Description Usage Arguments Value Note Author(s) References See Also Examples
It fits a correlation or covariance structure with
weighted least squares (WLS) estimation method where the inverse of the asymptotic covariance matrix is
used as the weight matrix. tssem2
conducts the second stage
analysis of the twostage structural equation modeling (TSSEM). tssem2
is a wrapper of wls
.
1 2 3 4 5 6 7  wls(Cov, aCov, n, Amatrix=NULL, Smatrix=NULL, Fmatrix=NULL,
diag.constraints=FALSE, cor.analysis=TRUE, intervals.type=c("z","LB"),
mx.algebras=NULL, model.name=NULL, suppressWarnings=TRUE,
silent=TRUE, run=TRUE, ...)
tssem2(tssem1.obj, Amatrix=NULL, Smatrix=NULL, Fmatrix=NULL,
diag.constraints=FALSE, intervals.type=c("z", "LB"), mx.algebras=NULL,
model.name=NULL, suppressWarnings=TRUE, silent=TRUE, run=TRUE, ...)

tssem1.obj 
An object of either class

Cov 
A p x p sample correlation/covariance matrix where p is the number of variables. 
aCov 
A p* x p* asymptotic sampling covariance
matrix of either 
n 
Sample size. 
Amatrix 
An asymmetric matrix in the RAM specification with

Smatrix 
A symmetric matrix in the RAM specification with

Fmatrix 
A filter matrix in the RAM specification with

diag.constraints 
Logical. This argument is ignored when

cor.analysis 
Logical. Analysis of correlation or covariance structure. If 
intervals.type 
Either 
mx.algebras 
A list of 
model.name 
A string for the model name in

suppressWarnings 
Logical. If 
silent 
Logical. The argument to be passed to 
run 
Logical. If 
... 
Further arguments to be passed to 
An object of class wls
with a list of
call 
The matched call 
Cov 
Input data of either a covariance or correlation matrix 
asyCov 
Asymptotic covariance matrix of the input data 
noObservedStat 
Number of observed statistics 
n 
Sample size 
cor.analysis 
logical 
noConstraints 
Number of constraints imposed on S 
indepModelChisq 
Chisquare statistic of the independent model
returned by 
indepModelDf 
Degrees of freedom of the independent model returned
by 
mx.fit 
A fitted object returned from

If the input is a list of tssem1.obj
, it returns a list of
results for each cluster.
Mike W.L. Cheung <[email protected]>
Bentler, P.M., & Savalei, V. (2010). Analysis of correlation structures: current status and open problems. In Kolenikov, S., Thombs, L., & Steinley, D. (Eds.). Recent Methodological Developments in Social Science Statistics (pp. 136). Hoboken, NJ: Wiley.
Cheung, M. W.L. (2010). Fixedeffects metaanalyses as multiplegroup structural equation models. Structural Equation Modeling, 17, 481509.
Cheung, M. W.L. (2014). Fixed and randomeffects metaanalytic structural equation modeling: Examples and analyses in R. Behavior Research Methods, 46, 2940.
Cheung, M. W.L., & Chan, W. (2005). Metaanalytic structural equation modeling: A twostage approach. Psychological Methods, 10, 4064.
Cheung, M. W.L., & Chan, W. (2009). A twostage approach to synthesizing covariance matrices in metaanalytic structural equation modeling. Structural Equation Modeling, 16, 2853.
Joreskog, K. G., Sorbom, D., Du Toit, S., & Du Toit, M. (1999). LISREL 8: New Statistical Features. Chicago: Scientific Software International.
McArdle, J. J., & MacDonald, R. P. (1984). Some algebraic properties of the Reticular Action Model for moment structures. British Journal of Mathematical and Statistical Psychology, 37, 234251.
tssem1
,
Becker92
, Digman97
,
Hunter83
, issp89
, issp05
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71  #### Analysis of correlation structure
R1 < matrix(c(1.00, 0.22, 0.24, 0.18,
0.22, 1.00, 0.30, 0.22,
0.24, 0.30, 1.00, 0.24,
0.18, 0.22, 0.24, 1.00), ncol=4, nrow=4)
n < 1000
acovR1 < asyCov(R1, n)
## Onefactor CFA model
(A1 < cbind(matrix(0, nrow=5, ncol=4),
matrix(c("0.2*a1","0.2*a2","0.2*a3","0.2*a4",0),
ncol=1)))
(S1 < Diag(c("0.2*e1","0.2*e2","0.2*e3","0.2*e4",1)))
## The first 4 variables are observed while the last one is latent.
(F1 < create.Fmatrix(c(1,1,1,1,0), name="F1"))
wls.fit1 < wls(Cov=R1, aCov=acovR1, n=n, Fmatrix=F1, Smatrix=S1, Amatrix=A1,
cor.analysis=TRUE, intervals="LB")
summary(wls.fit1)
#### Multiple regression analysis
## Variables in R2: y, x1, x2
R2 < matrix(c(1.00, 0.22, 0.24,
0.22, 1.00, 0.30,
0.24, 0.30, 1.00,
0.18, 0.22, 0.24), ncol=3, nrow=3)
acovR2 < asyCov(R2, n)
## A2: Regression coefficents
# y x1 x2
# y F T T
# x1 F F F
# x2 F F F
(A2 < mxMatrix("Full", ncol=3, nrow=3, byrow=TRUE,
free=c(FALSE, rep(TRUE, 2), rep(FALSE, 6)), name="A2"))
## S2: Covariance matrix of free parameters
# y x1 x2
# y T F F
# x1 F F F
# x2 F T F
(S2 < mxMatrix("Symm", ncol=3, nrow=3, values=c(0.2,0,0,1,0.2,1),
free=c(TRUE,FALSE,FALSE,FALSE,TRUE,FALSE), name="S2"))
## F may be ignored as there is no latent variable.
wls.fit2 < wls(Cov=R2, aCov=acovR2, n=n, Amatrix=A2, Smatrix=S2,
cor.analysis=TRUE, intervals="LB")
summary(wls.fit2)
#### Analysis of covariance structure
R3 < matrix(c(1.50, 0.22, 0.24, 0.18,
0.22, 1.60, 0.30, 0.22,
0.24, 0.30, 1.80, 0.24,
0.18, 0.22, 0.24, 1.30), ncol=4, nrow=4)
n < 1000
acovS3 < asyCov(R3, n, cor.analysis=FALSE)
(A3 < cbind(matrix(0, nrow=5, ncol=4),
matrix(c("0.2*a1","0.2*a2","0.2*a3","0.2*a4",0),ncol=1)))
(S3 < Diag(c("0.2*e1","0.2*e2","0.2*e3","0.2*e4",1)))
F3 < c(TRUE,TRUE,TRUE,TRUE,FALSE)
(F3 < create.Fmatrix(F3, name="F3", as.mxMatrix=FALSE))
wls.fit3 < wls(Cov=R3, aCov=acovS3, n=n, Amatrix=A3, Smatrix=S3,
Fmatrix=F3, cor.analysis=FALSE)
summary(wls.fit3)

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