The metaSEM Package
Table of Contents
1 Introduction
The metaSEM package provides functions to conducting univariate and multivariate meta-analysis using a structural equation modeling approach via the OpenMx package. It also implemented the two-stage structural equation modeling (TSSEM) approach to conducting fixed- and random-effects meta-analytic structural equation modeling (MASEM) on correlation/covariance matrices.
It is based on the following papers:
- Cheung, M.W.L. (2008). A model for integrating fixed-, random-, and mixed-effects meta-analyses into structural equation modeling. Psychological Methods, 13, 182-202.
- Cheung, M.W.L. (2009). Constructing approximate confidence intervals for parameters with structural equation models. Structural Equation Modeling, 16, 267–294.
- Cheung, M.W.L. (2010). Fixed-effects meta-analyses as multiple-group structural equation models. Structural Equation Modeling, 17, 481-509.
- Cheung, M.W.L. (2012). metaSEM: An R package for meta-analysis using structural equation modeling. Manuscript submitted for publication.
- Cheung, M.W.L. (2013). Implementing restricted maximum likelihood estimation in structural equation models. Structural Equation Modeling, 20, 157-167.
- Cheung, M.W.L. (in press). Fixed- and random-effects meta-analytic structural equation modeling: Examples and analyses in R. Behavior Research Methods.
- Cheung, M.W.L. (in press). Multivariate meta-analysis as structural equation models. Structural Equation Modeling.
- Cheung, M.W.L. (in press). Modeling dependent effect sizes with three-level meta-analyses: A structural equation modeling approach. Psychological Methods.
- Cheung, M.W.L., & Chan, W. (2004). Testing dependent correlation coefficients via structural equation modeling. Organizational Research Methods, 7, 206–223.
- Cheung, M.W.L., & Chan, W. (2005). Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods, 10, 40-64.
- Cheung, M.W.L., & Chan, W. (2009). A two-stage approach to synthesizing covariance matrices in meta-analytic structural equation modeling. Structural Equation Modeling, 6, 28-53.
2 Examples
Univariate random-effects model
## Load the library library(metaSEM) ## Show the first few studies of the data set head(Becker83) ## Random-effects meta-analysis with ML summary( meta(y=di, v=vi, data=Becker83, model.name="Univariate random effects model") )
Loading required package: OpenMx
study di vi percentage items
1 1 -0.33 0.03 25 2
2 2 0.07 0.03 25 2
3 3 -0.30 0.02 50 2
4 4 0.35 0.02 100 38
5 5 0.69 0.07 100 30
6 6 0.81 0.22 100 45
Running Univariate random effects model
Call:
meta(y = di, v = vi, data = Becker83, model.name = "Univariate random effects model")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept1 0.174734 0.113378 -0.047482 0.396950 1.5412 0.1233
Tau2_1_1 0.077376 0.054108 -0.028674 0.183426 1.4300 0.1527
Q statistic on homogeneity of effect sizes: 30.64949
Degrees of freedom of the Q statistic: 9
P value of the Q statistic: 0.0003399239
Heterogeneity indices (based on the estimated Tau2):
Estimate
Intercept1: I2 (Q statistic) 0.6718
Number of studies (or clusters): 10
Number of observed statistics: 10
Number of estimated parameters: 2
Degrees of freedom: 8
-2 log likelihood: 7.928307
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
Univariate mixed-effects model
