[R-sig-ME] Interpretation of lme output with correlation structure specification

[Guillaume Adeux]

"Almost the same" depends on how strong the 1|year or 1|month effect is
because the second part of the random structure is the same(1|month:year =
1|year:month, that is to say a random intercept for each combination of
year:month).

Guillaume ADEUX

2018-08-14 11:16 GMT+02:00 Bansal, Udita <udita.bansal17 using imperial.ac.uk>:

> On second thoughts, won’t it be almost the same? If
>
> ~1|year/month expands to 1|year + 1|year:month (a random intercept for
> each year plus for each month in each year)
>
> ~1|month/year expands to 1|month +1|month:year (here the random intercept
> for month will be the same for January 2016 or 2017)—This would mean that
> each month has an intercept and each year for each month (like the
> highlighted part?).
>
>
>
> At the end I would have
>
>    1. An intercept for each OR an intercept for each month
>    2. An intercept for each month in each year
>
>
>
> Am I right?
>
>
>
> Thanks
>
> Udita
>
>
>
> *From: *Guillaume Adeux <guillaumesimon.a2 using gmail.com>
> *Date: *Monday, 13 August 2018 at 2:31 PM
> *To: *"Bansal, Udita" <udita.bansal17 using imperial.ac.uk>
>
> *Subject: *Re: [R-sig-ME] Interpretation of lme output with correlation
> structure specification
>
>
>
> Indeed your original model makes more sense.
> ~1|year/month expants to 1|year + 1|year:month (a random intercept for
> each year plus for each month in each year)
>
> whereas
> ~1|month/year expands to 1|month +1|month:year (here the random intercept
> for month will be the same for January 2016 or 2017)
>
> Depending on how a variable is coded, it can be crossed or nested but here
> "month" has the same levels all the different years, so it has to be nested.
>
> Cheers,
>
> GA2
>
>
>
> 2018-08-13 11:41 GMT+02:00 Bansal, Udita <udita.bansal17 using imperial.ac.uk>:
>
> Also, in continuation of my previous mail, I found that the error is
> thrown for intervals() if the model is not correct.
>
> My original model included: ~1|year/month (doesn’t give confidence
> intervals)
> The new model: ~1|month/year (gives me the confidence intervals)
>
> Original model: looks at variation when going from one year to another
> (~1|year intercept), and whether the effect of going from one month to
> another changes for different years (~1|month %in% year intercept).
>
> New model: looks at variation when going from one month to another
> (~1|month), and whether the effect of going from one year to another
> changes for different months (~1| year %in% month).
>
> To me, the original model makes more sense. Am I not interpreting it
> correctly? I used the Pinheiro and Bates book for this but maybe I am not
> getting it right.
>
> Anybody has any understanding on this?
>
> Thanks
> Udita
>
> From: <mensurationist using gmail.com> on behalf of Andrew Robinson <
> A.Robinson using ms.unimelb.edu.au>
> Date: Monday, 13 August 2018 at 12:04 AM
> To: "Bansal, Udita" <udita.bansal17 using imperial.ac.uk>
> Cc: "r-sig-mixed-models using r-project.org" <r-sig-mixed-models using r-project.org>
> Subject: Re: [R-sig-ME] Interpretation of lme output with correlation
> structure specification
>
> Hi Udita,
>
> Q1 Yes.  The correlation is taken into account in the model.
>
> Q2 I am not sure that I know what you mean by that.  I tend to leave the
> value blank and it then gets estimated in the algorithm.
>
> Cheers,
>
> Andrew
>
>
> On 12 August 2018 at 19:45, Bansal, Udita <udita.bansal17 using imperial.ac.uk
> <mailto:udita.bansal17 using imperial.ac.uk>> wrote:
> Dear Andrew,
>
> Thank you for suggesting the book. I went through the relevant parts of
> the book which helped me clarify my third question.
>
> But I still am not clear on phi. What I understood is that it is the
> within group correlation (which is solved by the model?) whose value ranges
> from -1 to 1. What I didn’t understand is as follows:
> Q1: Is any value of phi acceptable since it is the correlation of the
> within group observations which is taken into account by the model?
> Q2: The AR1 parameter estimate (the “value”) I provide while specifying
> the model is calculated based on AR model. How does the phi value relate
> with that? The book did not say much on it.
>
> Any help will be appreciated!
>
> Thanks
> Udita Bansal
>
> From: Andrew Robinson <apro using unimelb.edu.au<mailto:apro using unimelb.edu.au>>
> Date: Saturday, 11 August 2018 at 11:16 PM
> To: "r-sig-mixed-models using r-project.org<mailto:r-sig-mixed-models@
> r-project.org>" <r-sig-mixed-models using r-project.org<mailto:
> r-sig-mixed-models using r-project.org>>, "Bansal, Udita" <
> udita.bansal17 using imperial.ac.uk<mailto:udita.bansal17 using imperial.ac.uk>>
> Subject: Re: [R-sig-ME] Interpretation of lme output with correlation
> structure specification
>
>
> Hi Udita,
>
> You should read the book cited in the package. It’s really worthwhile.
>
> Best wishes,
>
> Andrew
>
> --
> Andrew Robinson
> Director, CEBRA, School of BioSciences
> Reader & Associate Professor in Applied Statistics Tel: (+61) 0403 138 955
> School of Mathematics and Statistics Fax: (+61) 03 8344 4599
> University of Melbourne, VIC 3010 Australia
> Email: apro using unimelb.edu.au<mailto:apro using unimelb.edu.au>
> Website: http://cebra.unimelb.edu.au/
> On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <
> udita.bansal17 using imperial.ac.uk<mailto:udita.bansal17 using imperial.ac.uk>>,
> wrote:
>
> Hi all,
>
> I was modeling the laying date of bird nests against moving averages of
> weather variables for several years of data. I used Durbin-Watson test and
> found considerable amount of autocorrelation in the residuals of simple
> linear and mixed effect models (with month as a random factor). So, I
> decided to run lme models with correlation structure specified. When I
> compare the AIC of the models with and without the correlation structure, I
> find that the models with the correlation structure are better.
> Question 1.: How can I interpret the phi (parameter estimate for
> correlation structure) value in the model output?
> Question 2.: Does the interpretation of phi affect the interpretation of
> the random effect?
> Question 3.: How can I interpret the random effect (since this is
> different from what lmer output shows which I am used to of)?
>
> An example output is as below:
>
> Random effects:
> Formula: ~1 | month
> (Intercept) Residual
> StdDev: 12.53908 5.009051
>
> Correlation Structure: AR(1)
> Formula: ~1 | month
> Parameter estimate(s):
> Phi
> 0.324984
>
> I could not find much on the interpretation for these online. Any help
> will be much appreciated.
>
> Thanks
> Udita Bansal
>
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>
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>
>
> --
> Andrew Robinson
> Director, CEBRA, School of BioSciences
> Reader & Associate Professor in Applied Statistics  Tel: (+61) 0403 138 955
> School of Mathematics and Statistics                        Fax: (+61) 03
> 8344 4599
> University of Melbourne, VIC 3010 Australia
> Email: apro using unimelb.edu.au<mailto:apro using unimelb.edu.au>
>
> Website: http://www.ms.unimelb.edu.au/~andrewpr
>
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