Supplementary Material for Psychological Methods Website
1
Meta-analytic Structural Equation Modeling
Supplementary material for Psychological Methods website
Full version of Table 6
Relative Percentage Bias of Parameter Estimates in Stage 2 of Study 1 with Homogeneous Case
Sample size / Methods / 11 / 21 / 31 / 42 / 52 / 62 / 21 / 11 / 22 / 33 / 44 / 55 / 66Number of studies = 5
50 / univariate-r / -0.16 / -0.32 / 0.25 / 0.43 / -0.32 / -1.00 / -0.56 / -1.07 / -0.41 / -1.04 / -3.27 / -0.35 / 0.35
univariate-z / 0.26 / 0.16 / 0.84 / 0.92 / 0.14 / -0.41 / -0.13 / -2.58 / -1.32 / -1.70 / -5.01 / -1.23 / -0.31
GLS / 3.39 / 5.38 / 8.01 / 4.05 / 5.32 / 6.85 / 14.21 / -13.76 / -11.67 / -10.32 / -16.39 / -11.54 / -8.88
TSSEM / 1.12 / 1.44 / 2.23 / 1.34 / 1.28 / 1.62 / 2.79 / -5.39 / -3.81 / -3.25 / -6.40 / -3.46 / -2.60
100 / univariate-r / 0.24 / -0.02 / -0.92 / -0.13 / 0.18 / -0.17 / 0.10 / -1.68 / -0.45 / 0.67 / -0.40 / -0.87 / -0.18
univariate-z / 0.45 / 0.23 / -0.60 / 0.10 / 0.41 / 0.14 / 0.29 / -2.42 / -0.92 / 0.32 / -1.20 / -1.32 / -0.53
GLS / 1.75 / 2.93 / 3.13 / 1.67 / 2.99 / 3.71 / 7.15 / -6.96 / -6.19 / -3.97 / -6.70 / -6.33 / -4.63
TSSEM / 0.70 / 0.93 / 0.42 / 0.58 / 1.03 / 1.01 / 2.15 / -3.17 / -2.23 / -0.82 / -2.75 / -2.46 / -1.50
200 / univariate-r / 0.08 / -0.33 / 0.07 / 0.13 / -0.48 / -0.08 / -0.07 / -0.68 / 0.38 / -0.28 / -0.82 / 0.66 / -0.09
univariate-z / 0.19 / -0.19 / 0.22 / 0.23 / -0.35 / 0.07 / 0.01 / -1.08 / 0.12 / -0.45 / -1.19 / 0.42 / -0.26
GLS / 0.96 / 1.09 / 1.90 / 0.97 / 0.97 / 1.71 / 3.16 / -3.76 / -2.33 / -2.36 / -3.80 / -2.11 / -2.11
TSSEM / 0.39 / 0.08 / 0.63 / 0.46 / -0.01 / 0.45 / 0.94 / -1.74 / -0.37 / -0.91 / -1.95 / -0.20 / -0.68
500 / univariate-r / -0.04 / -0.04 / 0.02 / 0.19 / -0.28 / 0.02 / -0.13 / 0.00 / -0.02 / -0.09 / -0.85 / 0.46 / -0.10
univariate-z / 0.00 / 0.01 / 0.08 / 0.24 / -0.23 / 0.08 / -0.10 / -0.15 / -0.11 / -0.16 / -1.00 / 0.36 / -0.16
GLS / 0.31 / 0.53 / 0.73 / 0.49 / 0.31 / 0.73 / 1.15 / -1.24 / -1.10 / -0.89 / -1.88 / -0.68 / -0.90
TSSEM / 0.11 / 0.13 / 0.25 / 0.28 / -0.07 / 0.25 / 0.26 / -0.51 / -0.32 / -0.35 / -1.13 / 0.05 / -0.35
1000 / univariate-r / 0.03 / -0.09 / 0.03 / 0.05 / -0.08 / -0.09 / 0.06 / -0.19 / 0.13 / -0.06 / -0.25 / 0.10 / 0.07
univariate-z / 0.06 / -0.07 / 0.05 / 0.07 / -0.05 / -0.07 / 0.08 / -0.27 / 0.09 / -0.10 / -0.33 / 0.05 / 0.04
GLS / 0.14 / 0.23 / 0.44 / 0.24 / 0.22 / 0.25 / 0.70 / -0.56 / -0.48 / -0.53 / -0.92 / -0.47 / -0.31
TSSEM / 0.03 / 0.04 / 0.19 / 0.13 / 0.02 / 0.01 / 0.26 / -0.16 / -0.12 / -0.25 / -0.53 / -0.07 / -0.04
Note. Values underlined are those greater than 5%.
