| Type: | Package |
| Title: | Robust Structural Equation Modeling with Missing Data and Auxiliary Variables |
| Version: | 0.5.1 |
| Date: | 2023-08-26 |
| Author: | Ke-Hai Yuan and Zhiyong Zhang |
| Maintainer: | Zhiyong Zhang <zhiyongzhang@nd.edu> |
| Depends: | R (≥ 2.7), MASS, lavaan |
| Description: | A robust procedure is implemented to estimate means and covariance matrix of multiple variables with missing data using Huber weight and then to estimate a structural equation model. |
| License: | GPL-2 |
| URL: | https://bigdatalab.nd.edu |
| ZipData: | no |
| LazyLoad: | yes |
| NeedsCompilation: | no |
| Repository: | CRAN |
| Packaged: | 2023-08-26 20:08:52 UTC; zzhang4 |
| Date/Publication: | 2023-08-26 20:40:02 UTC |
Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Description
A robust procedure is implemented to estimate means and covariance matrix of multiple variables with missing data using Huber weight and then to estimate a structural equation model.
Details
| Package: | rsem |
| Type: | Package |
| License: | GPL-2 |
| LazyLoad: | yes |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang Maintainer: Zhiyong Zhang <zhiyongzhang@nd.edu>
References
Yuan, K.-H., & Zhang, Z. (2012). Robust structural equation modeling with missing data and auxiliary variables. Psychometrika, 77(4), 803-826. https://doi.org/10.1007/s11336-012-9282-4
Simulated data
Description
mardiamv25: Original data
mardiamv25_contaminated: Contaminated data with outliers
Usage
data(mardiamv25)
data(mardiamv25_contaminated)
The main function for robust SEM analysis
Description
This is the function to carry out all analysis.
Usage
rsem(dset, select, EQSmodel, moment=TRUE, varphi=.1, st='i', max.it=1000,
eqsdata='data.txt', eqsweight='weight.txt', EQSpgm="C:/Progra~1/EQS61/WINEQS.EXE",
serial="1234")
Arguments
dset |
A data matrix or a data frame |
select |
Variables to be seleted for SEM analysis. If omitted, all variables in the data set will be used. |
moment |
With mean structure. For covariance only, set moment=FALSE. |
EQSmodel |
The input file for EQS. If omitted, only the first-stage analysis will be conducted. |
varphi |
Proportion of data to be down-weighted. Default is 0.1. |
max.it |
Maximum number of iterations for EM. Default is 1000 |
st |
Starting values for EM algorithm. The default is 0 for mean and I for covariance. Alternative, the starting values can be estimated according to MCD. |
eqsdata |
Data file name used in EQS |
eqsweight |
File name for weight matrix |
EQSpgm |
The path to the installed EQS program |
serial |
The serial no of EQS |
Details
This function will run the robust analysis and output results.
Value
If EQSmodel is not supplied
sem |
Information for SEM analysis including estimated means, covariance matrix and their sandwich type covariance matrix in the order of mean first and then covariance matrix. |
misinfo |
Information related to missing data pattern |
em |
Results from expectation robust algorithm |
ascov |
Covariance matrix |
If EQSmodel is supplied,
sem |
Information for SEM analysis including estimated means, covariance matrix and their sandwich type covariance matrix according to the requirement of EQS. |
In addition, the following model parameters are from EQS
fit.stat |
Fit indices and associated p-values |
para |
Parameter estimates |
eqs |
All information from REQS |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
See Also
rsem.pattern, rsem.emmusig, rsem.Ascov
Examples
## Not run:
## an example
## to use eqs, first load the package semdiag
library(semdiag)
data(mardiamv25)
analysis<-rsem(mardiamv25, c(1,2,4,5), 'eqsinput.eqs')
## End(Not run)
Sandwich-type covariance matrix
Description
Returns the sandwich type covariance matrix. This function is not intended to use seperately from the rsem.emmusig function.
Usage
rsem.Ascov(xpattern, musig, varphi=.1)
Arguments
xpattern |
Missing data pattern output from |
musig |
Robust mean and covariance matrix from |
varphi |
Proportion of data to be down-weighted. Default is 0.1. |
Details
Data should be a matrix. To change a data frame to a matrix, using data.matrix(x).
