Last data update: 2014.03.03

R: Estimate Factor Analysis Models
FactanalR Documentation

Estimate Factor Analysis Models

Description

This function is intended for users and estimates a factor analysis model that has been set up previously with a call to make_manifest and a call to make_restrictions.

Usage

Factanal(manifest, restrictions, scores = "none", seeds = 12345, 
lower = sqrt(.Machine$double.eps), analytic = TRUE, reject = TRUE, 
NelderMead = TRUE, impatient = FALSE, ...)

Arguments

manifest

An object that inherits from manifest-class and is typically produced by make_manifest.

restrictions

An object that inherits from restrictions-class and is typically produced by make_restrictions.

scores

Type of factor scores to produce, if any. The default is "none". Other valid choices (which can be partially matched) are "regression", "Bartlett", "Thurstone", "Ledermann", "Anderson-Rubin", "McDonald",
"Krinjen", "Takeuchi", and "Harman". See Beauducel (2007) for formulae for these factor scores as well as proofs that all but "regression" and "Harman" produce the same correlation matrix.

seeds

A vector of length one or two to be used as the random number generator seeds corresponding to the unif.seed and int.seed arguments to genoud respectively. If seeds is a single number, this seed is used for both unif.seed and int.seed. These seeds override the defaults for genoud and make it easier to replicate an analysis exactly. If NULL, the default arguments for unif.seed and int.seed as specified in genoud are used. NULL should be used in simulations or else they will be horribly wrong.

lower

A lower bound. In exploratory factor analysis, lower is the minimum uniqueness and corresponds to the 'lower' element of the list specified for control in factanal. Otherwise, lower is the lower bound used for singular values when checking for positive-definiteness and ranks of matrices. If the unlikely event that you get errors referencing positive definiteness, try increasing the value of lower slightly.

analytic

A logical (default to TRUE) indicating whether analytic gradients should be used as much as possible. If FALSE, then numeric gradients will be calculated, which are slower and slightly less accurate but are necessary in some situations and useful for debugging analytic gradients.

reject

Logical indicating whether to reject starting values that fail the constraints required by the model; see create_start

NelderMead

Logical indicating whether to call optim with method = "Nelder-Mead" when the genetic algorithm has finished to further polish the solution. This option is not relevant or necessary for exploratory factor analysis models.

impatient

Logical that defaults to FALSE. If restrictions is of restrictions.factanal-class, setting it to TRUE will cause factanal to be used for optimization instead of genoud. In all other situations, setting it to TRUE will use factanal to to generate initial communality estimates instead of the slower default mechanism.

...

Further arguments that are passed to genoud. The following arguments to genoud are hard-coded and cannot be changed because they are logically required by the factor analyis estimator:

argument value why?
nvars restrictions@nvars
max FALSE minimizing the objective
hessian FALSE we roll our own
lexical TRUE (usually) for restricted optimization
Domains restrictions@Domains
data.type.int FALSE parameters are doubles
fn wrapper around fitS4
BFGSfn wrapper around bfgs_fitS4
BFGShelp wrapper around bfgs_helpS4
gr various it is complicated
unif.seed taken from seeds replicability
int.seed taken from seeds replicability

The following arguments to genoud default to values that differ from those documented at genoud but can be overridden by specifying them explicitly in the ... :

argument value why?
boundary.enforcement 1 usually 2 can cause problems
MemoryMatrix FALSE runs faster
print.level 1 output is not that helpful for >= 2
P9mix 1 to always accept the BFGS result
BFGSburnin -1 to delay the gradient check
max.generations 1000 big number is often necessary
project.path contains "Factanal.txt"
starting.values see the Details section

Other arguments to genoud will take the documented default values unless explicitly specified. In particular, you may want to change wait.generations and solution.tolerance. Also, if informative bounds were placed on any of the parameters in the call to make_restrictions it is usually preferable to specify that boundary.enforcement = 2 to use constrained optimization in the internal calls to optim. However, the "L-BFGS-B" optimizer is less robust than the default "BFGS" optimizer and occasionally causes fatal errors, largly due to misfortune.

Details

The call to Factanal is somewhat of a formality in the sense that most of the difficult decisions were already made in the call to make_restrictions and the call to make_manifest. The most important remaining detail is the specification of the values for the starting population in the genetic algorithm.

