Ten Studies of Correlation Matrices used by Becker (2009)
This dataset includes ten studies on the relationships between CSAI subscales and sports behavior. The original data were used in Craft et al. (2003), whereas a subset of them was illustrated in Becker (2009).
data("Becker09")A list of data with the following structure:
A list of 4x4 correlation matrices. The variables are Performance, Cognitive, Somatic, and Self_confidence
A vector of sample sizes
Samples based on Individual or Team
Craft, L. L., Magyar, T. M., Becker, B. J., & Feltz, D. L. (2003). The relationship between the Competitive State Anxiety Inventory-2 and sport performance: a meta-analysis. Journal of Sport and Exercise Psychology, 25(1), 44-65.
Becker, B. J. (2009). Model-based meta-analysis. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (2nd ed., pp. 377-395). New York: Russell Sage Foundation.
## Not run:
data(Becker09)
#### Fixed-effects model
## First stage analysis
fixed1 <- tssem1(Becker09$data, Becker09$n, method="FEM")
summary(fixed1)
## Prepare a regression model using create.mxMatrix()
A1 <- create.mxMatrix(c(0, "0.1*Cog2Per", "0.1*SO2Per", "0.1*SC2Per",
0, 0, 0, 0,
0, 0, 0, 0,
0, "0.1*Cog2SC", "0.1*SO2SC",0),
type="Full", byrow=TRUE, ncol=4, nrow=4,
as.mxMatrix=FALSE)
## This step is not necessary but it is useful for inspecting the model.
dimnames(A1)[[1]] <- dimnames(A1)[[2]] <- c("Performance", "Cognitive",
"Somatic", "Self_confidence")
## Display A1
A1
S1 <- create.mxMatrix(c("0.1*var_Per",
0, 1,
0, "0.1*cor", 1,
0, 0, 0, "0.1*var_SC"), byrow=TRUE, type="Symm",
as.mxMatrix=FALSE)
## This step is not necessary but it is useful for inspecting the model.
dimnames(S1)[[1]] <- dimnames(S1)[[2]] <- c("Performance", "Cognitive",
"Somatic", "Self_confidence")
## Display S1
S1
################################################################################
## Alternative model specification in lavaan model syntax
model <- "## Regression paths
Performance ~ Cog2Per*Cognitive + SO2Per*Somatic + SC2Per*Self_confidence
Self_confidence ~ Cog2SC*Cognitive + SO2SC*Somatic
## Fix the variances of Cog and SO at 1
Cognitive ~~ 1*Cognitive
Somatic ~~ 1*Somatic
## Label the correlation between Cog and SO
Cognitive ~~ cor*Somatic
## Label the error variances of Per and SC
Performance ~~ var_Per*Performance
Self_confidence ~~ var_SC*Self_confidence"
## Display the model
plot(model, layout="spring")
RAM <- lavaan2RAM(model, obs.variables=c("Performance", "Cognitive",
"Somatic", "Self_confidence"))
RAM
A1 <- RAM$A
S1 <- RAM$S
################################################################################
## Second stage analysis
fixed2 <- tssem2(fixed1, Amatrix=A1, Smatrix=S1, diag.constraints=TRUE,
intervals.type="LB", model.name="TSSEM2 Becker09",
mx.algebras=list( Cog=mxAlgebra(Cog2SC*SC2Per, name="Cog"),
SO=mxAlgebra(SO2SC*SC2Per, name="SO"),
Cog_SO=mxAlgebra(Cog2SC*SC2Per+SO2SC*SC2Per,
name="Cog_SO")) )
summary(fixed2)
## Display the model with the parameter estimates
plot(fixed2, layout="spring")
#### Fixed-effects model: with type of sport as cluster
## First stage analysis
cluster1 <- tssem1(Becker09$data, Becker09$n, method="FEM",
cluster=Becker09$Type_of_sport)
summary(cluster1)
## Second stage analysis
cluster2 <- tssem2(cluster1, Amatrix=A1, Smatrix=S1, diag.constraints=TRUE,
intervals.type="LB", model.name="TSSEM2 Becker09",
mx.algebras=list( Cog=mxAlgebra(Cog2SC*SC2Per, name="Cog"),
SO=mxAlgebra(SO2SC*SC2Per, name="SO"),
Cog_SO=mxAlgebra(Cog2SC*SC2Per+SO2SC*SC2Per,
name="Cog_SO")) )
summary(cluster2)
## Convert the model to semPlotModel object with 2 plots
## Use the short forms of the variable names
my.plots <- lapply(X=cluster2, FUN=meta2semPlot, manNames=c("Per","Cog","SO","SC") )
## Load the library
library("semPlot")
## Setup two plots
layout(t(1:2))
## The labels are overlapped. We may modify it by using layout="spring"
semPaths(my.plots[[1]], whatLabels="est", nCharNodes=10, color="orange",
layout="spring", edge.label.cex=0.8)
title("Individual sport")
semPaths(my.plots[[2]], whatLabels="est", nCharNodes=10, color="skyblue",
layout="spring", edge.label.cex=0.8)
title("Team sport")
#### Random-effects model
## First stage analysis
random1 <- tssem1(Becker09$data, Becker09$n, method="REM", RE.type="Diag")
summary(random1)
## Second stage analysis
random2 <- tssem2(random1, Amatrix=A1, Smatrix=S1, diag.constraints=TRUE,
intervals.type="LB", model.name="TSSEM2 Becker09",
mx.algebras=list( Cog=mxAlgebra(Cog2SC*SC2Per, name="Cog"),
SO=mxAlgebra(SO2SC*SC2Per, name="SO"),
Cog_SO=mxAlgebra(Cog2SC*SC2Per+SO2SC*SC2Per,
name="Cog_SO")) )
summary(random2)
## Display the model
plot(random2, what="path", layout="spring")
## Display the model with the parameter estimates
plot(random2, layout="spring", color="yellow")
#### Univariate r approach
#### First stage of the analysis
uni1 <- uniR1(Becker09$data, Becker09$n)
uni1
#### Second stage of analysis using OpenMx
model2 <- "## Regression paths
Performance ~ Cog2Per*Cognitive + SO2Per*Somatic + SC2Per*Self_confidence
Self_confidence ~ Cog2SC*Cognitive + SO2SC*Somatic
## Provide starting values for Cog and SO
Cognitive ~~ start(1)*Cognitive
Somatic ~~ start(1)*Somatic
## Label the correlation between Cog and SO
Cognitive ~~ cor*Somatic
## Label the error variances of Per and SC
Performance ~~ var_Per*Performance
Self_confidence ~~ var_SC*Self_confidence"
RAM2 <- lavaan2RAM(model2, obs.variables=c("Performance", "Cognitive",
"Somatic", "Self_confidence"))
RAM2
uni2mx <- uniR2mx(uni1, RAM=RAM2)
summary(uni2mx)
#### Second stage of analysis Using lavaan
model3 <- "## Regression paths
Performance ~ Cognitive + Somatic + Self_confidence
Self_confidence ~ Cognitive + Somatic"
uni2lavaan <- uniR2lavaan(uni1, model3)
lavaan::summary(uni2lavaan)
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