[R-sig-ME] "lack of fit" computation from LME model?

[Andrew Robinson]

Hi Lauren,

one way to approach the problem would be to fit a model with the
nitrogen variable discretized, and compare that with the current model
(both fit with ML, not ReML) using anova.  That's a lack-of-fit test.
So, approximately, 

m1 <- lme(plantgrowth ~ nitrogen, random=~1|site, method="ML")
m2 <- lme(plantgrowth ~ factor(nitrogen, ordered=TRUE), 
          random=~1|site, method="ML")

anova(m1, m2)

An alternative that might be acceptable would be to fit a spline
instead of discretization.  That would look something like

library(splines)

m3 <- lme(plantgrowth ~ bs(nitrogen), random=~1|site, method="ML")
anova(m1, m3)

I hope that this helps,

Andrew

On Tue, Sep 27, 2011 at 09:42:57PM +0000, L Quinn wrote:
> 
> Dear list,
> I recently submitted a paper in which I analyzed plant growth response to several environmental factors in several sites. I wanted to account for the variation attributable to the different sites, so I made "site" a random effect in a simple LME regression model (e.g. m<-lme(plantgrowth~nitrogen,random=~1|site,method="ML"); library nlme). I had 10 observations in each of 11 sites. Seemed fairly straightforward to me.
> When reviews came back, one reviewer and the editor requested that I compute a "lack of fit" term for my regressions without which they couldn't be confident that linear models were most appropriate for my data. I have not done this before, and I have not seen anything about this for LME models when I have searched. I have only seen it for regular regression tests, but I don't think I can apply what I would find in regular regression tests to this LME model because I would lose the random effect. I know about model checking via diagnostic plots, etc, but I don't think this is what they want. They seem to want me to generate an F statistic and a p value for this "lack of fit" term. 
> My questions are: 
> 1.) is this even possible/practical within a LME model? 
> 2.) if so, what steps should I take to complete this task?3.) if not, can you suggest other diagnostics that might satisfy what they're looking for?
> I have a feeling this is a fairly elementary question/procedure, so I hope I am not wasting anyone's time. Please help if you can. I am happy to provide any more information that may be needed.
> Please reply directly to lquinn at hotmail.com. Thank you in advance!
> Lauren Quinn
> 
> 
> 
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-- 
Andrew Robinson  
Deputy Director, ACERA 
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia               (prefer email)
http://www.ms.unimelb.edu.au/~andrewpr              Fax: +61-3-8344-4599
http://www.acera.unimelb.edu.au/

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