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

[Bansal, Udita]

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

[[alternative HTML version deleted]]

[Bansal, Udita]

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 <***@unimelb.edu.au>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-***@r-project.org" <r-sig-mixed-***@r-project.org>, "Bansal, Udita" <***@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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <***@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

[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

[[alternative HTML version deleted]]

[Andrew Robinson]

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

Post by Bansal, Udita
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
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
Date: Saturday, 11 August 2018 at 11:16 PM
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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <
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)?
Formula: ~1 | month
(Intercept) Residual
StdDev: 12.53908 5.009051
Correlation Structure: AR(1)
Formula: ~1 | month
Phi
0.324984
I could not find much on the interpretation for these online. Any help
will be much appreciated.
Thanks
Udita Bansal
[[alternative HTML version deleted]]
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
[[alternative HTML version deleted]]
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: (+61) 03
8344 4599
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au
Website: http://www.ms.unimelb.edu.au/~andrewpr

[[alternative HTML version deleted]]

[Bansal, Udita]

Hi Andrew,

Thanks for your response.

I had just one more question. I was using a nested random effect and the output looks like follows:

Random effects:
Formula: ~1 | year
(Intercept)
StdDev: 0.001158148

Formula: ~1 | month %in% year
(Intercept) Residual
StdDev: 7.551615 3.77298

From an example on non-nested random effect in the book, I understood that (Intercept) is the between group variance explained by the random effect and Residual value gives the within-group variance. And to get the StdDev, I should actually use the intervals command?

So, in the above case the Intercept for ~1|year gives the variance between years, the intercept for ~1|month %in% year gives the variance between months in a given year and the residual is the within month variance in a given year. Am I interpreting it correctly? I would divide each value by all the total sum to get the percentage variance explained? Also, why does the output say StdDev? Do I need to square it to actually get the variance for the groups?

Also, the intervals command doesn’t seem to work with lme models. Anyone has any idea about that?

Thanks
Udita

From: <***@gmail.com> on behalf of Andrew Robinson <***@ms.unimelb.edu.au>
Date: Monday, 13 August 2018 at 12:04 AM
To: "Bansal, Udita" <***@imperial.ac.uk>
Cc: "r-sig-mixed-***@r-project.org" <r-sig-mixed-***@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 <***@imperial.ac.uk<mailto:***@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 <***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>, "Bansal, Udita" <***@imperial.ac.uk<mailto:***@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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au>
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <***@imperial.ac.uk<mailto:***@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

[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au>
Website: http://www.ms.unimelb.edu.au/~andrewpr

[[alternative HTML version deleted]]

[Bansal, Udita]

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: <***@gmail.com> on behalf of Andrew Robinson <***@ms.unimelb.edu.au>
Date: Monday, 13 August 2018 at 12:04 AM
To: "Bansal, Udita" <***@imperial.ac.uk>
Cc: "r-sig-mixed-***@r-project.org" <r-sig-mixed-***@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 <***@imperial.ac.uk<mailto:***@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 <***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>, "Bansal, Udita" <***@imperial.ac.uk<mailto:***@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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au>
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <***@imperial.ac.uk<mailto:***@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

[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au>
Website: http://www.ms.unimelb.edu.au/~andrewpr

[[alternative HTML version deleted]]

[Bansal, Udita]

Thank you all for your response. I will try and explain a bit about my study and model and then maybe you can suggest why I get an error when I try to get confidence intervals for the coefficients in my original model.

