Simulating variables with predefined correlation and autocorrelation

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Simulating variables with predefined correlation and autocorrelation

AMITHA PURANIK
Hello everyone,

I'm trying to simulate a set of variables by specifying correlations. For
the simulated data, I also want to specify autocorrelations. Basically I am
trying to simulate data assuming spatial durbin model (a model which
accounts for autocorrelation in both Y and X). I came across the post
on ‘*Simulating
spatially autocorrelated data*’ in R-sig-geo (
https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html) where
similar query was discussed, however the focus there was on generating
autocorrelated dependent variable.

Can anyone assist me on this? Thanks in advance.

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Re: Simulating variables with predefined correlation and autocorrelation

Facundo Muñoz-2
Dear Amitha,

I'm not sure I understand well your question (but then, I don't know
this Durbin model). From what I quickly looked up it follows this
formulation:

y = \rho W y + \alpha 1_n + X \beta + W X \theta + \varepsilon

where y are the observations (thus, what you are trying to simulate if I
understood correctly), W, X and 1_n are fixed and known matrices, and
the greek letters are the unknown parameters.

For simulating y from this model, you should assign values to the greek
letters and compute:

y = (I_n - \rho W)^{-1} [\alpha 1_n + X \beta + W X \theta + \varepsilon]

Does this help?

ƒacu.-


On 8/21/19 8:52 AM, Amitha Puranik wrote:

> Hello everyone,
>
> I'm trying to simulate a set of variables by specifying correlations. For
> the simulated data, I also want to specify autocorrelations. Basically I am
> trying to simulate data assuming spatial durbin model (a model which
> accounts for autocorrelation in both Y and X). I came across the post
> on ‘*Simulating
> spatially autocorrelated data*’ in R-sig-geo (
> https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html) where
> similar query was discussed, however the focus there was on generating
> autocorrelated dependent variable.
>
> Can anyone assist me on this? Thanks in advance.
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo

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Re: Simulating variables with predefined correlation and autocorrelation

AMITHA PURANIK
In reply to this post by AMITHA PURANIK
Dear Prof Facundo Muñoz,



Thank you for a quick response. I am sorry for not phrasing my query
clearly.

I am interested to simulate 2 variables Y and X in such a way that the
resultant variables should possess the correlation coefficient of 0.6
between Y and X and autocorrelation of 0.7 in Y and 0.4 in X. The query
posted in the link (
https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html)
focussed on only the autocorrelation of Y (spatial lag model) whereas I
would like to introduce some autocorrelation in X too (spatial durbin
model).

Is there a way to do this? Should a covariance structure defining both
correlation and autocorrelation be specified while simulating variables? If
so, how to define such covariance structure? I will be grateful for your
assistance.

Thanks in advance.

Amitha Puranik

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Re: Simulating variables with predefined correlation and autocorrelation

Roger Bivand
Administrator
Could you please explain why you want to do this and whether you want to use the same weights for y and x? Maybe refer to https://doi.org/10.1111/j.1538-4632.1991.tb00235.x and work referred to there; I'll try to find other references later.

Roger Bivand
Norwegian School of Economics
Bergen, Norway



Fra: Amitha Puranik
Sendt: torsdag 22. august, 12.41
Emne: Re: [R-sig-Geo]  Simulating variables with predefined correlation and autocorrelation
Til: [hidden email]
Kopi: [hidden email]


Dear Prof Facundo Muñoz, Thank you for a quick response. I am sorry for not phrasing my query clearly. I am interested to simulate 2 variables Y and X in such a way that the resultant variables should possess the correlation coefficient of 0.6 between Y and X and autocorrelation of 0.7 in Y and 0.4 in X. The query posted in the link ( https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html) focussed on only the autocorrelation of Y (spatial lag model) whereas I would like to introduce some autocorrelation in X too (spatial durbin model). Is there a way to do this? Should a covariance structure defining both correlation and autocorrelation be specified while simulating variables? If so, how to define such covariance structure? I will be grateful for your assistance. Thanks in advance. Amitha Puranik [[alternative HTML version deleted]] _______________________________________________ R-sig-Geo mailing list [hidden email] https://stat.ethz.ch/mailman/listinfo/r-sig-geo


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Roger Bivand
Department of Economics
Norwegian School of Economics
Helleveien 30
N-5045 Bergen, Norway
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Re: Simulating variables with predefined correlation and autocorrelation

AMITHA PURANIK
Dear Prof. Bivand,



Thanks a lot for responding and providing the material to read. I will
definitely go through your paper and the references cited in it.