It is not necessary to provide starting values, since there are methods for this purpose; see create_start. Also, if starting.values = NA, then a population of starting values will be created using the typical mechanism in genoud, namely random uniform draws from the domain of the parameter.

Otherwise, if reject = TRUE, starting values that fail one or more constraints are rejected and new vectors of starting values are generated until the population is filled with admissable starting values. In some cases, the constraints are quite difficult to satisfy by chance, and it may be more practical to specify reject = FALSE or to supply starting values explicitly. If starting values are supplied, it is helpful if at least one member of the genetic population satisfies all the constraints imposed on the model. Note the rownames of restrictions@Domains, which indicate the proper order of the free parameters.

A matrix (or vector) of starting values can be passed as starting.values. (Also, it is possible to pass an object of FA-class to starting.values, in which case the estimates from the previous call to Factanal are used as the starting values.) If a matrix, it should have columns equal to the number of rows in restrictions@Domains in the specified order and one or more rows up to the number of genetic individuals in the population.

If starting.values is a vector, its length can be equal to the number of rows in restrictions@Domains in which case it is treated as a one-row matrix, or its length can be equal to the number of manifest variables, in which case it is passed to the start argument of create_start as a vector of initial communality estimes, thus avoiding the sometimes time-consuming process of generating good initial communality estimates. This process can also be accelerated by specifying impatient = TRUE.

Value

An object of that inherits from FA-class.

Note

The underlying genetic algorithm can print a variety of output as it progresses. On Windows, you either have to move the scrollbar periodically to flush the output to the screen or disable buffering by either going to the Misc menu or by clicking Control+W. The output will, by default, look something like this

Generation First Second ... Last Discrepancy
number constraint constraint constraint function
0 -1.0 -1.0 ... -1.0 double
1 -1.0 -1.0 ... -1.0 double
... ... ... ... ... ...
42 -1.0 -1.0 ... -1.0 double

The integer on the far left indicates the generation number. If it appears to skip one or more generations, that signifies that the best individual in the “missing” generation was no better than the best individual in the previous generation. The sequence of -1.0 indicates that various constraints are being satisfied by the best individual in the generation. Some of these constraints are hard-coded, some are added by the choices the user makes in the call to make_restrictions. The curious are referred to the source code, but for the most part users need not worry about them provided they are -1.0. If any but the last are not -1.0 after the first few generations, there is a major problem because no individual is satisfying all the constraints. The last number is a double-precision number indicating the value of the discrepancy function. This number will decrease, sometimes painfully slowly, sometimes intermittently, over the generations since the discrepancy function is being minimized, subject to the aforementioned constraints.

Author(s)

Ben Goodrich

References

Barthlomew, D. J. and Knott, M. (1990) Latent Variable Analysis and Factor Analysis. Second Edition, Arnold.

Beauducel, A. (2007) In spite of indeterminancy, many common factor score estimates yield an identical reproduced covariance matrix. Psychometrika, 72, 437–441.

Smith, G. A. and Stanley G. (1983) Clocking g: relating intelligence and measures of timed performance. Intelligence, 7, 353–368.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

make_manifest, make_restrictions, and Rotate

Examples

## Example from Venables and Ripley (2002, p. 323)
## Previously from Bartholomew and Knott  (1999, p. 68--72)
## Originally from Smith and Stanley (1983)
## Replicated from example(ability.cov)

man <- make_manifest(covmat = ability.cov)

## Not run: 
## Here is the easy way to set up a SEFA model, which uses pop-up menus
res <- make_restrictions(manifest = man, factors = 2, model = "SEFA")

## End(Not run)

## This is the hard way to set up a restrictions object without pop-up menus
beta <- matrix(NA_real_, nrow = nrow(cormat(man)), ncol = 2)
rownames(beta) <- rownames(cormat(man))
free <- is.na(beta)
beta <- new("parameter.coef.SEFA", x = beta, free = free, num_free = sum(free))

Phi  <- diag(2)
free <- lower.tri(Phi)
Phi  <- new("parameter.cormat", x = Phi, free = free, num_free = sum(free))
res  <- make_restrictions(manifest = man, beta = beta, Phi = Phi)

