),data=subset(data,crop=="soybean"),
>> start=c(a=1,b=1,c=1))
>> nls.ci.gr.soybean <-
>> nls(lai~eq(ci.gr,a,b,c),data=subset(data,crop=="soybean"),
>> start=c(a=1,b=1,c=1))
>>
>> #test interactions according to Introductory Statistics with R by Dalgaard
>> p. 213#
>> corn.soybean.interactions.ci.re.a <-
>>    abs((summary(nls.ci.re.corn)$coeff[1,1]-
>>    summary(nls.ci.re.soybean)$coeff[1,1])/
>>    sqrt(summary(nls.ci.re.corn)$coeff[1,2]^2+
>>    summary(nls.ci.re.soybean)$coeff[1,2]^2))
>>
>> corn.soybean.interactions.ci.gr.a <-
>>    abs((summary(nls.ci.gr.corn)$coeff[1,1]-
>>    summary(nls.ci.gr.soybean)$coeff[1,1])/
>>    sqrt(summary(nls.ci.gr.corn)$coeff[1,2]^2+
>>    summary(nls.ci.gr.soybean)$coeff[1,2]^2))
>>
>> corn.soybean.interactions.ci.re.a.p.value <-
>> pt(corn.soybean.interactions.ci.re.a,df=summary(nls.ci.re.corn)$df[2],lower.tail=FALSE)
>> corn.soybean.interactions.ci.gr.a.p.value <-
>> pt(corn.soybean.interactions.ci.gr.a,df=summary(nls.ci.gr.corn)$df[2],lower.tail=FALSE)
>
> There is an anova.nls method: anova(model1, model2)

Just to be clear the two models would each include both groups -- one
model would assume the parameters are the same for the two groups so
it would have 3 parameters and the other model would allow them to be
different (up to 6 parameters depending on how many parameters you
wish to allow to be different between the two groups) -- these are not
the models shown above.


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