## Mixed-effects meta-analysis with "log(items)" as the predictor summary( meta(y=di, v=vi, x=log(items), data=Becker83, model.name="Univariate mixed effects model") )
Running Univariate mixed effects model
Call:
meta(y = di, v = vi, x = log(items), data = Becker83, model.name = "Univariate mixed effects model")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept1 -3.2015e-01 1.0981e-01 -5.3539e-01 -1.0492e-01 -2.9154 0.003552
Slope1_1 2.1088e-01 4.5084e-02 1.2251e-01 2.9924e-01 4.6774 2.905e-06
Tau2_1_1 1.0000e-10 2.0095e-02 -3.9386e-02 3.9386e-02 0.0000 1.000000
Intercept1 **
Slope1_1 ***
Tau2_1_1
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Q statistic on homogeneity of effect sizes: 30.64949
Degrees of freedom of the Q statistic: 9
P value of the Q statistic: 0.0003399239
Explained variances (R2):
y1
Tau2 (no predictor) 0.0774
Tau2 (with predictors) 0.0000
R2 1.0000
Number of studies (or clusters): 10
Number of observed statistics: 10
Number of estimated parameters: 3
Degrees of freedom: 7
-2 log likelihood: -4.208024
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
Multivariate random-effects model
## Show the data set Berkey98 ## Multivariate meta-analysis with a random-effects model summary( mult1 <- meta(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL), data=Berkey98, model.name="Multivariate random effects model") )
trial pub_year no_of_patients PD AL var_PD cov_PD_AL var_AL
1 1 1983 14 0.47 -0.32 0.0075 0.0030 0.0077
2 2 1982 15 0.20 -0.60 0.0057 0.0009 0.0008
3 3 1979 78 0.40 -0.12 0.0021 0.0007 0.0014
4 4 1987 89 0.26 -0.31 0.0029 0.0009 0.0015
5 5 1988 16 0.56 -0.39 0.0148 0.0072 0.0304
Running Multivariate random effects model
Call:
meta(y = cbind(PD, AL), v = cbind(var_PD, cov_PD_AL, var_AL),
data = Berkey98, model.name = "Multivariate random effects model")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept1 0.3448390 0.0536312 0.2397238 0.4499542 6.4298 1.278e-10 ***
Intercept2 -0.3379383 0.0812479 -0.4971813 -0.1786953 -4.1593 3.192e-05 ***
Tau2_1_1 0.0070020 0.0090497 -0.0107351 0.0247391 0.7737 0.4391
Tau2_2_1 0.0094607 0.0099698 -0.0100797 0.0290010 0.9489 0.3427
Tau2_2_2 0.0261445 0.0177409 -0.0086270 0.0609161 1.4737 0.1406
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Q statistic on homogeneity of effect sizes: 128.2267
Degrees of freedom of the Q statistic: 8
P value of the Q statistic: 0
Heterogeneity indices (based on the estimated Tau2):
Estimate
Intercept1: I2 (Q statistic) 0.6021
Intercept2: I2 (Q statistic) 0.9250
Number of studies (or clusters): 5
Number of observed statistics: 10
Number of estimated parameters: 5
Degrees of freedom: 5
-2 log likelihood: -11.68131
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
## Plot the effect sizes plot(mult1)
Multivariate mixed-effects model
## Multivariate meta-analysis with "publication year-1979" as a predictor summary( meta(y=cbind(PD, AL), v=cbind(var_PD, cov_PD_AL, var_AL), data=Berkey98, x=scale(pub_year, center=1979), model.name="Multivariate mixed effects model") )
Running Multivariate mixed effects model
Call:
meta(y = cbind(PD, AL), v = cbind(var_PD, cov_PD_AL, var_AL),
x = scale(pub_year, center = 1979), data = Berkey98, model.name = "Multivariate mixed effects model")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept1 0.3440001 0.0857659 0.1759021 0.5120982 4.0109 6.048e-05 ***
