impliedR {metaSEM}

Create or Generate the Model Implied Correlation or Covariance Matrices

Description

It creates or generates the model implied correlation or covariance matrices based on the RAM model specification.

Usage

impliedR(RAM, Amatrix, Smatrix, Fmatrix, Mmatrix, corr=TRUE, labels, ...)
rimpliedR(RAM, Amatrix, Smatrix, Fmatrix, AmatrixSD, SmatrixSD,
          k=1, corr=TRUE, nonPD.pop=c("replace", "nearPD", "accept"))

Arguments

RAM

A RAM object including a list of matrices of the model returned from lavaan2RAM.

Amatrix

If RAM is not specified, an Amatrix is required. An asymmetric matrix in the RAM specification with MxMatrix-class. If it is a matrix, it will be converted into MxMatrix-class by the as.mxMatrix function.

Smatrix

If RAM is not specified, an Smatrix is required.A symmetric matrix in the RAM specification with MxMatrix-class. If it is a matrix, it will be converted into MxMatrix-class by the as.mxMatrix function.

Fmatrix

A filter matrix in the RAM specification with MxMatrix-class. If it is missing, an identity matrix with the same dimensions of Smatrix will be created, which means that all variables are observed. If it is a matrix, it will be converted into MxMatrix-class by the as.mxMatrix function. It is not required when there is no latent variable.

Mmatrix

An optional matrix of the mean vector. It is assumed zeros if missing.

AmatrixSD

Standard deviations (SD) of the elements in the Amatrix. If it is missing, a matrix of zero is created.

SmatrixSD

Standard deviations (SD) of the elements in the Smatrix. If it is missing, a matrix of zero is created.

k

Number of studies.

corr

Logical. The output is either the model implied correlation matrix or the covariance matrix.

labels

A character vector of the observed and latent variables with the same dimensions as that in the Amatrix and Smatrix.

nonPD.pop

If it is replace, generated non-positive definite matrices are replaced by generated new ones which are positive definite. If it is nearPD, they are replaced by nearly positive definite matrices by calling Matrix::nearPD(). If it is accept, they are accepted.

...

Not used.

Details

This function can be used to generate the model implied correlation matrix for the standardized parameters with the corr=TRUE argument. Suppose we want to calculate the population correlation matrix for a mediation model with x, m, and y. We only need to specify the population path coefficients among x, m, and y in the Amatrix. We do not need to specify the population error variances of m and y. We treat the error variances as unknown parameters by giving them starting values in the Smatrix matrix. When the covariance matrix is requested by specifying corr=FALSE, it simply calculates the population model covariance matrix by treating the values in Smatrix as the population values.

Value

A list of RAM matrices, the model implied correlation or covariance matrix of the observed variables (SigmaObs), of both observed and latent variables (SigmaAll), the minimum fit (minFit) which should be zero, and the status code of the optimization (status) which should also be zero when the optimization is fine. The last object is mx.fit which is the output after running the model. It can be used in the diagnosis.

Note

It is important to ensure that all the population values in Amatrix must be set as fixed parameters; otherwise, these values may be altered with the corr=TRUE argument. When there is an error or warning message about the status code, there is a high chance that some of the values in Amatrix are incorrectly set as free parameters.

Author(s)

Mike W.-L. Cheung <[e-mail]>

Examples

set.seed(100)

## A one-factor CFA model
model <- "f =~ 0.3*x1 + 0.4*x2 + 0.5*x3
          f ~~ 1*f"

RAM <- lavaan2RAM(model)

impliedR(RAM, corr=TRUE)

## A simple mediation model
## All are population parameters in the A matrix
A1 <- matrix(c(0, 0, 0,
               0.3, 0, 0,
               0.2, 0.4, 0), nrow=3, ncol=3, byrow=TRUE,
             dimnames=list(c("x", "m", "y"), c("x", "m", "y")))
A1             

## Variance of x is fixed at 1 while the other variances are free.
S1 <- matrix(c(1, 0, 0,
               0, "0.1*ErrVarM",0,
               0, 0, "0.1*ErrVarY"), nrow=3, ncol=3,
             dimnames=list(c("x", "m", "y"), c("x", "m", "y")))
S1

impliedR(Amatrix=A1, Smatrix=S1)

## SD of A1
A1SD <- matrix(c(0, 0, 0,
                 0.1, 0, 0,
                 0.1, 0.1, 0), nrow=3, ncol=3, byrow=TRUE,
               dimnames=list(c("x", "m", "y"), c("x", "m", "y")))
A1SD

rimpliedR(Amatrix=A1, Smatrix=S1, AmatrixSD=A1SD, k=2)

## A CFA model
A2 <- matrix(c(0, 0, 0, 0.3,
               0, 0, 0, 0.4,
               0, 0, 0, 0.5,
               0, 0, 0, 0), nrow=4, ncol=4, byrow=TRUE,
             dimnames=list(c("x1", "x2", "x3", "f"),
                           c("x1", "x2", "x3", "f")))
A2

## Variance of f is fixed at 1 while the other variances are free.
S2 <- matrix(c("0.7*Err1", 0, 0, 0,
                0, "0.7*Err2", 0, 0,
                0, 0, "0.7*Err3", 0,
                0, 0, 0, 1), nrow=4, ncol=4,
            dimnames=list(c("x1", "x2", "x3", "f"), c("x1", "x2", "x3", "f")))
S2

F2 <- create.Fmatrix(c(1,1,1,0), as.mxMatrix=FALSE)
F2

## Model implied correlation matrix
impliedR(Amatrix=A2, Smatrix=S2, Fmatrix=F2, corr=TRUE)

## Model implied covariance matrix
impliedR(Amatrix=A2, Smatrix=S2, Fmatrix=F2, corr=FALSE)

## SD of A2
A2SD <- matrix(c(0, 0, 0, 0.1,
                 0, 0, 0, 0.1,
                 0, 0, 0, 0.1,
                 0, 0, 0, 0), nrow=4, ncol=4, byrow=TRUE,
               dimnames=list(c("x1", "x2", "x3", "f"),
                             c("x1", "x2", "x3", "f")))               
A2SD

## SD of S2: correlated between x1 and x2
S2SD <- matrix(c(0, 0.1, 0, 0,
                 0.1, 0, 0, 0,
                 0, 0, 0, 0.1,
                 0, 0, 0, 0), nrow=4, ncol=4, byrow=TRUE,
               dimnames=list(c("x1", "x2", "x3", "f"),
                             c("x1", "x2", "x3", "f")))               
S2SD

rimpliedR(Amatrix=A2, Smatrix=S2, Fmatrix=F2, AmatrixSD=A2SD,
          SmatrixSD=S2SD, k=2)