Value
Abeta |
A matrix |
Bbeta |
B matrix |
Gamma |
Sandwich type covariance matrix |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
See Also
Examples
#dset<-read.table('MardiaMV25.dat.txt', na.string='-99')
#dset<-data.matrix(dset)
#n<-dim(dset)[1]
#p<-dim(dset)[2]
#miss_pattern<-rsem.pattern(n,p,dset)
#misinfo<-miss_pattern$misinfo
#V_forana<-c(1,2,4,5)
#em_results<-rsem.emmusig(dset,misinfo)
#hmu1<-em_results$mu
#hsigma1<-em_results$sigma
#rsem.Ascov(x, hmu1, hsigma1)
Generate a duplication matrix
Description
Generate a duplication matrix
Usage
rsem.DP(x)
Arguments
x |
A matrix |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Examples
x<-array(1:6, c(2,3))
rsem.DP(x)
Robust mean and covariance matrix using Huber-type weight
Description
Robust mean and covariance matrix using Huber-type weight.
Usage
rsem.emmusig(xpattern, varphi=.1, max.it=1000, st='i')
Arguments
xpattern |
Missing data pattern output from |
varphi |
Proportion of data to be down-weighted. Default is 0.1. |
max.it |
Maximum number of iterations for EM. Default is 1000 |
st |
Starting values for EM algorithm. The default is 0 for mean and I for covariance. Alternative, the starting values can be estimated according to MCD. |
Details
Estimate mean and covariance matrix using the expectation robust (ER) algorithm.
Value
err |
Error code. 0: good. 1: maximum iterations are exceeded. |
mu |
Mean vector |
sigma |
Covariance matrix |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
See Also
Examples
#dset<-read.table('MardiaMV25.dat.txt', na.string='-99')
#dset<-data.matrix(dset)
#n<-dim(dset)[1]
#p<-dim(dset)[2]
#miss_pattern<-rsem.pattern(n,p,dset)
#misinfo<-miss_pattern$misinfo
#V_forana<-c(1,2,4,5)
#em_results<-rsem.emmusig(dset,misinfo)
#em_results
Calculate robust test statistics
Description
Calculate robust test statistics
Usage
rsem.fit(object, gamma, musig)
Arguments
object |
Output from lavaan analysis, such as growth, factor, sem functions. |
gamma |
Robust covariance matrix for saturated mean and covariances |
musig |
Robust saturated mean and covariances |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Examples
x<-array(1:6, c(2,3))
rsem.vec(x)
Internal function
Description
Internal function
Usage
rsem.gname(name)
Arguments
name |
Variable names. |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
rsem.index function
Description
To be added
Usage
rsem.index(p, oj)
Arguments
p |
number of variables |
oj |
observed variables |
rsem.indexv function
Description
Internal function.
Usage
rsem.indexv(p, select)
Arguments
p |
number of variables |
select |
variables to be used |
rsem.indexvc function
Description
Internal function.
Usage
rsem.indexvc(p, select)
Arguments
p |
number of variables |
select |
variables to be used |
Conduct robust SEM analysis using lavaan
Description
Conduct robust SEM analysis using lavaan
Usage
rsem.lavaan(dset, model, select, varphi=.1, max.it=1000)
Arguments
dset |
A data matrix or a data frame |
select |
Variables to be seleted for SEM analysis. If omitted, all variables in the data set will be used. |
model |
The model using lavaan syntax |
varphi |
Proportion of data to be down-weighted. Default is 0.1. |
max.it |
Maximum number of iterations for EM. Default is 1000 |
Details
This function will run the robust analysis and output results.
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Yuan, K.-H., & Zhang, Z. (2012). Robust Structural Equation Modeling with Missing Data and Auxiliary Variables. Psychometrika, 77(4), 803-826.
See Also
rsem.pattern, rsem.emmusig, rsem.Ascov
Examples
data(mardiamv25)
names(mardiamv25)<-paste('V', 1:5, sep='')
fa.model<-'f1 =~ V1 + V2
f2 =~ V4 + V5
f1 ~ 1
f2 ~ 1
V1 ~0*1
V2 ~0*1
V4 ~0*1
V5 ~0*1'
analysis<-rsem.lavaan(mardiamv25, fa.model, c(1,2,4,5))
Obtaining missing data patterns
Description
This function obtains the missing data patterns and the number of cases in each patterns. It also tells the number of observed variables and their indices for each pattern.
Usage
rsem.pattern(x, print=FALSE)
Arguments
x |
A matrix as data |
print |
Whether to print the missing data pattern. The default is FALSE. |
Details
The missing data pattern matrix has 2+p columns. The first column is the number cases in that pattern. The second column is the number of observed variables. The last p columns are a matrix with 1 denoting observed data and 0 denoting missing data.
Value
x |
Data ordered according to missing data pattern |
misinfo |
Missing data pattern matrix |
mispat |
Missing data pattern in better readable form. |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Examples
#dset<-read.table('MardiaMV25.dat.txt', na.string='-99')
#dset<-data.matrix(dset)
#n<-dim(dset)[1]
#p<-dim(dset)[2]
#miss_pattern<-rsem.pattern(n,p,dset)
#miss_pattern
Organize the output for Lavaan with robust s.e. and test statistics
Description
Organize the output for Lavaan with robust s.e. and test statistics. Modified from the print function of Lavaan.
