ANOVA with correlated errors

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ANOVA with correlated errors

Jose A. Hernandez
Dear R colleagues,

My name is Jose Hernandez and work in the analysis of on-farm experiments.

I've been a R user for sometime now, however am still struggling figuring
out some of my spatial analysis using R.

Most of my experiments have the following model:

Y_ij = Mu + r_i + T_j + e_ij

Where:
r_i is some replication and T_j some fixed treatment effect.

I many cases there is significant within block heterogeneity and therefore
I can't assume that e_ij are iid.

An alternative is to use:

Y_ij = Mu + T_j + e_ij

And assume that:

e_ij follows some spatial covariance model such as exponential, spherical, etc.


Are there any R packages that will integrate spatial variability into the
model ?

Thanks and advance and best regards !

Jose


--
Jose A. Hernandez
Ph.D. Candidate
Precision Agriculture Center

Department of Soil, Water, and Climate
University of Minnesota
1991 Upper Buford Circle
St. Paul, MN 55108

Ph. (612) 625-0445, Fax. (612) 625-2208



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ANOVA with correlated errors

Paulo Justiniano Ribeiro Jr
Hi Jose
The function likfit() in the package geoR will fit those models.
Actually there is a data-set in the package with a similar structure
see:

require(geoR)
data(hoef)
help(hoef)

best
P.J.



On Thu, 13 May 2004, Jose A. Hernandez wrote:

> Dear R colleagues,
>
> My name is Jose Hernandez and work in the analysis of on-farm experiments.
>
> I've been a R user for sometime now, however am still struggling figuring
> out some of my spatial analysis using R.
>
> Most of my experiments have the following model:
>
> Y_ij = Mu + r_i + T_j + e_ij
>
> Where:
> r_i is some replication and T_j some fixed treatment effect.
>
> I many cases there is significant within block heterogeneity and therefore
> I can't assume that e_ij are iid.
>
> An alternative is to use:
>
> Y_ij = Mu + T_j + e_ij
>
> And assume that:
>
> e_ij follows some spatial covariance model such as exponential, spherical, etc.
>
>
> Are there any R packages that will integrate spatial variability into the
> model ?
>
> Thanks and advance and best regards !
>
> Jose
>
>
> --
> Jose A. Hernandez
> Ph.D. Candidate
> Precision Agriculture Center
>
> Department of Soil, Water, and Climate
> University of Minnesota
> 1991 Upper Buford Circle
> St. Paul, MN 55108
>
> Ph. (612) 625-0445, Fax. (612) 625-2208
>
> _______________________________________________
> R-sig-Geo mailing list
> R-sig-Geo at stat.math.ethz.ch
> https://www.stat.math.ethz.ch/mailman/listinfo/r-sig-geo
>
>

Paulo Justiniano Ribeiro Jr
Departamento de Estat?stica
Universidade Federal do Paran?
Caixa Postal 19.081
CEP 81.531-990
Curitiba, PR  -  Brasil
Tel: (+55) 41 361 3471
Fax: (+55) 41 361 3141
e-mail: pj at est.ufpr.br
http://www.est.ufpr.br/~paulojus



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ANOVA with correlated errors

Ole F. Christensen
Paulo

I think you need to provide a few more details here about how to fit
those models using your function in geoR.
* note the r_i term, which means that the replications have different
means. How would you specify this in your function ?
* I Assume the quantity of interest are the contrasts in T_j. Guess some
manual fiddling is needed to obtain confidence intervals for these
contrast ?

Alternatively, since the model is a multivariate Guassian, so it is
definetely possible to do inference by figuring out what the mean vector
and covariance matrix of the vector Y={Y_ij | i,j= ....} looks like,
write down the likelihood function and use the nlm or optim function for
maximising it.

Best regards Ole


Paulo Justiniano Ribeiro Jr wrote:

>Hi Jose
>The function likfit() in the package geoR will fit those models.
>Actually there is a data-set in the package with a similar structure
>see:
>
>require(geoR)
>data(hoef)
>help(hoef)
>
>best
>P.J.
>
>
>
>On Thu, 13 May 2004, Jose A. Hernandez wrote:
>
>  
>
>>Dear R colleagues,
>>
>>My name is Jose Hernandez and work in the analysis of on-farm experiments.
>>
>>I've been a R user for sometime now, however am still struggling figuring
>>out some of my spatial analysis using R.
>>
>>Most of my experiments have the following model:
>>
>>Y_ij = Mu + r_i + T_j + e_ij
>>
>>Where:
>>r_i is some replication and T_j some fixed treatment effect.
>>
>>I many cases there is significant within block heterogeneity and therefore
>>I can't assume that e_ij are iid.
>>
>>An alternative is to use:
>>
>>Y_ij = Mu + T_j + e_ij
>>
>>And assume that:
>>
>>e_ij follows some spatial covariance model such as exponential, spherical, etc.
>>
>>
>>Are there any R packages that will integrate spatial variability into the
>>model ?
>>
>>Thanks and advance and best regards !
>>
>>Jose
>>
>>
>>--
>>Jose A. Hernandez
>>Ph.D. Candidate
>>Precision Agriculture Center
>>
>>Department of Soil, Water, and Climate
>>University of Minnesota
>>1991 Upper Buford Circle
>>St. Paul, MN 55108
>>
>>Ph. (612) 625-0445, Fax. (612) 625-2208
>>
>>_______________________________________________
>>R-sig-Geo mailing list
>>R-sig-Geo at stat.math.ethz.ch
>>https://www.stat.math.ethz.ch/mailman/listinfo/r-sig-geo
>>
>>
>>    
>>
>
>Paulo Justiniano Ribeiro Jr
>Departamento de Estat?stica
>Universidade Federal do Paran?
>Caixa Postal 19.081
>CEP 81.531-990
>Curitiba, PR  -  Brasil
>Tel: (+55) 41 361 3471
>Fax: (+55) 41 361 3141
>e-mail: pj at est.ufpr.br
>http://www.est.ufpr.br/~paulojus
>
>_______________________________________________
>R-sig-Geo mailing list
>R-sig-Geo at stat.math.ethz.ch
>https://www.stat.math.ethz.ch/mailman/listinfo/r-sig-geo
>
>
>  
>

--
Ole F. Christensen
BiRC - Bioinformatics Research Center
University of Aarhus
H?egh-Guldbergs Gade 10, Building 090
DK-8000 Aarhus C
Denmark



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ANOVA with correlated errors

Edzer J. Pebesma
In reply to this post by Jose A. Hernandez
Jose, I think package nlme can deal with such models as well, and
it may be slightly more oriented towards the analysis of experiments
than geoR is, please correct me if I'm wrong.

Best regards,
--
Edzer

Jose A. Hernandez wrote:

> Dear R colleagues,
>
> My name is Jose Hernandez and work in the analysis of on-farm
> experiments.
>
> I've been a R user for sometime now, however am still struggling
> figuring out some of my spatial analysis using R.
>
> Most of my experiments have the following model:
>
> Y_ij = Mu + r_i + T_j + e_ij
>
> Where:
> r_i is some replication and T_j some fixed treatment effect.
>
> I many cases there is significant within block heterogeneity and
> therefore I can't assume that e_ij are iid.
>
> An alternative is to use:
>
> Y_ij = Mu + T_j + e_ij
>
> And assume that:
>
> e_ij follows some spatial covariance model such as exponential,
> spherical, etc.
>
>
> Are there any R packages that will integrate spatial variability into
> the model ?
>
> Thanks and advance and best regards !
>
> Jose
>
>