metaSEM (version 1.4.0)

Becker92: Six Studies of Correlation Matrices reported by Becker (1992; 1995)

Description

This data set includes six studies of correlation matrices reported by Becker (1992; 1995).

Usage

data(Becker92)

Details

A list of data with the following structure:

data

A list of 6 studies of correlation matrices. The variables are Math (math aptitude), Spatial (spatial ability), and Verbal (verbal ability)

n

A vector of sample sizes

Examples

# \donttest{
data(Becker92)

#### Fixed-effects model
## First stage analysis
## Replicate Becker's (1992) analysis using 4 studies only

fixed1 <- tssem1(Becker92$data[1:4], Becker92$n[1:4], method="FEM")
summary(fixed1)

## ## Prepare a regression model using create.mxMatrix()
## A1 <- create.mxMatrix(c(0,0,0,"0.2*Spatial2Math",
##                         0,0,"0.2*Verbal2Math",0,0), type="Full",
##                         ncol=3, nrow=3, as.mxMatrix=FALSE)

## var.names <- c("Math_aptitude","Spatial","Verbal") 

## ## This step is not necessary but it is useful for inspecting the model.
## dimnames(A1)[[1]] <- dimnames(A1)[[2]] <- var.names

## ## Display A1
## A1

## S1 <- create.mxMatrix(c("0.2*ErrorVarMath",0,0,1,"0.2*CorSpatialVerbal",1),
##                         type="Symm", as.mxMatrix=FALSE)

## ## This step is not necessary but it is useful for inspecting the model.
## dimnames(S1)[[1]] <- dimnames(S1)[[2]] <- var.names

## ## Display S1
## S1

################################################################################
## Alternative model specification in lavaan model syntax
model <- "## Regression paths
          Math ~ Spatial2Math*Spatial + Verbal2Math*Verbal
          Spatial ~~ CorSpatialVerbal*Verbal
          ## Fix the variances of Spatial and Verbal at 1
          Spatial ~~ 1*Spatial
          Verbal ~~ 1*Verbal
          ## Label the error variance of Math
          Math ~~ ErrorVarMath*Math + start(0.2)*Math"

## Display the model
plot(model)

RAM <- lavaan2RAM(model, obs.variables=c("Math", "Spatial", "Verbal"))
RAM

################################################################################

## Fixed-effects model: Second stage analysis
## Two equivalent versions to calculate the R2 and its 95% LBCI
fixed2 <- tssem2(fixed1, RAM=RAM, intervals.type="LB",
                 mx.algebras=list(R1=mxAlgebra(Spatial2Math^2+Verbal2Math^2
                        +2*CorSpatialVerbal*Spatial2Math*Verbal2Math, name="R1"),
                        R2=mxAlgebra(One-Smatrix[1,1], name="R2"),
                        One=mxMatrix("Iden", ncol=1, nrow=1, name="One")))
summary(fixed2)

## Display the model with the parameter estimates
plot(fixed2)

#### Random-effects model
## First stage analysis
## No random effects for off-diagonal elements
random1 <- tssem1(Becker92$data, Becker92$n, method="REM", RE.type="Diag")
summary(random1)

## Random-effects model: Second stage analysis
random2 <- tssem2(random1, RAM=RAM)
summary(random2)

## Display the model with the parameter estimates
plot(random2, color="yellow")

#### Similar to conventional fixed-effects GLS approach
## First stage analysis
## No random effects
## Replicate Becker's (1992) analysis using 4 studies only
gls1 <- tssem1(Becker92$data[1:4], Becker92$n[1:4], method="REM", RE.type="Zero",
               model.name="Fixed effects GLS Stage 1")
summary(gls1)

## Fixed-effects GLS model: Second stage analysis
gls2 <- tssem2(gls1, RAM=RAM, model.name="Fixed effects GLS Stage 2")
summary(gls2)
# }