Intercept2 -0.2918175 0.1312796 -0.5491208 -0.0345141 -2.2229 0.02622 *
Slope1_1 0.0063540 0.1078235 -0.2049761 0.2176842 0.0589 0.95301
Slope2_1 -0.0705888 0.1620965 -0.3882921 0.2471146 -0.4355 0.66322
Tau2_1_1 0.0080405 0.0101206 -0.0117955 0.0278766 0.7945 0.42692
Tau2_2_1 0.0093413 0.0105515 -0.0113392 0.0300218 0.8853 0.37599
Tau2_2_2 0.0250135 0.0170788 -0.0084603 0.0584873 1.4646 0.14303
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Q statistic on homogeneity of effect sizes: 128.2267
Degrees of freedom of the Q statistic: 8
P value of the Q statistic: 0
Explained variances (R2):
y1 y2
Tau2 (no predictor) 0.0070020 0.0261
Tau2 (with predictors) 0.0080405 0.0250
R2 0.0000000 0.0433
Number of studies (or clusters): 5
Number of observed statistics: 10
Number of estimated parameters: 7
Degrees of freedom: 3
-2 log likelihood: -12.00859
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
Three-level mixed-effects model
## Show the data set head(Cooper03) ## No predictor summary( meta3(y=y, v=v, cluster=District, data=Cooper03, model.name="Three level random effects model") )
District Study y v Year
1 11 1 -0.18 0.118 1976
2 11 2 -0.22 0.118 1976
3 11 3 0.23 0.144 1976
4 11 4 -0.30 0.144 1976
5 12 5 0.13 0.014 1989
6 12 6 -0.26 0.014 1989
Running Three level random effects model
Call:
meta3(y = y, v = v, cluster = District, data = Cooper03, model.name = "Three level random effects model")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept 0.1844554 0.0805411 0.0265977 0.3423130 2.2902 0.022010 *
Tau2_2 0.0328648 0.0111397 0.0110314 0.0546982 2.9502 0.003175 **
Tau2_3 0.0577384 0.0307423 -0.0025154 0.1179921 1.8781 0.060362 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Q statistic on homogeneity of effect sizes: 578.864
Degrees of freedom of the Q statistic: 55
P value of the Q statistic: 0
Heterogeneity indices (based on the estimated Tau2):
Estimate
I2_2 (Typical v: Q statistic) 0.3440
I2_3 (Typical v: Q statistic) 0.6043
Number of studies (or clusters): 11
Number of observed statistics: 56
Number of estimated parameters: 3
Degrees of freedom: 53
-2 log likelihood: 16.78987
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
## Year as a predictor summary( meta3(y=y, v=v, cluster=District, x=scale(Year, scale=FALSE), data=Cooper03, model.name="Three level mixed effects model") )
Running Three level mixed effects model
Call:
meta3(y = y, v = v, cluster = District, x = scale(Year, scale = FALSE),
data = Cooper03, model.name = "Three level mixed effects model")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept 0.1780268 0.0805219 0.0202067 0.3358469 2.2109 0.027042 *
Slope_1 0.0050737 0.0085266 -0.0116382 0.0217856 0.5950 0.551814
Tau2_2 0.0329390 0.0111620 0.0110618 0.0548162 2.9510 0.003168 **
Tau2_3 0.0564628 0.0300330 -0.0024007 0.1153264 1.8800 0.060104 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Q statistic on homogeneity of effect sizes: 578.864
Degrees of freedom of the Q statistic: 55
P value of the Q statistic: 0
Explained variances (R2):
Level 2 Level 3
Tau2 (no predictor) 0.032865 0.0577
Tau2 (with predictors) 0.032939 0.0565
R2 0.000000 0.0221
Number of studies (or clusters): 11
Number of observed statistics: 56
Number of estimated parameters: 4
Degrees of freedom: 52
