factanal.bi: Gaussian factor analysis: common and bi-factor

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

Gaussian factor analysis: common and bi-factor

Usage

pfactnllk(rhvec,Robs,nsize)
bifactnllk(rhvec,grsize,Robs,nsize)
trifactnllk(rhvec,grsize,sbgrsize,Robs,nsize)
factanal.co(factors,start,data=1,cormat=NULL,n=100,prlevel=0,mxiter=100)
factanal.bi(grsize,start,data=1,cormat=NULL,n=100,prlevel=0,mxiter=100)
factanal.tri(grsize,sbgrsize,start,data=1,cormat=NULL,n=100,prlevel=0,mxiter=150)

Arguments

factors	the number of factors p for factanal.co
rhvec	For pfactnllk: vector of length d*p of partial correlations, first d are correlations with factor 1, then partial correlations with factor k given previous factors for k=2,...,p. For bifactnllk: vector of length d*2; first d correlations with common factor, then partial correlations with group factor given common factor. For trifactnllk: vector of length d*3; first d correlations with common factor, then partial correlations with group factor given common factor, and finally partial correlations with subfactor given common and groups factors.
Robs	dxd correlation matrix
nsize	sample size
grsize	vector of group sizes for the bi-factor and tri-factor models
sbgrsize	vector of subgroup sizes for the tri-factor model
start	starting point for nlm() to find p-factor or bi-factor or tri-factor parameters to minimize the Gaussian negative log-likelihood
data	nsize x d data set to compute the correlation matrix
cormat	dxd correlation matrix
n	sample size
prlevel	print.level for nlm
mxiter	maximum number of iterations for nlm

Details

The output of factanal.co should be similar to that of factanal(). The algorithm is different so that it may fail to converge depending on the starting point (when p is larger).

pfactnllk, bifactnllk and trifactnllk return the gradient vector in order that gradient calculations are faster and maybe the number of iterations in nlm() can be reduced .

Value

For pfactnllk, bifactnllk and trifactnllk, a value for negative Gaussian log-likelihood and the gradient vector with respect to rhvec.

For factanal.co, a list with $nllk, $rhmat= dxp matrix of partial correlations, $loading=dxp loading matrix after varimax, $rotmat=pxp rotation matrix used by varimax. Note that the loading matrix and matrix of partial correlations are not unique for p>=2.

For factanal.bi, a list with $nllk, $rhmat= dx2 matrix of correlations and partial correlations.

For factanal.tri, a list with $nllk, $rhmat= dx3 matrix of correlations and partial correlations.

See Also

bifct mvtfact

Examples

rhpar=c( 0.81,  0.84,0.84, 0.54,0.57,0.49, 0.51,0.54,0.55,0.70,
  0.53,0.56,0.53,0.67,0.70)
Robs=corvec2mat(rhpar)
n=100
d=6
rhvec=c(rep(.5,d),rep(.4,d))
pfactnllk(rhvec,Robs,n)
factanal.co(2,start=rhvec,cormat=Robs,n=100,prlevel=1)
# bi-factor
grsize=c(3,3)
bifactnllk(rhvec,grsize,Robs,n)
factanal.bi(grsize,start=rhvec,cormat=Robs,n=100,prlevel=1)
# tri-factor
grsize=c(4,4)
sbgrsize=c(2,2,2,2)
d=sum(grsize)
p=3
tripar=((d*p):1)/(d*p+1)
param1=tripar[1:d]
param2=tripar[(d+1):(2*d)]
param3=tripar[(2*d+1):(3*d)]
n=50
robj=trifct(grsize,sbgrsize,param1,param2,param3)
achol=chol(robj$fctmat)
set.seed(123)
z=matrix(rnorm(n*d),n,d)
z=z
zdata=nscore(z,iopt=TRUE)
Robs=cor(zdata)
trifactnllk(tripar,grsize,sbgrsize,Robs,n)
factanal.tri(grsize,sbgrsize,start=tripar,cormat=Robs,n=50,prlevel=1,mxiter=150)

YafeiXu/CopulaModel documentation built on May 9, 2019, 11:07 p.m.