I am studying the effects of temperature and precipitation across years on the breeding season of a particular bird for which I have data from three different populations. I have the following columns in my dataset:

1. Laying date of nest: Date when the clutch was completed for each nest, in Julian days starting from January of each year
2. Pre-laying period average temperature: Average temperature for a 30-day period prior to the laying date of each nest
3. Pre-laying period average precipitation: Average precipitation for a 30-day period prior to the laying date of each nest
4. Population: factor with 3 levels
5. Month: month for each laying date (goes from March to July usually)
6. Year: 1988-1994, 1994-2017 with a few missing years

My model looks as follows:

lme_m2 <- lme(LD_julian_day ~ prelaying_tmean + prelaying_prec_mean
+ prelaying_tmean*prelaying_prec_mean + population
+ prelaying_prec_mean*population + prelaying_tmean*population
+ prelaying_prec_mean*prelaying_tmean*population,
random = ~1|month/year,
correlation = corARMA(0.7623, ~1|month/year, 1, 0, fixed = F),
data = plovers, method = "ML")

If I use ~1|year/month, it runs the model but throws an error as follows :

Error in intervals.lme(lme_m2) :
cannot get confidence intervals on var-cov components: Non-positive definite approximate variance-covariance
Consider 'which = "fixed"

Since I want estimates of the random effects as well, I am not putting in which= fixed. If this is just something the package does then I can go ahead without confidence intervals.

Thanks
Udita

From: Guillaume Adeux <***@gmail.com>
Date: Monday, 13 August 2018 at 2:31 PM
To: "Bansal, Udita" <***@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 <***@imperial.ac.uk<mailto:***@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: <***@gmail.com<mailto:***@gmail.com>> on behalf of Andrew Robinson <***@ms.unimelb.edu.au<mailto:***@ms.unimelb.edu.au>>
Date: Monday, 13 August 2018 at 12:04 AM
To: "Bansal, Udita" <***@imperial.ac.uk<mailto:***@imperial.ac.uk>>
Cc: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@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 <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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 <***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org><mailto:r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org><mailto:r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>>, "Bansal, Udita" <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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

[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org><mailto:R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org>> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

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R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org><mailto:R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org>> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Website: http://www.ms.unimelb.edu.au/~andrewpr

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_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models


[[alternative HTML version deleted]]

[Bansal, Udita]

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 <***@gmail.com>
Date: Monday, 13 August 2018 at 2:31 PM
To: "Bansal, Udita" <***@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 <***@imperial.ac.uk<mailto:***@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: <***@gmail.com<mailto:***@gmail.com>> on behalf of Andrew Robinson <***@ms.unimelb.edu.au<mailto:***@ms.unimelb.edu.au>>
Date: Monday, 13 August 2018 at 12:04 AM
To: "Bansal, Udita" <***@imperial.ac.uk<mailto:***@imperial.ac.uk>>
Cc: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@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 <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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 <***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org><mailto:r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org><mailto:r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>>, "Bansal, Udita" <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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

[[alternative HTML version deleted]]

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https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Website: http://www.ms.unimelb.edu.au/~andrewpr

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[[alternative HTML version deleted]]

[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

Post by Bansal, Udita
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
*Date: *Monday, 13 August 2018 at 2:31 PM
*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
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
Date: Monday, 13 August 2018 at 12:04 AM
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
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
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
Date: Saturday, 11 August 2018 at 11:16 PM
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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <
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)?
Formula: ~1 | month
(Intercept) Residual
StdDev: 12.53908 5.009051
Correlation Structure: AR(1)
Formula: ~1 | month
Phi
0.324984
I could not find much on the interpretation for these online. Any help
will be much appreciated.
Thanks
Udita Bansal
[[alternative HTML version deleted]]
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
[[alternative HTML version deleted]]
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Website: http://www.ms.unimelb.edu.au/~andrewpr
[[alternative HTML version deleted]]
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

[[alternative HTML version deleted]]

[Bansal, Udita]

Yes, that’s what I wanted to confirm. The second part is the same. Thanks a lot!