-2 log likelihood: 16.43629
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
Fixed-effects MASEM
## Show the first 2 studies in Digman97 head(Digman97$data, n=2) ## Show the first 2 sample sizes in Digman97 head(Digman97$n, n=2) ## Stage 1 analysis fixed1 <- tssem1(Digman97$data, Digman97$n, method="FEM", model.name="Fixed effects model Stage 1 analysis") summary(fixed1)
$`Digman 1 (1994)`
A C ES E I
A 1.00 0.62 0.41 -0.48 0.00
C 0.62 1.00 0.59 -0.10 0.35
ES 0.41 0.59 1.00 0.27 0.41
E -0.48 -0.10 0.27 1.00 0.37
I 0.00 0.35 0.41 0.37 1.00
$`Digman 2 (1994)`
A C ES E I
A 1.00 0.39 0.53 -0.30 -0.05
C 0.39 1.00 0.59 0.07 0.44
ES 0.53 0.59 1.00 0.09 0.22
E -0.30 0.07 0.09 1.00 0.45
I -0.05 0.44 0.22 0.45 1.00
[1] 102 149
Running Fixed effects model Stage 1 analysis
Call:
tssem1FEM(my.df = my.df, n = n, cor.analysis = cor.analysis,
model.name = model.name, cluster = cluster, suppressWarnings = suppressWarnings)
Coefficients:
Estimate Std.Error z value Pr(>|z|)
S[1,2] 0.363116 0.013391 27.1171 < 2.2e-16 ***
S[1,3] 0.390176 0.012903 30.2388 < 2.2e-16 ***
S[1,4] 0.103751 0.015070 6.8846 5.796e-12 ***
S[1,5] 0.092246 0.015071 6.1207 9.318e-10 ***
S[2,3] 0.415999 0.012540 33.1741 < 2.2e-16 ***
S[2,4] 0.135208 0.014799 9.1363 < 2.2e-16 ***
S[2,5] 0.141213 0.014891 9.4834 < 2.2e-16 ***
S[3,4] 0.244505 0.014175 17.2488 < 2.2e-16 ***
S[3,5] 0.138167 0.014858 9.2992 < 2.2e-16 ***
S[4,5] 0.424514 0.012396 34.2468 < 2.2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Goodness-of-fit indices:
Value
Sample size 4496.0000
Chi-square of target model 1499.7340
DF of target model 130.0000
p value of target model 0.0000
Chi-square of independence model 4454.5995
DF of independence model 140.0000
RMSEA 0.1812
SRMR 0.1750
TLI 0.6581
CFI 0.6825
AIC 1239.7340
BIC 406.3114
OpenMx status: 0 ("0" and "1": considered fine; other values indicate problems)
## Model specification is based on the RAM formulation ## S matrix Phi <- matrix(c(1,"0.3*cor","0.3*cor",1), ncol=2, nrow=2) S1 <- bdiagMat(list(Diag(c("0.2*e1","0.2*e2","0.2*e3","0.2*e4","0.2*e5")), Phi)) (S1 <- as.mxMatrix(S1)) ## A matrix Lambda <- matrix(c(0,".3*f1_x2",".3*f1_x3",".3*f1_x4",0,".3*f2_x1",0,0,0,".3*f2_x5"), ncol=2, nrow=5) A1 <- rbind( cbind(matrix(0,ncol=5,nrow=5), Lambda), matrix(0, ncol=7, nrow=2) ) (A1 <- as.mxMatrix(A1)) (F1 <- create.Fmatrix(c(1,1,1,1,1,0,0), name="F1"))
FullMatrix 'S1'
@labels
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] "e1" NA NA NA NA NA NA
[2,] NA "e2" NA NA NA NA NA
[3,] NA NA "e3" NA NA NA NA
[4,] NA NA NA "e4" NA NA NA
[5,] NA NA NA NA "e5" NA NA
[6,] NA NA NA NA NA NA "cor"
[7,] NA NA NA NA NA "cor" NA
@values
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.2 0.0 0.0 0.0 0.0 0.0 0.0
[2,] 0.0 0.2 0.0 0.0 0.0 0.0 0.0
[3,] 0.0 0.0 0.2 0.0 0.0 0.0 0.0
[4,] 0.0 0.0 0.0 0.2 0.0 0.0 0.0
[5,] 0.0 0.0 0.0 0.0 0.2 0.0 0.0
[6,] 0.0 0.0 0.0 0.0 0.0 1.0 0.3
[7,] 0.0 0.0 0.0 0.0 0.0 0.3 1.0
@free
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] TRUE FALSE FALSE FALSE FALSE FALSE FALSE
[2,] FALSE TRUE FALSE FALSE FALSE FALSE FALSE
[3,] FALSE FALSE TRUE FALSE FALSE FALSE FALSE
[4,] FALSE FALSE FALSE TRUE FALSE FALSE FALSE
[5,] FALSE FALSE FALSE FALSE TRUE FALSE FALSE
[6,] FALSE FALSE FALSE FALSE FALSE FALSE TRUE
[7,] FALSE FALSE FALSE FALSE FALSE TRUE FALSE
@lbound: No lower bounds assigned.