# This is how to make starting values where Phi is the correlation matrix 
# among factors, beta is the matrix of coefficients, and the scales are
# the logarithm of the sample standard deviations. It is also the MLE.
starts <- c( 4.46294498156615e-01, #  Phi_{21}
             4.67036349420035e-01, # beta_{11}
             6.42220238211291e-01, # beta_{21}
             8.88564379236454e-01, # beta_{31}
             4.77779639176941e-01, # beta_{41}
            -7.13405536379741e-02, # beta_{51}
            -9.47782525342137e-08, # beta_{61}
             4.04993872375487e-01, # beta_{12}
            -1.04604290549591e-08, # beta_{22}
            -9.44950629176182e-03, # beta_{32}
             2.63078925240678e-04, # beta_{42}
             9.38038168787216e-01, # beta_{52}
             8.43618801925473e-01, # beta_{62}
             log(man@sds))         # log manifest standard deviations

sefa <- Factanal(manifest = man, restrictions = res, 
                 # NOTE: Do NOT specify any of the following tiny values in a  
                 # real research situation; it is done here solely for speed
                 starting.values = starts, pop.size = 2, max.generations = 6,
                 wait.generations = 1)
nsim <- 101 # number of simulations, also too small for real work
show(sefa)
summary(sefa, nsim = nsim)
model_comparison(sefa, nsim = nsim)

stuff <- list() # output list for various methods
stuff$model.matrix <- model.matrix(sefa) # sample correlation matrix
stuff$fitted <- fitted(sefa, reduced = TRUE) # reduced covariance matrix
stuff$residuals <- residuals(sefa) # difference between model.matrix and fitted
stuff$rstandard <- rstandard(sefa) # normalized residual matrix
stuff$weights <- weights(sefa) # (scaled) approximate weights for residuals
stuff$influence <- influence(sefa) # weights * residuals
stuff$cormat <- cormat(sefa,  matrix = "RF") # reference factor correlations
stuff$uniquenesses <- uniquenesses(sefa, standardized = FALSE) # uniquenesses
stuff$FC <- loadings(sefa, matrix = "FC") # factor contribution matrix
stuff$draws <- FA2draws(sefa, nsim = nsim) # draws from sampling distribution

if(require(nFactors)) screeplot(sefa)  # Enhanced scree plot
profile(sefa) # profile plots of non-free parameters
pairs(sefa) # Thurstone-style plot
if(require(Rgraphviz)) plot(sefa) # DAG

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FAiR)
Loading required package: rgenoud
##  rgenoud (Version 5.7-12.4, Build Date: 2015-07-19)
##  See http://sekhon.berkeley.edu/rgenoud for additional documentation.
##  Please cite software as:
##   Walter Mebane, Jr. and Jasjeet S. Sekhon. 2011.
##   ``Genetic Optimization Using Derivatives: The rgenoud package for R.''
##   Journal of Statistical Software, 42(11): 1-26. 
##

Loading required package: gWidgetsRGtk2
Loading required package: RGtk2
Loading required package: gWidgets
Loading required package: cairoDevice
Loading required package: stats4
Loading required package: rrcov
Loading required package: robustbase
Scalable Robust Estimators with High Breakdown Point (version 1.3-11)

