CircE.BFGS: Circumplex models estimation

In CircE: Circumplex models Estimation

Description

This function fits circumplex models for correlation matrices as described in Browne (1992). Results are convergent with those obtained using CIRCUM program wrote by Michael W. Browne and Stephen H.C. Du Toit (1992), available for download at this address http://faculty.psy.ohio-state.edu/browne/software.php.

Usage

CircE.BFGS(R, v.names, m, N, r = 1, equal.com = FALSE, equal.ang = FALSE, 
           mcsc = "unconstrained", start.values="IFA",ci.level=0.95,factr = 1e+09, 
           pgtol = 0, lmm = NULL, iterlim = 250, upper = NULL, lower = NULL,  
           print.level = 1, file = NULL, title = "Circumplex Estimation",
           try.refit.BFGS=FALSE)

Arguments

R	input covariance/correlation matrix. If the matrix is obtained trough cov or cor, the precision to be used (decimal places) must be specified with round.
v.names	a string that contains the name of the variable used in R.
m	numbers of betas to use in the Fourier correlation function.
N	number of observation.
r	the reference variable in the correlation matrix. This variable will be positioned at 0 degree.
equal.com	logical: does the communality (radius length) for each variable have to been considered as equal? Default equal.com=FALSE.
equal.ang	logical: does the circular position of the variables have to been considered as equal spaced? Default equal.ang=FALSE.
mcsc	minimum common score correlation value: "unconstrained" (default), "-1" or "0".
start.values	if start.values="IFA" (default), initial estimates are provided by the factor analysis method described in Browne (1992; section 6.7) and based on Image Factor Analysis (IFA). When the input covariance/correlation matrix is not positive definite, the IFA cannot be carried out; in this case the Principal Factor Analysis (PFA) supply likely starting values (start.values="IFA").
ci.level	level for confidence interval for the parameter estimates (default is .95).
factr	controls the convergence of the "L-BFGS-B" method. Convergence occurs when the reduction in the objective is within this factor of the machine tolerance. Default is 1e09, that is a tolerance of about 2e-07.
pgtol	helps control the convergence of the "L-BFGS-B" method. It is a tolerance on the projected gradient in the current search direction. This defaults to zero, when the check is suppressed.
lmm	is an integer giving the number of BFGS updates retained in the "L-BFGS-B" method. It defaults to number of free parameters estimated.
iterlim	maximum number of iterations.
upper,lower	Bounds on the variables for the "L-BFGS-B" method. See bound.assign
print.level	Integer. Higher values may produce more tracing information on the progress of the optimization (print.level=0 no information is generated,print.level=1 print F value at every iterations, print.level=3 print F and also ||proj g||).
file	a connection or a character string naming the file to write to, or NULL (default) for do not send R output to a file.
title	title for the output (for identification purpose).
try.refit.BFGS	if TRUE, attempt to refit the model removing default box constraints on z,v, and a parameters, if L-BFGS-B fails to converge.

Details

Optimization is based on L-BFGS-B algorithm. See optim for further details.

Value

AGFI	adjusted goodness-of-fit index
AIC	Akaike Information Criterion
BCI	ECVI- expected cross-validation index
BIC	Schwarz's Bayesian Information Criterion
CAIC	Bozdogans's Consistent AIC
CFI	Bentler CFI
CNI	Hoelter's critical N (CN) index
Cs	reproduced covariance matrix
Fzero	population discrepancy function value; point estimate
Fzero.L	population discrepancy function value; lower 90% confidence limit
Fzero.U	population discrepancy function value; upper 90% confidence limit
GFI	goodness-of-fit index
MCSC	minimum common score correlation
NFI	Bentler-Bonnett NFI
NNFI	Tucker-Lewis TLI (or NNFI)
Pc	reproduced common score correlation matrix
R	observed covariance/correlation matrix
RMSEA	root mean square error of approximation; point estimate
RMSEA.L	root mean square error of approximation; lower 90% confidence limit
RMSEA.U	root mean square error of approximation; upper 90% confidence limit
S	reproduced correlation matrix
SRMR	standardized root mean squared residual
beta	Fourier correlation function's betas
chisq	the chisquare test statistic for the model
chisqNull	the chisquare value associated with a null model in which all of the observed variables are uncorrelated
coeff	data frame containing parameters value and their standard errors after convergence
communality	communality values for each observed variable
communality.index	communality index values for each observed variable
criterion	sample discrepancy function value
d	degree of freedom of the model
dfNull	degree of freedom of the Null model
equal.ang	if TRUE, the variables are constrained to be equally distributed on the circumference. The default is FALSE
equal.com	if TRUE, the communality indices are constrained to be equal. The default is FALSE
m	number of free parameters in the Fourier correlation function
n	number of observations
polar.angles	data frame containing the estimated polar angles, the lower (L) and the upper (U) limits of an approximate 95% confidence interval for each variable
q	effective number of parameters
residuals	The residuals are defined as R - S (or R- Cs), where R is the sample correlation (or sample covariance) matrix of the observed variables and S (or Cs) is the model-reproduced correlation (or covariance) matrix
standardized.residuals	The standardized residual covariance for a pair of variables divides the residual covariance by the product of the sample standard deviations of the two variables
v.names	variable names

Author(s)

Michele Grassi [e-mail]

References

Grassi, M., Luccio, R., \& Di Blas, L. (2010) CircE: An R implementation of Browne's circular stochastic process model. Behavior Research Methods, 42(1), pp. 55-73.
Browne, M. W. (1992) Circumplex models for correlation matrices. Psychometrika, 57, pp. 469-497.
Browne, M. W., \& Du Toit, S. H. C. (1992) Automated fitting of nonstandard models. Multivariate Behavioral Research, 27, pp. 269-300.

Examples

#______ Vocational Interests Scale: Sample Correlation Matrix. N=175 _____
 
R.vocational=matrix(c(
1,0,0,0,0,0,0,
0.654,1,0,0,0,0,0,
0.453,0.644,1,0,0,0,0,
0.251,0.440,0.757,1,0,0,0,
0.122,0.158,0.551,0.493,1,0,0,
0.218,0.210,0.570,0.463,0.754,1,0,
0.496,0.264,0.366,0.202,0.471,0.650,1
),7,7,byrow=TRUE)
R=R.vocational+t(R.vocational)-diag(diag(R.vocational))


v.names=c("Health","Science","Technology","Trades","Business Operations",
          "Business Contact","Social")
dimnames(R)=list(v.names,v.names)


model=CircE.BFGS(R,v.names,m=3,N=175,r=1)


#______ Some useful residual matrix with residual.CircE() function...

residual.CircE(model,digits=3)

#______ Save output on .txt file at the current directory ___________________
# get current directory
getwd()

# save the example.txt file at the current directory with 
## Not run: 
CircE.BFGS(R,v.names,m=3,N=175,r=1,file="example CircE.BFGS.txt")

## End(Not run)
 

CircE documentation built on May 30, 2017, 4:14 a.m.