CircE (version 1.1)

CircE.BFGS: 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.

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

Details

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

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)