Loading required package: Matrix
##  FAiR Version 0.4-15 Build Date: 2014-02-08
## See http://wiki.r-project.org/rwiki/doku.php?id=packages:cran:fair for more info
FAiR  Copyright (C) 2008 -- 2012  Benjamin King Goodrich
This program comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome to redistribute it
under certain conditions, namely those specified in the LICENSE file
in the root directory of the source code.
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FAiR/03Factanal.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Factanal
> ### Title: Estimate Factor Analysis Models
> ### Aliases: Factanal
> ### Keywords: multivariate models
> 
> ### ** Examples
> 
> ## Example from Venables and Ripley (2002, p. 323)
> ## Previously from Bartholomew and Knott  (1999, p. 68--72)
> ## Originally from Smith and Stanley (1983)
> ## Replicated from example(ability.cov)
> 
> man <- make_manifest(covmat = ability.cov)
Warning message:
In FAiR_make_manifest_list(covmat, shrink) :
  it is strongly preferable to pass the raw data to make_manifest()
> 
> ## Not run: 
> ##D ## Here is the easy way to set up a SEFA model, which uses pop-up menus
> ##D res <- make_restrictions(manifest = man, factors = 2, model = "SEFA")
> ## End(Not run)
> 
> ## This is the hard way to set up a restrictions object without pop-up menus
> beta <- matrix(NA_real_, nrow = nrow(cormat(man)), ncol = 2)
> rownames(beta) <- rownames(cormat(man))
> free <- is.na(beta)
> beta <- new("parameter.coef.SEFA", x = beta, free = free, num_free = sum(free))
> 
> Phi  <- diag(2)
> free <- lower.tri(Phi)
> Phi  <- new("parameter.cormat", x = Phi, free = free, num_free = sum(free))
> res  <- make_restrictions(manifest = man, beta = beta, Phi = Phi)
> 
> # This is how to make starting values where Phi is the correlation matrix 
> # among factors, beta is the matrix of coefficients, and the scales are
> # the logarithm of the sample standard deviations. It is also the MLE.
> starts <- c( 4.46294498156615e-01, #  Phi_{21}
+              4.67036349420035e-01, # beta_{11}
+              6.42220238211291e-01, # beta_{21}
+              8.88564379236454e-01, # beta_{31}
+              4.77779639176941e-01, # beta_{41}
+             -7.13405536379741e-02, # beta_{51}
+             -9.47782525342137e-08, # beta_{61}
+              4.04993872375487e-01, # beta_{12}
+             -1.04604290549591e-08, # beta_{22}
+             -9.44950629176182e-03, # beta_{32}
+              2.63078925240678e-04, # beta_{42}
+              9.38038168787216e-01, # beta_{52}
+              8.43618801925473e-01, # beta_{62}
+              log(man@sds))         # log manifest standard deviations
> 
> sefa <- Factanal(manifest = man, restrictions = res, 
+                  # NOTE: Do NOT specify any of the following tiny values in a  
+                  # real research situation; it is done here solely for speed
+                  starting.values = starts, pop.size = 2, max.generations = 6,
+                  wait.generations = 1)


Mon Jul  4 17:53:27 2016
Domains:
 -1.000000e+00   <=  X1   <=    1.000000e+00 
 -1.500000e+00   <=  X2   <=    1.500000e+00 
 -1.500000e+00   <=  X3   <=    1.500000e+00 
 -1.500000e+00   <=  X4   <=    1.500000e+00 
 -1.500000e+00   <=  X5   <=    1.500000e+00 
 -1.500000e+00   <=  X6   <=    1.500000e+00 
 -1.500000e+00   <=  X7   <=    1.500000e+00 
 -1.500000e+00   <=  X8   <=    1.500000e+00 
 -1.500000e+00   <=  X9   <=    1.500000e+00 
 -1.500000e+00   <=  X10  <=    1.500000e+00 
 -1.500000e+00   <=  X11  <=    1.500000e+00 
 -1.500000e+00   <=  X12  <=    1.500000e+00 
 -1.500000e+00   <=  X13  <=    1.500000e+00 
 -1.800000e+01   <=  X14  <=    2.295353e+00 
 -1.800000e+01   <=  X15  <=    1.644201e+00 
 -1.800000e+01   <=  X16  <=    3.197901e+00 
 -1.800000e+01   <=  X17  <=    1.964381e+00 
 -1.800000e+01   <=  X18  <=    2.674543e+00 
 -1.800000e+01   <=  X19  <=    3.146865e+00 

Data Type: Floating Point
Operators (code number, name, population) 
	(1) Cloning........................... 	1
	(2) Uniform Mutation.................. 	0
	(3) Boundary Mutation................. 	0
	(4) Non-Uniform Mutation.............. 	0
	(5) Polytope Crossover................ 	0
	(6) Simple Crossover.................. 	0
	(7) Whole Non-Uniform Mutation........ 	0
	(8) Heuristic Crossover............... 	0
	(9) Local-Minimum Crossover........... 	0

HARD Maximum Number of Generations: 6
Maximum Nonchanging Generations: 1
Population size       : 2
Convergence Tolerance: 1.000000e-03

Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Checking Gradients before Stopping.
Not Using Out of Bounds Individuals But Allowing Trespassing.

Minimization Problem.


Generation#	    Solution Values (lexical)

      0 	-1.000000e+00  -1.000000e+00  -1.000000e+00  -1.000000e+00  6.356664e-02  

'wait.generations' limit reached.
No significant improvement in 1 generations.