I am working on simulating various scenarios where autocorrelation exists
in Y or X or both and also in the residuals and compare the model
performances on these data. At present I have planned to assign same
weights (distance based) for both X and Y. I have found solution to
simulate autocorrelated Y based on your response in the link (
https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html). But I
have not found a way to induce autocorrelation in even the independent
variables(s). Hence I posted this query. Thanks in advance.

Regards,

Amitha Puranik.















On Thu, Aug 22, 2019 at 7:06 PM Roger Bivand <[hidden email]> wrote:

> Could you please explain why you want to do this and whether you want to
> use the same weights for y and x? Maybe refer to
> https://doi.org/10.1111/j.1538-4632.1991.tb00235.x and work referred to
> there; I'll try to find other references later.
>
> Roger Bivand
> Norwegian School of Economics
> Bergen, Norway
>
>
>
> Fra: Amitha Puranik
> Sendt: torsdag 22. august, 12.41
> Emne: Re: [R-sig-Geo]  Simulating variables with predefined correlation
> and autocorrelation
> Til: [hidden email]
> Kopi: [hidden email]
>
>
> Dear Prof Facundo Muñoz, Thank you for a quick response. I am sorry for
> not phrasing my query clearly. I am interested to simulate 2 variables Y
> and X in such a way that the resultant variables should possess the
> correlation coefficient of 0.6 between Y and X and autocorrelation of 0.7
> in Y and 0.4 in X. The query posted in the link (
> https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html)
> focussed on only the autocorrelation of Y (spatial lag model) whereas I
> would like to introduce some autocorrelation in X too (spatial durbin
> model). Is there a way to do this? Should a covariance structure defining
> both correlation and autocorrelation be specified while simulating
> variables? If so, how to define such covariance structure? I will be
> grateful for your assistance. Thanks in advance. Amitha Puranik
> [[alternative HTML version deleted]]
> _______________________________________________ R-sig-Geo mailing list
> [hidden email] https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
>

        [[alternative HTML version deleted]]

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Re: Simulating variables with predefined correlation and autocorrelation

Tobias Rüttenauer
Dear Amitha,

If understand your query correctly, you could also have a look at my preprint on Monte Carlo simulations of different spatial regression models: https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5630.

The replication materials are online available (https://github.com/ruettenauer/Reproduction-Material-Spatial-Monte-Carlo-Experiments). The '01_Monte Carlo Simulation Spatial_Program.R' scipt provides a function to set up data with different constellations of autocorrelation. Maybe the code is useful for your purposes as well.

Best,
Tobias


-----Original Message-----
From: R-sig-Geo <[hidden email]> On Behalf Of Amitha Puranik
Sent: 22 August 2019 17:19
To: [hidden email]
Cc: [hidden email]
Subject: Re: [R-sig-Geo] Simulating variables with predefined correlation and autocorrelation

Dear Prof. Bivand,



Thanks a lot for responding and providing the material to read. I will definitely go through your paper and the references cited in it.

I am working on simulating various scenarios where autocorrelation exists in Y or X or both and also in the residuals and compare the model performances on these data. At present I have planned to assign same weights (distance based) for both X and Y. I have found solution to simulate autocorrelated Y based on your response in the link ( https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html). But I have not found a way to induce autocorrelation in even the independent variables(s). Hence I posted this query. Thanks in advance.

Regards,

Amitha Puranik.















On Thu, Aug 22, 2019 at 7:06 PM Roger Bivand <[hidden email]> wrote:

