CorReg-package: Quick tutorial for CorReg package
In CorReg: Linear Regression Based on Linear Structure Between Variables
Description
Details
Author(s)
References
Examples
Description
Sequential linear regression based on a structural equation model(explicit correlations).
It permits to face highly correlated datasets.
We first search for an explicit model of correlations within the covariates by linear regression,
then this structure is interpreted and used to reduce dimension and correlations for the main regression on the response variable.
Details
CorReg: see www.correg.org for article and Phd Thesis about CorReg.
Author(s)
Maintainer: Clement THERY <clement.thery@arcelormittal.com>
References
Model-based covariable decorrelation in linear regression (CorReg): application to missing data and to steel industry. C Thery - 2015. see http://www.theses.fr/2015LIL10060 to read the associated PhD Thesis.
Examples
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## Not run:
require(CorReg)
#dataset generation
base=mixture_generator(n=15,p=10,ratio=0.4,tp1=1,tp2=1,tp3=1,positive=0.5,
R2Y=0.8,R2=0.9,scale=TRUE,max_compl=3,lambda=1)
X_appr=base$X_appr #learning sample
Y_appr=base$Y_appr #response variable for the learning sample
Y_test=base$Y_test #responsee variable for the validation sample
X_test=base$X_test #validation sample
TrueZ=base$Z#True generative structure (binary adjacency matrix)
#Z_i,j=1 means that Xj linearly depends on Xi
#density estimation for the MCMC (with Gaussian Mixtures)
density=density_estimation(X=X_appr,nbclustmax=10,detailed=TRUE)
Bic_null_vect=density$BIC_vect# vector of the BIC found (1 value per covariate)
#MCMC to find the structure
res=structureFinder(X=X_appr,verbose=0,reject=0,Maxiter=900,
nbini=20,candidates=-1,Bic_null_vect=Bic_null_vect,star=TRUE,p1max=15,clean=TRUE)
hatZ=res$Z_opt #found structure (adjacency matrix)
hatBic=res$bic_opt #associated BIC
#BIC comparison between true and found structure
bicopt_vect=BicZ(X=X_appr,Z=hatZ,Bic_null_vect=Bic_null_vect)
bicopt_vrai=BicZ(X=X_appr,Z=TrueZ,Bic_null_vect=Bic_null_vect)
sum(bicopt_vect);sum(bicopt_vrai)
#Structure comparison
compZ=compare_struct(trueZ=TrueZ,Zalgo=hatZ)#qualitative comparison
#interpretation of found and true structure ordered by increasing R2
readZ(Z=hatZ,crit="R2",X=X_appr,output="all",order=1)# <NA>line : name of subregressed covariate
readZ(Z=TrueZ,crit="R2",X=X_appr,output="all",order=1)# <NA>line : name of subregressed covariate
#Regression coefficients estimation
select="NULL"#without variable selection (otherwise, choose "lar" for example)
resY=correg(X=X_appr,Y=Y_appr,Z=hatZ,compl=TRUE,expl=TRUE,pred=TRUE,
select=select,K=10)
#MSE computation
MSE_complete=MSE_loc(Y=Y_test,X=X_test,A=resY$compl$A)#classical model on X
MSE_marginal=MSE_loc(Y=Y_test,X=X_test,A=resY$expl$A)#reduced model without correlations
MSE_plugin=MSE_loc(Y=Y_test,X=X_test,A=resY$pred$A)#plug-in model
MSE_true=MSE_loc(Y=Y_test,X=X_test,A=base$A)# True model
#MSE comparison
MSE=data.frame(MSE_complete,MSE_marginal,MSE_plugin,MSE_true)
MSE#estimated structure
