Covariance and Sigma Functions

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Description

The "concordance" functions end with "cov_cppforR" and sigma functions end with "Sig_cppforR". Check table below and the examples for details and usage. Documentation for some of these functions is missing. Let K be a given covariance matrix, D be a given Euclidean distance matrix, let q be the dimension of desired sigma or covariance matrices.

Arguments

params

a numeric vector for the parameters (a mapping of the original parameters)

data

a numeric matrix (see examples and details)

Details

function name function ref params data formula
IdentSig_cppforR Ident 1 matrix(q,1,1) A=σ I_q
ar1hetcov_cppforR ar1het q matrix(q,1,1) A_{ij}=σ_iσ_jρ^{|i-j|},
σ_1=1
arma11cov_cppforR arma11 2 matrix(q,1,1) A_{ij}=(λρ^{|i-j|-1}*
1(i\neq j)+1(i=j))
FA1hetSig_cppforR FA1het 2q-2 matrix(q,1,1) f_if_j+σ_{ii}1(i=j)
f_1=1, σ_1=1
FA1homSig_cppforR FA1hom q matrix(q,1,1) f_if_j+σ 1(i=j)
f_1=1
compsymmcov_cppforR compsymm 1 matrix(q,1,1) A_{ij}=ρ, i\neq j;
A_{ij}=1, i=j
compsymmhetSig_cppforR compsymmhet q+1 matrix(q,1,1) A_{ij}=σ_iσ_jρ, i\neq j
A_{ij}=σ_iσ_j, i= j
compsymmhetcov_cppforR compsymmhet q matrix(q,1,1) A_{ij}=σ_iσ_jρ, i\neq j
A_{ij}=σ_iσ_j, i= j
σ_1=1
compsymmhomSig_cppforR compsymmhom 2 matrix(q,1,1) A_{ij}=σρ, i\neq j;
A_{ij}=σ, i=j
diagSig_cppforR diag q matrix(q,1,1) diag(σ_1,..,σ_q)
diagcov_cppforR Diag q-1 matrix(q,1,1) diag(1,σ_2,..,σ_q)
expcov_cppforR exp 1 M exp(-σ*d_{ij})
M defines D
lincombcov_cppforR lincomb k (K_1;…; K_k) ∑^k_{j=1}w_jK_j
rbfcov_cppforR rbf 1 M exp(-σ*d^2_{ij})
M defines D
ar1cov_cppforR ar1 1 matrix(nrow, 1,1) A_{ij}=ρ^{|i-j|}
relmatcov_cppforR RelMat 1 M Genetic Similarity+
M is coded as -1, 0, 1 σ I
unstrcov_cppforR unstr \frac{q(q+1)}{2}-1 matrix(q,1,1) A_{ij}=σ_iσ_jρ_{ij}
σ_1=1,
ρ_{ii}=1
ConstMatcov_cppforR Const 0 K A=K
expdistcov_cppforR expdist 1 D exp(-σ d_{ij})
rbfdistcov_cppforR rbfdist 1 D exp(-σ d^2_{ij})
splincov_cppforR splin 1 D 1-ρ d_{ij}, ρ d_{ij}≤q 1
0, ρ d_{ij}> 1
sppowcov_cppforR sppow 1 D ρ^{d_{ij}}

Value

A concordance or sigma matrix.

Author(s)

Deniz Akdemir

Examples

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## Not run: 
library(SAMM)
n=100
nsample=80
rhotrans=5
ar1cov_cppforR(c(rhotrans),matrix(5))
rho=(2/pi)*atan(rhotrans)
rho
tan((pi/2)*(rho))

M1<-matrix(rbinom(n*300, 2, .2)-1, nrow=n)
K1<-relmatcov_cppforR(c(.01), M1)

M2<-matrix(rbinom(n*300, 2, .2)-1, nrow=n)
K2<-relmatcov_cppforR(c(0.03), M2)
W=(diag(5)[sample(1:5,n, replace=TRUE),])
covY<-3*K1+5*K2+10*(W%*%ar1cov_cppforR(c(rhotrans),matrix(5))%*%t(W))
K1[1:5,1:5]
dim(W)
dim(ar1cov_cppforR(c(6),matrix(5)))
Y<-10+crossprod(chol(covY),rnorm(n))


#training set
Trainset<-sample(1:n,nsample)
ytrain=Y[Trainset]
Xtrain=matrix(rep(1, n)[Trainset], ncol=1)
Ztrain=diag(n)[Trainset,]
Wtrain=W[Trainset,]

samout<-SAMM(Y=matrix(ytrain,ncol=1),X=Xtrain,
Zlist=list(Ztrain, Ztrain), Klist=list(K1,K2),
lambda=0, W=Wtrain,R=list("ar1",c(0),matrix(5,1,1)),
Siglist=list("","",""), corfunc=c(F,F,T), corfuncfixed=c(F,F,F),
sigfunc=c(F,F,F),mmalg="dermm_reml2", tolparconv=1e-10,
tolparinv=1e-10,maxiter=1000,geterrors=F)
samout$corfuncparamslist[[3]]
rhohat=(2/pi)*atan(samout$corfuncparamslist[[3]])
rhohat
ar1cov_cppforR(c(samout$corfuncparamslist[[3]]),matrix(5,1,1))

## End(Not run)