| Title: | 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. |
| Authors: | Ke-Hai Yuan and Zhiyong Zhang |
| Maintainer: | Zhiyong Zhang <[email protected]> |
| License: | GPL-2 |
| Version: | 0.5.1 |
| Built: | 2025-02-28 04:00:57 UTC |
| Source: | https://github.com/cran/rsem |
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.
| Package: | rsem |
| Type: | Package |
| License: | GPL-2 |
| LazyLoad: | yes |
Ke-Hai Yuan and Zhiyong Zhang Maintainer: Zhiyong Zhang <[email protected]>
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
mardiamv25: Original data
mardiamv25_contaminated: Contaminated data with outliers
data(mardiamv25) data(mardiamv25_contaminated)data(mardiamv25) data(mardiamv25_contaminated)
This is the function to carry out all analysis.
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")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")
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 |
This function will run the robust analysis and output results.
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 |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
rsem.pattern, rsem.emmusig, rsem.Ascov
## 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)## 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)
Returns the sandwich type covariance matrix. This function is not intended to use seperately from the rsem.emmusig function.
rsem.Ascov(xpattern, musig, varphi=.1)rsem.Ascov(xpattern, musig, varphi=.1)
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. |
Data should be a matrix. To change a data frame to a matrix, using data.matrix(x).
Abeta |
A matrix |
Bbeta |
B matrix |
Gamma |
Sandwich type covariance matrix |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
#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$sigma #rsem.Ascov(x, hmu1, hsigma1)#dset<-read.table('MardiaMV25.dat.txt', na.string='-99') #dset<-data.matrix(dset) #n<-dim(dset)[1] #p<-dim(dset)[2] #miss_pattern<-rsem.pattern(n,p,dset) #misinfo<-miss_pattern$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
rsem.DP(x)rsem.DP(x)
x |
A matrix |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
x<-array(1:6, c(2,3)) rsem.DP(x)x<-array(1:6, c(2,3)) rsem.DP(x)
Robust mean and covariance matrix using Huber-type weight.
rsem.emmusig(xpattern, varphi=.1, max.it=1000, st='i')rsem.emmusig(xpattern, varphi=.1, max.it=1000, st='i')
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. |
Estimate mean and covariance matrix using the expectation robust (ER) algorithm.
err |
Error code. 0: good. 1: maximum iterations are exceeded. |
mu |
Mean vector |
sigma |
Covariance matrix |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
#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$misinfo #V_forana<-c(1,2,4,5) #em_results<-rsem.emmusig(dset,misinfo) #em_results#dset<-read.table('MardiaMV25.dat.txt', na.string='-99') #dset<-data.matrix(dset) #n<-dim(dset)[1] #p<-dim(dset)[2] #miss_pattern<-rsem.pattern(n,p,dset) #misinfo<-miss_pattern$misinfo #V_forana<-c(1,2,4,5) #em_results<-rsem.emmusig(dset,misinfo) #em_results
Calculate robust test statistics
rsem.fit(object, gamma, musig)rsem.fit(object, gamma, musig)
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 |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
x<-array(1:6, c(2,3)) rsem.vec(x)x<-array(1:6, c(2,3)) rsem.vec(x)
Internal function
rsem.gname(name)rsem.gname(name)
name |
Variable names. |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
To be added
rsem.index(p, oj)rsem.index(p, oj)
p |
number of variables |
oj |
observed variables |
Internal function.
rsem.indexv(p, select)rsem.indexv(p, select)
p |
number of variables |
select |
variables to be used |
Internal function.
rsem.indexvc(p, select)rsem.indexvc(p, select)
p |
number of variables |
select |
variables to be used |
Conduct robust SEM analysis using lavaan
rsem.lavaan(dset, model, select, varphi=.1, max.it=1000)rsem.lavaan(dset, model, select, varphi=.1, max.it=1000)
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 |
This function will run the robust analysis and output results.