compZ$true_left;compZ$false_left
barplot(as.matrix(MSE),main="MSE on validation dataset", sub=paste("select=",select))
abline(h=MSE_complete,col="red")
## End(Not run)
Example output
CCCCCCCCCCCCC RRRRRRRRRRRRRRRRR
CCC::::::::::::C R::::::::::::::::R
CC:::::::::::::::C R::::::RRRRRR:::::R
C:::::CCCCCCCC::::C RR:::::R R:::::R
C:::::C CCCCCC ooooooooooo rrrrr rrrrrrrrr R::::R R:::::R eeeeeeeeeeee ggggggggg ggggg
C:::::C oo:::::::::::oo r::::rrr:::::::::r R::::R R:::::R ee::::::::::::ee g:::::::::ggg::::g
C:::::C o:::::::::::::::o r:::::::::::::::::r R::::RRRRRR:::::R e::::::eeeee:::::ee g:::::::::::::::::g
C:::::C o:::::ooooo:::::or r::::::rrrrr::::::r R:::::::::::::RR e::::::e e:::::eg::::::ggggg::::::gg
C:::::C o::::o o::::o r:::::r r:::::r R::::RRRRRR:::::R e:::::::eeeee::::::eg:::::g g:::::g
C:::::C o::::o o::::o r:::::r rrrrrrr R::::R R:::::R e:::::::::::::::::e g:::::g g:::::g
C:::::C o::::o o::::o r:::::r R::::R R:::::R e::::::eeeeeeeeeee g:::::g g:::::g
C:::::C CCCCCC o::::o o::::o r:::::r R::::R R:::::R e:::::::e g::::::g g:::::g
C:::::CCCCCCCC::::C o:::::ooooo:::::o r:::::r RR:::::R R:::::R e::::::::e g:::::::ggggg:::::g
CC:::::::::::::::C o:::::::::::::::o r:::::r R::::::R R:::::R e::::::::eeeeeeee g::::::::::::::::g
CCC::::::::::::C oo:::::::::::oo r:::::r R::::::R R:::::R ee:::::::::::::e gg::::::::::::::g
CCCCCCCCCCCCC ooooooooooo rrrrrrr RRRRRRRR RRRRRRR eeeeeeeeeeeeee gggggggg::::::g
g:::::g
gggggg g:::::g
g:::::gg gg:::::g
g::::::ggg:::::::g
gg:::::::::::::g
ggg::::::ggg
gggggg
The Concept, the Method, the Power
[1] 304.0965
[1] 309.8015
[[1]]
coefs var
1 0.860796064728701 R2
2 <NA> 4
3 0.6689332903619 intercept
4 -0.110153788136904 1
5 -0.0701316998801885 2
6 -0.0947649813258923 3
7 0.546137123454117 5
8 -0.306034391822208 6
9 0.499799163689978 10
[[2]]
coefs var
1 0.906694566324102 R2
2 <NA> 8
3 0.662721471933004 intercept
4 -0.350154869623452 1
5 -0.609547545858945 2
6 0.303872429803662 3
7 0.122547651878245 5
8 -0.0907174627644957 6
9 -0.0852283244538394 10
[[3]]
coefs var
1 0.947612765244848 R2
2 <NA> 7
3 -0.834996674689482 intercept
4 0.28704785644588 2
5 0.130256671379444 3
6 -0.492989687235268 6
7 0.189741588018843 10
[[4]]
coefs var
1 0.968872850107611 R2
2 <NA> 9
3 -0.904092630593816 intercept
4 0.0350337710754986 1
5 0.0296776573723411 2
6 -0.0935515819021165 3
7 0.237736279084439 5
8 -0.228564405596821 6
[[1]]
coefs var
1 0.849541328696498 R2
2 <NA> 4
3 0.687068057281914 intercept
4 0.489960095634011 5
5 -0.320208553629766 6
6 0.46618613829287 10
[[2]]
coefs var
1 0.88690253151389 R2
2 <NA> 8
3 0.652080922923104 intercept
4 -0.333852189881848 1
5 -0.587227722879119 2
6 0.307561471711988 3
[[3]]
coefs var
1 0.912457752498476 R2
2 <NA> 7
3 -0.849879599145825 intercept
4 0.304525304143961 2
5 -0.477494586113415 6
6 0.199889055208016 10
[[4]]
coefs var
1 0.952057272825782 R2
2 <NA> 9
3 -0.903578686360595 intercept
4 -0.100809529628965 3
5 0.252299016357404 5
6 -0.229812761317557 6
MSE_complete MSE_marginal MSE_plugin MSE_true
1 628.4427 404.3436 612.0733 267.9941
[1] 4
[1] 0
CorReg documentation built on Sept. 6, 2019, 3 a.m.