@ubound: No upper bounds assigned.
FullMatrix 'A1'
@labels
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] NA NA NA NA NA NA "f2_x1"
[2,] NA NA NA NA NA "f1_x2" NA
[3,] NA NA NA NA NA "f1_x3" NA
[4,] NA NA NA NA NA "f1_x4" NA
[5,] NA NA NA NA NA NA "f2_x5"
[6,] NA NA NA NA NA NA NA
[7,] NA NA NA NA NA NA NA
@values
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0 0 0 0 0 0.0 0.3
[2,] 0 0 0 0 0 0.3 0.0
[3,] 0 0 0 0 0 0.3 0.0
[4,] 0 0 0 0 0 0.3 0.0
[5,] 0 0 0 0 0 0.0 0.3
[6,] 0 0 0 0 0 0.0 0.0
[7,] 0 0 0 0 0 0.0 0.0
@free
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] FALSE FALSE FALSE FALSE FALSE FALSE TRUE
[2,] FALSE FALSE FALSE FALSE FALSE TRUE FALSE
[3,] FALSE FALSE FALSE FALSE FALSE TRUE FALSE
[4,] FALSE FALSE FALSE FALSE FALSE TRUE FALSE
[5,] FALSE FALSE FALSE FALSE FALSE FALSE TRUE
[6,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
[7,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
@lbound: No lower bounds assigned.
@ubound: No upper bounds assigned.
FullMatrix 'F1'
@labels: No labels assigned.
@values
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 1 0 0 0 0 0 0
[2,] 0 1 0 0 0 0 0
[3,] 0 0 1 0 0 0 0
[4,] 0 0 0 1 0 0 0
[5,] 0 0 0 0 1 0 0
@free: No free parameters.
@lbound: No lower bounds assigned.
@ubound: No upper bounds assigned.
## Stage 2 analysis fixed2 <- tssem2(fixed1, Amatrix=A1, Smatrix=S1, Fmatrix=F1, diag.constraints=TRUE, intervals.type="LB", model.name="Fixed effects model Stage 2 analysis") summary(fixed2)
Running Fixed effects model Stage 2 analysis
Call:
wls(Cov = tssem1.obj$pooledS, asyCov = tssem1.obj$acovS, n = tssem1.obj$total.n,
Amatrix = Amatrix, Smatrix = Smatrix, Fmatrix = Fmatrix,
diag.constraints = diag.constraints, cor.analysis = cor.analysis,
intervals.type = intervals.type, mx.algebras = mx.algebras,
model.name = model.name, suppressWarnings = suppressWarnings)
95% confidence intervals: Likelihood-based statistic
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Amatrix[1,7] 0.48342 NA 0.44872 0.51787 NA NA
Amatrix[2,6] 0.56418 NA 0.53680 0.59150 NA NA
Amatrix[3,6] 0.66160 NA 0.63533 0.68791 NA NA
Amatrix[4,6] 0.57257 NA 0.54256 0.60243 NA NA
Amatrix[5,7] 0.47160 NA 0.43552 0.50736 NA NA
Smatrix[1,1] 0.76630 NA 0.73181 0.79865 NA NA
Smatrix[2,2] 0.68171 NA 0.65012 0.71184 NA NA
Smatrix[3,3] 0.56229 NA 0.52677 0.59636 NA NA
Smatrix[4,4] 0.67216 NA 0.63707 0.70563 NA NA
Smatrix[5,5] 0.77759 NA 0.74258 0.81032 NA NA
Smatrix[7,6] 1.08188 NA 1.02603 1.14539 NA NA
Goodness-of-fit indices:
Value
Sample size 4496.0000
Chi-square of target model 680.5811
DF of target model 4.0000
p value of target model 0.0000
Number of constraints imposed on "Smatrix" 5.0000
DF manually adjusted 0.0000
Chi-square of independence model 3100.6516
DF of independence model 10.0000
RMSEA 0.1940
SRMR 0.1404
TLI 0.4527
CFI 0.7811
AIC 672.5811