Solution Lexical Fitness Value:
-1.000000e+00  -1.000000e+00  -1.000000e+00  -1.000000e+00  6.356664e-02  

Parameters at the Solution (parameter, gradient):

 X[ 1] :	4.462945e-01	G[ 1] :	-1.506061e-05
 X[ 2] :	4.670363e-01	G[ 2] :	-2.910233e-05
 X[ 3] :	6.422202e-01	G[ 3] :	-2.225256e-05
 X[ 4] :	8.885644e-01	G[ 4] :	-5.605264e-05
 X[ 5] :	4.777796e-01	G[ 5] :	-6.675071e-06
 X[ 6] :	-7.134055e-02	G[ 6] :	-0.000000e+00
 X[ 7] :	-9.477825e-08	G[ 7] :	-0.000000e+00
 X[ 8] :	4.049939e-01	G[ 8] :	-1.463011e-05
 X[ 9] :	-1.046043e-08	G[ 9] :	-0.000000e+00
 X[10] :	-9.449506e-03	G[10] :	-2.643417e-05
 X[11] :	2.630789e-04	G[11] :	0.000000e+00
 X[12] :	9.380382e-01	G[12] :	4.832929e-06
 X[13] :	8.436188e-01	G[13] :	-7.343759e-06
 X[14] :	1.602206e+00	G[14] :	1.174018e-05
 X[15] :	9.510538e-01	G[15] :	9.504571e-06
 X[16] :	2.504754e+00	G[16] :	2.032664e-05
 X[17] :	1.271234e+00	G[17] :	3.728702e-06
 X[18] :	1.981396e+00	G[18] :	1.588892e-06
 X[19] :	2.453718e+00	G[19] :	1.738531e-06

Solution Found Generation 1
Number of Generations Run 2

Mon Jul  4 17:53:27 2016
Total run time : 0 hours 0 minutes and 0 seconds
Nelder-Mead resulted in no improvement;  convergence presumably achieved
> nsim <- 101 # number of simulations, also too small for real work
> show(sefa)

Call:
Factanal(manifest = man, restrictions = res, starting.values = starts, 
    pop.size = 2, max.generations = 6, wait.generations = 1)

Number of observations:  112 

Discrepancy:  7.055898 

Semi-exploratory factor analysis with  2 factors
All free factor intercorrelations are on the [-1,1] interval

All coefficients on the [ -1.5 , 1.5 ] interval

Zeros per factor
      A B
zeros 2 2
Mapping rule: default

Discrepancy function:  MLE 

 6 degrees of freedom

> summary(sefa, nsim = nsim)
[1] "100 simulations remaining"
[1] "0 simulations remaining"

Call:
Factanal(manifest = man, restrictions = res, starting.values = starts, 
    pop.size = 2, max.generations = 6, wait.generations = 1)

Point estimates (blanks, if any, are exact zeros):
        F1     F2            Uniqueness
general  0.467  0.405         0.449    
picture  0.642                0.588    
blocks   0.889 -0.009         0.218    
maze     0.478                0.772    
reading         0.938         0.120    
vocab           0.844         0.288    
                                       
F1       1.000  0.446                  
F2       0.446  1.000                  

Upper confidence bounds (blanks, if any, are restricted)
        F1    F2          Uniqueness
general 0.612 0.614       0.550     
picture 0.818             0.760     
blocks  1.030 0.335       0.459     
maze    0.650             0.896     
reading       0.991       0.264     
vocab         0.936       0.409     
                                    
F1      1.000 0.627                 
F2      0.627 1.000                 

Lower confidence bounds (blanks, if any, are restricted)
        F1     F2            Uniqueness
general  0.329  0.257         0.311    
picture  0.489                0.331    
blocks   0.631 -0.223         0.085    
maze     0.322                0.578    
reading         0.858         0.018    
vocab           0.769         0.124    
                                       
F1       1.000  0.192                  
F2       0.192  1.000                  
> model_comparison(sefa, nsim = nsim)
$restrictions

Semi-exploratory factor analysis with  2 factors
All free factor intercorrelations are on the [-1,1] interval

All coefficients on the [ -1.5 , 1.5 ] interval

Zeros per factor
      A B
zeros 2 2
Mapping rule: default

Discrepancy function:  MLE 

 6 degrees of freedom

$exact_fit
$exact_fit$T_ML

	Test of Exact Fit

data:  
T ( Swain correction ) = 17.505, df = 6, p-value = 0.007597
alternative hypothesis: true discrepancy is greater than 0