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Description Details Author(s) References Examples
Description
Sequential linear regression based on a structural equation model(explicit correlations). It permits to face highly correlated datasets. We first search for an explicit model of correlations within the covariates by linear regression, then this structure is interpreted and used to reduce dimension and correlations for the main regression on the response variable.
Details
CorReg: see www.correg.org for article and Phd Thesis about CorReg.
Author(s)
Maintainer: Clement THERY <clement.thery@arcelormittal.com>
References
Model-based covariable decorrelation in linear regression (CorReg): application to missing data and to steel industry. C Thery - 2015. see http://www.theses.fr/2015LIL10060 to read the associated PhD Thesis.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | ## Not run:
require(CorReg)
#dataset generation
base=mixture_generator(n=15,p=10,ratio=0.4,tp1=1,tp2=1,tp3=1,positive=0.5,
R2Y=0.8,R2=0.9,scale=TRUE,max_compl=3,lambda=1)
X_appr=base$X_appr #learning sample
Y_appr=base$Y_appr #response variable for the learning sample
Y_test=base$Y_test #responsee variable for the validation sample
X_test=base$X_test #validation sample
TrueZ=base$Z#True generative structure (binary adjacency matrix)
#Z_i,j=1 means that Xj linearly depends on Xi
#density estimation for the MCMC (with Gaussian Mixtures)
density=density_estimation(X=X_appr,nbclustmax=10,detailed=TRUE)
Bic_null_vect=density$BIC_vect# vector of the BIC found (1 value per covariate)
#MCMC to find the structure
res=structureFinder(X=X_appr,verbose=0,reject=0,Maxiter=900,
nbini=20,candidates=-1,Bic_null_vect=Bic_null_vect,star=TRUE,p1max=15,clean=TRUE)
hatZ=res$Z_opt #found structure (adjacency matrix)
hatBic=res$bic_opt #associated BIC
#BIC comparison between true and found structure
bicopt_vect=BicZ(X=X_appr,Z=hatZ,Bic_null_vect=Bic_null_vect)
bicopt_vrai=BicZ(X=X_appr,Z=TrueZ,Bic_null_vect=Bic_null_vect)
sum(bicopt_vect);sum(bicopt_vrai)
#Structure comparison
compZ=compare_struct(trueZ=TrueZ,Zalgo=hatZ)#qualitative comparison
#interpretation of found and true structure ordered by increasing R2
readZ(Z=hatZ,crit="R2",X=X_appr,output="all",order=1)# <NA>line : name of subregressed covariate
readZ(Z=TrueZ,crit="R2",X=X_appr,output="all",order=1)# <NA>line : name of subregressed covariate
#Regression coefficients estimation
select="NULL"#without variable selection (otherwise, choose "lar" for example)
resY=correg(X=X_appr,Y=Y_appr,Z=hatZ,compl=TRUE,expl=TRUE,pred=TRUE,
select=select,K=10)
#MSE computation
MSE_complete=MSE_loc(Y=Y_test,X=X_test,A=resY$compl$A)#classical model on X
MSE_marginal=MSE_loc(Y=Y_test,X=X_test,A=resY$expl$A)#reduced model without correlations
MSE_plugin=MSE_loc(Y=Y_test,X=X_test,A=resY$pred$A)#plug-in model
MSE_true=MSE_loc(Y=Y_test,X=X_test,A=base$A)# True model
#MSE comparison
MSE=data.frame(MSE_complete,MSE_marginal,MSE_plugin,MSE_true)
MSE#estimated structure
compZ$true_left;compZ$false_left