> Could you please explain why you want to do this and whether you want
> to use the same weights for y and x? Maybe refer to
> https://doi.org/10.1111/j.1538-4632.1991.tb00235.x and work referred
> to there; I'll try to find other references later.
>
> Roger Bivand
> Norwegian School of Economics
> Bergen, Norway
>
>
>
> Fra: Amitha Puranik
> Sendt: torsdag 22. august, 12.41
> Emne: Re: [R-sig-Geo]  Simulating variables with predefined
> correlation and autocorrelation
> Til: [hidden email]
> Kopi: [hidden email]
>
>
> Dear Prof Facundo Muñoz, Thank you for a quick response. I am sorry
> for not phrasing my query clearly. I am interested to simulate 2
> variables Y and X in such a way that the resultant variables should
> possess the correlation coefficient of 0.6 between Y and X and
> autocorrelation of 0.7 in Y and 0.4 in X. The query posted in the link
> (
> https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html)
> focussed on only the autocorrelation of Y (spatial lag model) whereas
> I would like to introduce some autocorrelation in X too (spatial
> durbin model). Is there a way to do this? Should a covariance
> structure defining both correlation and autocorrelation be specified
> while simulating variables? If so, how to define such covariance
> structure? I will be grateful for your assistance. Thanks in advance.
> Amitha Puranik [[alternative HTML version deleted]]
> _______________________________________________ R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
>

        [[alternative HTML version deleted]]

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Re: Simulating variables with predefined correlation and autocorrelation

AMITHA PURANIK
Dear Dr Tobias,

Thanks a lot for sharing the materials. This means a lot!












On Tue, Sep 3, 2019 at 1:05 PM Tobias Rüttenauer <[hidden email]>
wrote:

> Dear Amitha,
>
> If understand your query correctly, you could also have a look at my
> preprint on Monte Carlo simulations of different spatial regression models:
> https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/5630.
>
> The replication materials are online available (
> https://github.com/ruettenauer/Reproduction-Material-Spatial-Monte-Carlo-Experiments).
> The '01_Monte Carlo Simulation Spatial_Program.R' scipt provides a function
> to set up data with different constellations of autocorrelation. Maybe the
> code is useful for your purposes as well.
>
> Best,
> Tobias
>
>
> -----Original Message-----
> From: R-sig-Geo <[hidden email]> On Behalf Of Amitha
> Puranik
> Sent: 22 August 2019 17:19
> To: [hidden email]
> Cc: [hidden email]
> Subject: Re: [R-sig-Geo] Simulating variables with predefined correlation
> and autocorrelation
>
> Dear Prof. Bivand,
>
>
>
> Thanks a lot for responding and providing the material to read. I will
> definitely go through your paper and the references cited in it.
>
> I am working on simulating various scenarios where autocorrelation exists
> in Y or X or both and also in the residuals and compare the model
> performances on these data. At present I have planned to assign same
> weights (distance based) for both X and Y. I have found solution to
> simulate autocorrelated Y based on your response in the link (
> https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html). But
> I have not found a way to induce autocorrelation in even the independent
> variables(s). Hence I posted this query. Thanks in advance.
>
> Regards,
>
> Amitha Puranik.
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> On Thu, Aug 22, 2019 at 7:06 PM Roger Bivand <[hidden email]> wrote:
>
> > Could you please explain why you want to do this and whether you want
> > to use the same weights for y and x? Maybe refer to
> > https://doi.org/10.1111/j.1538-4632.1991.tb00235.x and work referred
> > to there; I'll try to find other references later.
> >
> > Roger Bivand
> > Norwegian School of Economics
> > Bergen, Norway
> >
> >
> >
> > Fra: Amitha Puranik
> > Sendt: torsdag 22. august, 12.41
> > Emne: Re: [R-sig-Geo]  Simulating variables with predefined
> > correlation and autocorrelation
> > Til: [hidden email]
> > Kopi: [hidden email]
> >
> >
> > Dear Prof Facundo Muñoz, Thank you for a quick response. I am sorry
> > for not phrasing my query clearly. I am interested to simulate 2
> > variables Y and X in such a way that the resultant variables should
> > possess the correlation coefficient of 0.6 between Y and X and
> > autocorrelation of 0.7 in Y and 0.4 in X. The query posted in the link
> > (
> > https://stat.ethz.ch/pipermail/r-sig-geo/2011-September/012728.html)
> > focussed on only the autocorrelation of Y (spatial lag model) whereas
> > I would like to introduce some autocorrelation in X too (spatial
> > durbin model). Is there a way to do this? Should a covariance
> > structure defining both correlation and autocorrelation be specified
> > while simulating variables? If so, how to define such covariance
> > structure? I will be grateful for your assistance. Thanks in advance.
> > Amitha Puranik [[alternative HTML version deleted]]
> > _______________________________________________ R-sig-Geo mailing list
> > [hidden email]
> > https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> >
> >
>
>         [[alternative HTML version deleted]]
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>
>

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