BIC 646.9373
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
Random-effects MASEM
## Stage 1 analysis random1 <- tssem1(Digman97$data, Digman97$n, method="REM", RE.type="Diag", model.name="Random effects model Stage 1 analysis") summary(random1)
Running Random effects model Stage 1 analysis
Call:
meta(y = ES, v = acovR, RE.constraints = Diag(x = paste(RE.startvalues,
"*Tau2_", 1:no.es, "_", 1:no.es, sep = "")), RE.lbound = RE.lbound,
I2 = I2, model.name = model.name)
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept1 3.9465e-01 5.4223e-02 2.8837e-01 5.0092e-01 7.2782 3.384e-13
Intercept10 4.4413e-01 3.2547e-02 3.8034e-01 5.0792e-01 13.6460 < 2.2e-16
Intercept2 4.4009e-01 4.1258e-02 3.5923e-01 5.2096e-01 10.6668 < 2.2e-16
Intercept3 5.4542e-02 6.1716e-02 -6.6418e-02 1.7550e-01 0.8838 0.376821
Intercept4 9.8668e-02 4.6219e-02 8.0812e-03 1.8926e-01 2.1348 0.032776
Intercept5 4.2966e-01 4.0156e-02 3.5096e-01 5.0837e-01 10.6999 < 2.2e-16
Intercept6 1.2851e-01 4.0816e-02 4.8514e-02 2.0851e-01 3.1486 0.001641
Intercept7 2.0526e-01 4.9591e-02 1.0806e-01 3.0245e-01 4.1390 3.488e-05
Intercept8 2.3994e-01 3.1924e-02 1.7737e-01 3.0251e-01 7.5159 5.662e-14
Intercept9 1.8910e-01 4.3014e-02 1.0480e-01 2.7341e-01 4.3963 1.101e-05
Tau2_10_10 1.1151e-02 5.0467e-03 1.2591e-03 2.1042e-02 2.2095 0.027143
Tau2_1_1 3.7207e-02 1.5000e-02 7.8079e-03 6.6607e-02 2.4805 0.013120
Tau2_2_2 2.0305e-02 8.4348e-03 3.7735e-03 3.6837e-02 2.4073 0.016069
Tau2_3_3 4.8220e-02 1.9723e-02 9.5631e-03 8.6876e-02 2.4448 0.014492
Tau2_4_4 2.4610e-02 1.0624e-02 3.7872e-03 4.5434e-02 2.3164 0.020535
Tau2_5_5 1.8725e-02 8.2474e-03 2.5602e-03 3.4889e-02 2.2704 0.023184
Tau2_6_6 1.8256e-02 8.7889e-03 1.0302e-03 3.5482e-02 2.0772 0.037785
Tau2_7_7 2.9424e-02 1.2263e-02 5.3894e-03 5.3459e-02 2.3995 0.016420
Tau2_8_8 9.6511e-03 4.8824e-03 8.1691e-05 1.9220e-02 1.9767 0.048076
Tau2_9_9 2.0934e-02 9.1280e-03 3.0430e-03 3.8824e-02 2.2933 0.021829
Intercept1 ***
Intercept10 ***
Intercept2 ***
Intercept3
Intercept4 *
Intercept5 ***
Intercept6 **
Intercept7 ***
Intercept8 ***
Intercept9 ***
Tau2_10_10 *
Tau2_1_1 *
Tau2_2_2 *
Tau2_3_3 *
Tau2_4_4 *
Tau2_5_5 *
Tau2_6_6 *
Tau2_7_7 *
Tau2_8_8 *
Tau2_9_9 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Q statistic on homogeneity of effect sizes: 2381.004
Degrees of freedom of the Q statistic: 130
P value of the Q statistic: 0
Heterogeneity indices (based on the estimated Tau2):
Estimate
Intercept1: I2 (Q statistic) 0.9487
Intercept2: I2 (Q statistic) 0.9082
Intercept3: I2 (Q statistic) 0.9414
Intercept4: I2 (Q statistic) 0.8894
Intercept5: I2 (Q statistic) 0.9005
Intercept6: I2 (Q statistic) 0.8537
Intercept7: I2 (Q statistic) 0.9093
Intercept8: I2 (Q statistic) 0.7714
Intercept9: I2 (Q statistic) 0.8746
Intercept10: I2 (Q statistic) 0.8431
Number of studies (or clusters): 14