$infocriteria
$infocriteria$BIC
[1] 2869.069

$infocriteria$BIC_saturated
[1] 2879.394

$infocriteria$BIC_null
[1] 3126.466

$infocriteria$SIC
[1] 1440.894

$infocriteria$SIC_saturated
[1] 1508.444

$infocriteria$SIC_null
[1] 1569.592


$close_fit
$close_fit$RMSEA

	Test of Close Fit

data:  
T ( Swain correction ) = 17.505, df = 6, p-value = 0.03022
alternative hypothesis: true discrepancy is greater than 0.05
90 percent confidence interval:
 0.06224984 0.20515226
sample estimates:
    RMSEA 
0.1314315 


$close_fit$gamma

	Gamma Fit Index (Steiger)

data:  

90 percent confidence interval:
 0.9223604 0.9923095
sample estimates:
  Gamma_1 
0.9666053 



$fit_indices
$fit_indices$GFI
[1] 0.9453479

$fit_indices$AGFI
[1] 0.8087177

$fit_indices$McDonald

	Centrality Index (McDonald)

data:  

sample estimates:
    Index 
0.9499366 


$fit_indices$SRMR
[1] 0.05592103

$fit_indices$TLI
T ( Swain correction ) 
             0.8863219 

$fit_indices$CFI
[1] 0.9545287

$fit_indices$NFI
T ( Swain correction ) 
             0.9346864 

$fit_indices$NNFI
T ( Swain correction ) 
             0.8863219 


> 
> stuff <- list() # output list for various methods
> stuff$model.matrix <- model.matrix(sefa) # sample correlation matrix
> stuff$fitted <- fitted(sefa, reduced = TRUE) # reduced covariance matrix
> stuff$residuals <- residuals(sefa) # difference between model.matrix and fitted
> stuff$rstandard <- rstandard(sefa) # normalized residual matrix
> stuff$weights <- weights(sefa) # (scaled) approximate weights for residuals
> stuff$influence <- influence(sefa) # weights * residuals
> stuff$cormat <- cormat(sefa,  matrix = "RF") # reference factor correlations
> stuff$uniquenesses <- uniquenesses(sefa, standardized = FALSE) # uniquenesses
> stuff$FC <- loadings(sefa, matrix = "FC") # factor contribution matrix
> stuff$draws <- FA2draws(sefa, nsim = nsim) # draws from sampling distribution
[1] "100 simulations remaining"
[1] "0 simulations remaining"
> 
> if(require(nFactors)) screeplot(sefa)  # Enhanced scree plot
Loading required package: nFactors
Loading required package: MASS
Loading required package: psych

Attaching package: 'psych'

The following object is masked from 'package:robustbase':

    cushny

Loading required package: boot

Attaching package: 'boot'

The following object is masked from 'package:psych':

    logit

The following object is masked from 'package:robustbase':

    salinity

Loading required package: lattice

Attaching package: 'lattice'

The following object is masked from 'package:boot':

    melanoma


Attaching package: 'nFactors'

The following object is masked from 'package:lattice':

    parallel

> profile(sefa) # profile plots of non-free parameters
Factors may arbitrarily be plotted in a different order than they  appear in summary()
> pairs(sefa) # Thurstone-style plot
> if(require(Rgraphviz)) plot(sefa) # DAG
Loading required package: Rgraphviz
Loading required package: graph
Loading required package: BiocGenerics
Loading required package: parallel

Attaching package: 'BiocGenerics'

The following objects are masked from 'package:parallel':

    clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
    clusterExport, clusterMap, parApply, parCapply, parLapply,
    parLapplyLB, parRapply, parSapply, parSapplyLB

The following objects are masked from 'package:stats':

    IQR, mad, xtabs

The following objects are masked from 'package:base':

    Filter, Find, Map, Position, Reduce, anyDuplicated, append,
    as.data.frame, cbind, colnames, do.call, duplicated, eval, evalq,
    get, grep, grepl, intersect, is.unsorted, lapply, lengths, mapply,
    match, mget, order, paste, pmax, pmax.int, pmin, pmin.int, rank,
    rbind, rownames, sapply, setdiff, sort, table, tapply, union,
    unique, unsplit

Loading required package: grid
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> 
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> dev.off()
null device 
          1 
>