Becker92 | R Documentation |
This data set includes six studies of correlation matrices reported by Becker (1992; 1995).
data(Becker92)
A list of data with the following structure:
A list of 6 studies of correlation matrices. The variables are Math (math aptitude), Spatial (spatial ability), and Verbal (verbal ability)
A vector of sample sizes
Becker, B. J. (1992). Using results from replicated studies to estimate linear models. Journal of Educational Statistics, 17(4), 341-362. doi:10.3102/10769986017004341
Becker, B. J. (1995). Corrections to "Using Results from Replicated Studies to Estimate Linear Models." Journal of Educational and Behavioral Statistics, 20(1), 100-102. doi:10.2307/1165390
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)
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