Number of observed statistics: 140
Number of estimated parameters: 20
Degrees of freedom: 120
-2 log likelihood: -110.8452
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
## Stage 2 analysis random2 <- tssem2(random1, Amatrix=A1, Smatrix=S1, Fmatrix=F1, diag.constraints=TRUE, intervals.type="LB", model.name="Random effects model Stage 2 analysis") summary(random2)
Running Random effects model Stage 2 analysis
Call:
wls(Cov = pooledS, asyCov = asyCov, n = tssem1.obj$total.n, Amatrix = Amatrix,
Smatrix = Smatrix, Fmatrix = Fmatrix, diag.constraints = diag.constraints,
cor.analysis = cor.analysis, intervals.type = intervals.type,
mx.algebras = mx.algebras, model.name = model.name, suppressWarnings = suppressWarnings)
95% confidence intervals: Likelihood-based statistic
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Amatrix[1,7] 0.36536 NA 0.19503 0.49058 NA NA
Amatrix[2,6] 0.52490 NA 0.44022 0.61202 NA NA
Amatrix[3,6] 0.58913 NA 0.50941 0.67414 NA NA
Amatrix[4,6] 0.48656 NA 0.41528 0.56025 NA NA
Amatrix[5,7] 0.34785 NA 0.18556 0.46774 NA NA
Smatrix[1,1] 0.86651 NA 0.75933 0.96185 NA NA
Smatrix[2,2] 0.72448 NA 0.62542 0.80620 NA NA
Smatrix[3,3] 0.65292 NA 0.54551 0.74050 NA NA
Smatrix[4,4] 0.76326 NA 0.68611 0.82754 NA NA
Smatrix[5,5] 0.87900 NA 0.78123 0.96547 NA NA
Smatrix[7,6] 1.74738 NA 1.29139 3.41224 NA NA
Goodness-of-fit indices:
Value
Sample size 4496.0000
Chi-square of target model 81.2046
DF of target model 4.0000
p value of target model 0.0000
Number of constraints imposed on "Smatrix" 5.0000
DF manually adjusted 0.0000
Chi-square of independence model 514.5603
DF of independence model 10.0000
RMSEA 0.0655
SRMR 0.1305
TLI 0.6175
CFI 0.8470
AIC 73.2046
BIC 47.5608
OpenMx status1: 0 ("0" and "1": considered fine; other values indicate problems)
- More examples
3 Installation
The current version is 0.8-4:
First of all, you need R to run it. Since metaSEM uses OpenMx as the workhorse, OpenMx has to be installed. To install OpenMx, run the following command inside an R session:
install.packages('OpenMx', repos='http://openmx.psyc.virginia.edu/packages/')
See http://openmx.psyc.virginia.edu/installing-openmx for the details on how to install OpenMx. Moreover, metaSEM also depends on the ellipse and MASS packages that can be installed by the following command inside an R session:
install.packages(c('ellipse','MASS'))
Windows platform
Download the Windows binary of metaSEM. If the file is saved at d:\. Run the following command inside an R session:
install.packages(pkgs="d:/metaSEM_0.8-4.zip", repos=NULL)
Please note that d:\ in Windows is represented by either d:/ or d:\\ in R.
Linux and Mac OS X platform
Download the source package of metaSEM. Run the following command (as Root) inside an R session:
install.packages(pkgs="metaSEM_0.8-4.tar.gz", repos=NULL, type="source")