Usage
rsem.print(object, robust.se, robust.fit, estimates=TRUE, fit.measures=FALSE,
standardized=FALSE, rsquare=FALSE, std.nox=FALSE, modindices=FALSE)
Arguments
object |
Output from lavaan analysis, such as growth, factor, sem functions. |
robust.se |
Robust standard error from the function rsem.se |
robust.fit |
Robust fit statistics from the function rsem.fit |
estimates |
Show parameter estimates |
fit.measures |
Show fit statistics of lavaan (no need for it) |
standardized |
standardized coefficients |
rsquare |
R square for dependent variables. |
std.nox |
to add |
modindices |
Modification indices |
Details
This function will run the robust analysis and output results.
Value
If EQSmodel is not supplied
sem |
Information for SEM analysis including estimated means, covariance matrix and their sandwich type covariance matrix in the order of mean first and then covariance matrix. |
misinfo |
Information related to missing data pattern |
em |
Results from expectation robust algorithm |
ascov |
Covariance matrix |
If EQSmodel is supplied,
sem |
Information for SEM analysis including estimated means, covariance matrix and their sandwich type covariance matrix according to the requirement of EQS. |
In addition, the following model parameters are from EQS
fit.stat |
Fit indices and associated p-values |
para |
Parameter estimates |
eqs |
All information from REQS |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
See Also
rsem.pattern, rsem.emmusig, rsem.Ascov
Examples
##\dontrun{
## an example
data(mardiamv25)
names(mardiamv25)<-paste('V', 1:5, sep='')
fa.model<-'f1 =~ V1 + V2
f2 =~ V4 + V5
f1 ~ 1
f2 ~ 1
V1 ~0*1
V2 ~0*1
V4 ~0*1
V5 ~0*1'
pat<-rsem.pattern(mardiamv25)
phi<-0.1
musig<-rsem.emmusig(pat, varphi=phi)
res.lavaan<-sem(fa.model, sample.cov=musig$sigma, sample.mean=musig$mu, sample.nobs=88,mimic='EQS')
ascov<-rsem.Ascov(pat, musig, varphi=phi)
robust.se<-rsem.se(res.lavaan, ascov$Gamma)
robust.fit <- rsem.fit(res.lavaan, ascov$Gamma, musig)
rsem.print(res.lavaan, robust.se, robust.fit)
## }
Calculate robust standard errors
Description
Calculate robust standard errors
Usage
rsem.se(object, gamma)
Arguments
object |
Output from lavaan analysis, such as growth, factor, sem functions. |
gamma |
Robust covariance matrix for saturated mean and covariances |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Examples
x<-array(1:6, c(2,3))
rsem.vec(x)
Calculate the squared sum of a matrix
Description
Calculate the squared sum of a matrix
Usage
rsem.ssq(x)
Arguments
x |
A matrix |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Examples
x<-array(1:6, c(2,3))
rsem.ssq(x)
swith function
Description
swith function
Usage
rsem.switch(p)
Arguments
p |
number of variables |
Internal function
Description
Internal function
Usage
rsem.switch.gamma(gamma, ov.names)
Arguments
gamma |
Robust covariance matrix for saturated mean and covariances |
ov.names |
Observed variable names. |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Stacking a matrix to a vector
Description
Stacking a matrix to a vector
Usage
rsem.vec(x)
Arguments
x |
A matrix |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Examples
x<-array(1:6, c(2,3))
rsem.vec(x)
Stacking lower triange of a matrix to a vector
Description
Stacking lower triange of a matrix to a vector
Usage
rsem.vech(x)
Arguments
x |
A matrix |
Author(s)
Ke-Hai Yuan and Zhiyong Zhang
References
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Examples
x<-array(1:9, c(3,3))
rsem.vec(x)
Calculate weight for each subject
Description
Calculate weight for each subject in estimating the mean and covariance matrix.
Usage
rsem.weight(x, varphi, mu0, sig0)
Arguments
x |
Data |
varphi |
Downweight rate. |
mu0 |
Robust mean |
sig0 |
Robust covariance matrix. |
Value
w1 |
Weight for robust mean estimates |
w2 |
Weight for robust covariance estimates |
Author(s)
Zhiyong Zhang and Ke-Hai Yuan
References
Yuan, K.-H., & Zhang, Z. (2012). Robust Structural Equation Modeling with Missing Data and Auxiliary Variables. Psychometrika, 77(4), 803-826.