barplot(as.matrix(MSE),main="MSE on validation dataset", sub=paste("select=",select))
abline(h=MSE_complete,col="red")
## End(Not run)
|
Example output
CCCCCCCCCCCCC RRRRRRRRRRRRRRRRR
CCC::::::::::::C R::::::::::::::::R
CC:::::::::::::::C R::::::RRRRRR:::::R
C:::::CCCCCCCC::::C RR:::::R R:::::R
C:::::C CCCCCC ooooooooooo rrrrr rrrrrrrrr R::::R R:::::R eeeeeeeeeeee ggggggggg ggggg
C:::::C oo:::::::::::oo r::::rrr:::::::::r R::::R R:::::R ee::::::::::::ee g:::::::::ggg::::g
C:::::C o:::::::::::::::o r:::::::::::::::::r R::::RRRRRR:::::R e::::::eeeee:::::ee g:::::::::::::::::g
C:::::C o:::::ooooo:::::or r::::::rrrrr::::::r R:::::::::::::RR e::::::e e:::::eg::::::ggggg::::::gg
C:::::C o::::o o::::o r:::::r r:::::r R::::RRRRRR:::::R e:::::::eeeee::::::eg:::::g g:::::g
C:::::C o::::o o::::o r:::::r rrrrrrr R::::R R:::::R e:::::::::::::::::e g:::::g g:::::g
C:::::C o::::o o::::o r:::::r R::::R R:::::R e::::::eeeeeeeeeee g:::::g g:::::g
C:::::C CCCCCC o::::o o::::o r:::::r R::::R R:::::R e:::::::e g::::::g g:::::g
C:::::CCCCCCCC::::C o:::::ooooo:::::o r:::::r RR:::::R R:::::R e::::::::e g:::::::ggggg:::::g
CC:::::::::::::::C o:::::::::::::::o r:::::r R::::::R R:::::R e::::::::eeeeeeee g::::::::::::::::g
CCC::::::::::::C oo:::::::::::oo r:::::r R::::::R R:::::R ee:::::::::::::e gg::::::::::::::g
CCCCCCCCCCCCC ooooooooooo rrrrrrr RRRRRRRR RRRRRRR eeeeeeeeeeeeee gggggggg::::::g
g:::::g
gggggg g:::::g
g:::::gg gg:::::g
g::::::ggg:::::::g
gg:::::::::::::g
ggg::::::ggg
gggggg
The Concept, the Method, the Power
[1] 304.0965
[1] 309.8015
[[1]]
coefs var
1 0.860796064728701 R2
2 <NA> 4
3 0.6689332903619 intercept
4 -0.110153788136904 1
5 -0.0701316998801885 2
6 -0.0947649813258923 3
7 0.546137123454117 5
8 -0.306034391822208 6
9 0.499799163689978 10
[[2]]
coefs var
1 0.906694566324102 R2
2 <NA> 8
3 0.662721471933004 intercept
4 -0.350154869623452 1
5 -0.609547545858945 2
6 0.303872429803662 3
7 0.122547651878245 5
8 -0.0907174627644957 6
9 -0.0852283244538394 10
[[3]]
coefs var
1 0.947612765244848 R2
2 <NA> 7
3 -0.834996674689482 intercept
4 0.28704785644588 2
5 0.130256671379444 3
6 -0.492989687235268 6
7 0.189741588018843 10
[[4]]
coefs var
1 0.968872850107611 R2
2 <NA> 9
3 -0.904092630593816 intercept
4 0.0350337710754986 1
5 0.0296776573723411 2
6 -0.0935515819021165 3
7 0.237736279084439 5
8 -0.228564405596821 6
[[1]]
coefs var
1 0.849541328696498 R2
2 <NA> 4
3 0.687068057281914 intercept
4 0.489960095634011 5
5 -0.320208553629766 6
6 0.46618613829287 10
[[2]]
coefs var
1 0.88690253151389 R2
2 <NA> 8
3 0.652080922923104 intercept
4 -0.333852189881848 1
5 -0.587227722879119 2
6 0.307561471711988 3
[[3]]
coefs var
1 0.912457752498476 R2
2 <NA> 7
3 -0.849879599145825 intercept
4 0.304525304143961 2
5 -0.477494586113415 6
6 0.199889055208016 10
[[4]]
coefs var
1 0.952057272825782 R2
2 <NA> 9
3 -0.903578686360595 intercept
4 -0.100809529628965 3
5 0.252299016357404 5
6 -0.229812761317557 6
MSE_complete MSE_marginal MSE_plugin MSE_true
1 628.4427 404.3436 612.0733 267.9941
[1] 4
[1] 0
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