Ke-Hai Yuan and Zhiyong Zhang
Yuan, K.-H., & Zhang, Z. (2012). Robust Structural Equation Modeling with Missing Data and Auxiliary Variables. Psychometrika, 77(4), 803-826.
rsem.pattern, rsem.emmusig, rsem.Ascov
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))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))
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.
rsem.pattern(x, print=FALSE)rsem.pattern(x, print=FALSE)
x |
A matrix as data |
print |
Whether to print the missing data pattern. The default is FALSE. |
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.
x |
Data ordered according to missing data pattern |
misinfo |
Missing data pattern matrix |
mispat |
Missing data pattern in better readable form. |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
#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#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. Modified from the print function of Lavaan.
rsem.print(object, robust.se, robust.fit, estimates=TRUE, fit.measures=FALSE, standardized=FALSE, rsquare=FALSE, std.nox=FALSE, modindices=FALSE)rsem.print(object, robust.se, robust.fit, estimates=TRUE, fit.measures=FALSE, standardized=FALSE, rsquare=FALSE, std.nox=FALSE, modindices=FALSE)
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 |
This function will run the robust analysis and output results.
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 |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
rsem.pattern, rsem.emmusig, rsem.Ascov
##\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) ## }##\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
rsem.se(object, gamma)rsem.se(object, gamma)
object |
Output from lavaan analysis, such as growth, factor, sem functions. |
gamma |
Robust covariance matrix for saturated mean and covariances |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
x<-array(1:6, c(2,3)) rsem.vec(x)x<-array(1:6, c(2,3)) rsem.vec(x)
Calculate the squared sum of a matrix
rsem.ssq(x)rsem.ssq(x)
x |
A matrix |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
x<-array(1:6, c(2,3)) rsem.ssq(x)x<-array(1:6, c(2,3)) rsem.ssq(x)
swith function
rsem.switch(p)rsem.switch(p)
p |
number of variables |
Internal function
rsem.switch.gamma(gamma, ov.names)rsem.switch.gamma(gamma, ov.names)
gamma |
Robust covariance matrix for saturated mean and covariances |
ov.names |
Observed variable names. |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
Stacking a matrix to a vector
rsem.vec(x)rsem.vec(x)
x |
A matrix |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
x<-array(1:6, c(2,3)) rsem.vec(x)x<-array(1:6, c(2,3)) rsem.vec(x)
Stacking lower triange of a matrix to a vector
rsem.vech(x)rsem.vech(x)
x |
A matrix |
Ke-Hai Yuan and Zhiyong Zhang
Ke-Hai Yuan and Zhiyong Zhang (2011) Robust Structural Equation Modeling with Missing Data and Auxiliary Variables
x<-array(1:9, c(3,3)) rsem.vec(x)x<-array(1:9, c(3,3)) rsem.vec(x)
Calculate weight for each subject in estimating the mean and covariance matrix.
rsem.weight(x, varphi, mu0, sig0)rsem.weight(x, varphi, mu0, sig0)
x |
Data |
varphi |
Downweight rate. |
mu0 |
Robust mean |
sig0 |
Robust covariance matrix. |
w1 |
Weight for robust mean estimates |
w2 |
Weight for robust covariance estimates |
Zhiyong Zhang and Ke-Hai Yuan
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
semdiag.combinations(n, r)semdiag.combinations(n, r)
n |
Size of the source vector |
r |
Size of the target vectors |
This function reads EQS output files (.ets, .CBK and .ETP) into R and stores the results as objects.
semdiag.read.eqs(file)semdiag.read.eqs(file)
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. |
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.
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 |
Patrick Mair, Eric Wu
Bentler, P. M. (2008). EQS Program Manual. Encino, CA: Multivariate Software Inc.
semdiag.call.eqs, semdiag.run.eqs
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.
semdiag.run.eqs(EQSpgm, EQSmodel, serial, Rmatrix = NA, datname = NA, LEN = 2000000) semdiag.call.eqs(EQSpgm, EQSmodel, serial, Rmatrix = NA, datname = NA, LEN = 2000000)semdiag.run.eqs(EQSpgm, EQSmodel, serial, Rmatrix = NA, datname = NA, LEN = 2000000) semdiag.call.eqs(EQSpgm, EQSmodel, serial, Rmatrix = NA, datname = NA, LEN = 2000000)
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 |
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.
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 |
Patrick Mair, Eric Wu
Bentler, P. M. (1995). EQS Program Manual. Encino, CA: Multivariate Software Inc.
semdiag.read.eqs, semdiag.call.eqs