Enumerate the Combinations of the Elements of a Vector
Description
Enumerate the Combinations of the Elements of a Vector
Usage
semdiag.combinations(n, r)
Arguments
n |
Size of the source vector |
r |
Size of the target vectors |
Import of EQS outputs into R
Description
This function reads EQS output files (.ets, .CBK and .ETP) into R and stores the results as objects.
Usage
semdiag.read.eqs(file)
Arguments
file |
The name (string) of the .ets file or the full path which the data are to be read from. If it does not contain an absolute path, the file name is relative to the current working directory, 'getwd()'. A .CBK and .ETP file have to be of the same name and in the same directory. |
Details
The value list below provides objects for the full EQS output. If in EQS some objects are not computed, the corresponding values in R are NA.
Value
Returns a list with the following objects:
model.info |
General model information |
pval |
p-values for various test statistics |
fit.indices |
Variuos fit indices |
model.desc |
Descriptive measures |
Phi |
Phi matrix |
Gamma |
Gamma matrix |
Beta |
Beta matrix |
par.table |
Parameter table (with standard errors) |
sample.cov |
Sample covariance matrix |
sigma.hat |
Model covariance matrix |
inv.infmat |
Inverse information matrix |
rinv.infmat |
Robust inverse information matrix |
cinv.infmat |
Corrected inverse information matrix |
derivatives |
First derivatives |
moment4 |
Matrix with 4th moments |
ssolution |
Standardized elements |
Rsquared |
R-squared measures |
fac.means |
Factor means |
var.desc |
Descriptive measures for the variables (univariate statistics) |
indstd |
Independent variable standardization vector |
depstd |
Dependent variable standardization vector |
Author(s)
Patrick Mair, Eric Wu
References
Bentler, P. M. (2008). EQS Program Manual. Encino, CA: Multivariate Software Inc.
See Also
semdiag.call.eqs, semdiag.run.eqs
Run EQS from R
Description
Calls an EQS script file from R, executes EQS, and imports the results into R. Basically
it is a wrapper function of call.eqs and the subsequent read.eqs.
Usage
semdiag.run.eqs(EQSpgm, EQSmodel, serial, Rmatrix = NA, datname = NA, LEN = 2000000)
semdiag.call.eqs(EQSpgm, EQSmodel, serial, Rmatrix = NA, datname = NA, LEN = 2000000)
Arguments
EQSpgm |
String containing path where EQS is located (see details) |
EQSmodel |
String containing path where .eqs script file is located (see details) |
serial |
EQS serial number as integer value |
Rmatrix |
Optional matrix argument if data or covariances are stored in R |
datname |
If |
LEN |
Integer containing number of working array units. By default, it is 2000000 8 bytes units |
Details
If the path in EQSpgm and EQSmodel contains a blank, single quotes and double quotes
are required in argument. See EQSpgm argument in examples. The last statement in the EQSpgm argument refers
to the name of the executable program file. Under Windows it is ".../WINEQS" (referring to WINEQS.exe), under Mac ".../MACEQS" and
under Linux ".../EQS". When specifying the path, use slash instead of backslash.
The .ETS, .CBK and .ETP files are written in the directory where the .eqs file is located. Note that these 3 files must be in the same directory than the .eqs file.
The argument datname must match with the input data specified in the corresponding .eqs file.
This option can be used for simulations: Generate data in R, run.eqs() on with the corresponding
data argument, pick out the relevant return values.
The value list below provides objects for the full EQS output. If in EQS some objects are not computed, the corresponding values in R are NA.
Value
Returns a list with the following objects:
success |
|
model.info |
General model information |
pval |
p-values for various test statistics |
fit.indices |
Variuos fit indices |
model.desc |
Descriptive measures |
Phi |
Phi matrix |
Gamma |
Gamma matrix |
Beta |
Beta matrix |
par.table |
Parameter table (with standard errors) |
sample.cov |
Sample covariance matrix |
sigma.hat |
Model covariance matrix |
inv.infmat |
Inverse information matrix |
rinv.infmat |
Robust inverse information matrix |
cinv.infmat |
Corrected inverse information matrix |
derivatives |
First derivatives |
moment4 |
Matrix with 4th moments |
ssolution |
Standardized elements |
Rsquared |
R-squared measures |
fac.means |
Factor means |
var.desc |
Descriptive measures for the variables (univariate statistics) |
indstd |
Independent variable standardization vector |
depstd |
Dependent variable standardization vector |
Author(s)
Patrick Mair, Eric Wu
References
Bentler, P. M. (1995). EQS Program Manual. Encino, CA: Multivariate Software Inc.