Udita

From: Guillaume Adeux <***@gmail.com>
Date: Tuesday, 14 August 2018 at 5:57 PM
To: "Bansal, Udita" <***@imperial.ac.uk>
Cc: "r-sig-mixed-***@r-project.org" <r-sig-mixed-***@r-project.org>
Subject: Re: [R-sig-ME] Interpretation of lme output with correlation structure specification

"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 <***@imperial.ac.uk<mailto:***@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 <***@gmail.com<mailto:***@gmail.com>>
Date: Monday, 13 August 2018 at 2:31 PM
To: "Bansal, Udita" <***@imperial.ac.uk<mailto:***@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 <***@imperial.ac.uk<mailto:***@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: <***@gmail.com<mailto:***@gmail.com>> on behalf of Andrew Robinson <***@ms.unimelb.edu.au<mailto:***@ms.unimelb.edu.au>>
Date: Monday, 13 August 2018 at 12:04 AM
To: "Bansal, Udita" <***@imperial.ac.uk<mailto:***@imperial.ac.uk>>
Cc: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@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 <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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 <***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>>
Date: Saturday, 11 August 2018 at 11:16 PM
To: "r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org><mailto:r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>" <r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org><mailto:r-sig-mixed-***@r-project.org<mailto:r-sig-mixed-***@r-project.org>>>, "Bansal, Udita" <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <***@imperial.ac.uk<mailto:***@imperial.ac.uk><mailto:***@imperial.ac.uk<mailto:***@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

[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org><mailto:R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org>> mailing list
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[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org><mailto:R-sig-mixed-***@r-project.org<mailto:R-sig-mixed-***@r-project.org>> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au<mailto:***@unimelb.edu.au><mailto:***@unimelb.edu.au<mailto:***@unimelb.edu.au>>
Website: http://www.ms.unimelb.edu.au/~andrewpr

[[alternative HTML version deleted]]

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[Andrew Robinson]

What you write seems reasonable. I can't say more because I don't know how
you fit the model or anything about your data.

Andrew

Post by Bansal, Udita
Hi Andrew,
Thanks for your response.
I had just one more question. I was using a nested random effect and the
Formula: ~1 | year
(Intercept)
StdDev: 0.001158148
Formula: ~1 | month %in% year
(Intercept) Residual
StdDev: 7.551615 3.77298
From an example on non-nested random effect in the book, I understood that
(Intercept) is the between group variance explained by the random effect
and Residual value gives the within-group variance. And to get the StdDev,
I should actually use the intervals command?
So, in the above case the Intercept for ~1|year gives the variance between
years, the intercept for ~1|month %in% year gives the variance between
months in a given year and the residual is the within month variance in a
given year. Am I interpreting it correctly? I would divide each value by
all the total sum to get the percentage variance explained? Also, why does
the output say StdDev? Do I need to square it to actually get the variance
for the groups?
Also, the intervals command doesn’t seem to work with lme models. Anyone
has any idea about that?
Thanks
Udita
*Date: *Monday, 13 August 2018 at 12:04 AM
*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
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
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
Date: Saturday, 11 August 2018 at 11:16 PM
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: [phone]
School of Mathematics and Statistics Fax: [phone]
University of Melbourne, VIC 3010 Australia
Website: http://cebra.unimelb.edu.au/
On 12 Aug 2018, 7:34 AM +1000, Bansal, Udita <
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)?
Formula: ~1 | month
(Intercept) Residual
StdDev: 12.53908 5.009051
Correlation Structure: AR(1)
Formula: ~1 | month
Phi
0.324984
I could not find much on the interpretation for these online. Any help
will be much appreciated.
Thanks
Udita Bansal
[[alternative HTML version deleted]]
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
[[alternative HTML version deleted]]
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: (+61) 03
8344 4599
University of Melbourne, VIC 3010 Australia
Website: http://www.ms.unimelb.edu.au/~andrewpr

--
Andrew Robinson
Director, CEBRA, School of BioSciences
Reader & Associate Professor in Applied Statistics Tel: [phone]
School of Mathematics and Statistics Fax: (+61) 03
8344 4599
University of Melbourne, VIC 3010 Australia
Email: ***@unimelb.edu.au
Website: http://www.ms.unimelb.edu.au/~andrewpr

[[alternative HTML version deleted]]