Full version of Table 6 (continued)
Sample size / Methods / 11 / 21 / 31 / 42 / 52 / 62 / 21 / 11 / 22 / 33 / 44 / 55 / 66Number of studies = 10
50 / univariate-r / 0.08 / -0.32 / -0.23 / 0.08 / -0.43 / -0.75 / 0.34 / -1.40 / -0.02 / -0.27 / -1.48 / 0.15 / 0.29
univariate-z / 0.56 / 0.32 / 0.48 / 0.57 / 0.22 / -0.08 / 0.68 / -3.12 / -1.26 / -1.07 / -3.18 / -1.12 / -0.46
GLS / 3.15 / 4.98 / 7.56 / 3.86 / 5.03 / 6.42 / 11.96 / -12.42 / -10.49 / -9.43 / -15.05 / -10.64 / -8.09
TSSEM / 0.88 / 1.15 / 2.03 / 1.17 / 0.99 / 1.45 / 2.49 / -4.02 / -2.80 / -2.82 / -5.15 / -2.52 / -2.16
100 / univariate-r / -0.10 / -0.49 / -0.25 / 0.02 / -0.24 / -0.30 / -0.17 / -0.18 / 0.61 / 0.05 / -0.60 / 0.14 / 0.07
univariate-z / 0.14 / -0.19 / 0.08 / 0.25 / 0.09 / 0.08 / 0.01 / -1.04 / 0.04 / -0.33 / -1.43 / -0.48 / -0.35
GLS / 1.44 / 2.16 / 3.41 / 1.67 / 2.49 / 3.25 / 5.56 / -5.57 / -4.51 / -4.15 / -6.48 / -5.17 / -3.99
TSSEM / 0.33 / 0.23 / 0.86 / 0.48 / 0.50 / 0.72 / 1.03 / -1.59 / -0.73 / -1.19 / -2.17 / -1.26 / -1.06
200 / univariate-r / 0.12 / -0.09 / -0.42 / -0.10 / -0.14 / -0.13 / 0.01 / -0.71 / 0.01 / 0.34 / 0.09 / 0.12 / 0.03
univariate-z / 0.25 / 0.07 / -0.25 / 0.02 / 0.02 / 0.05 / 0.08 / -1.16 / -0.29 / 0.15 / -0.33 / -0.18 / -0.17
GLS / 0.90 / 1.24 / 1.40 / 0.76 / 1.20 / 1.58 / 2.46 / -3.44 / -2.54 / -1.71 / -2.93 / -2.46 / -1.91
TSSEM / 0.34 / 0.27 / 0.11 / 0.15 / 0.22 / 0.36 / 0.51 / -1.42 / -0.65 / -0.24 / -0.73 / -0.54 / -0.52
500 / univariate-r / 0.09 / -0.16 / -0.03 / -0.12 / -0.03 / 0.02 / 0.36 / -0.43 / 0.24 / -0.01 / 0.34 / 0.01 / -0.07
univariate-z / 0.14 / -0.09 / 0.04 / -0.07 / 0.03 / 0.09 / 0.39 / -0.61 / 0.12 / -0.09 / 0.17 / -0.11 / -0.15
GLS / 0.35 / 0.41 / 0.67 / 0.24 / 0.47 / 0.68 / 1.15 / -1.35 / -0.84 / -0.80 / -0.95 / -0.96 / -0.81
TSSEM / 0.14 / 0.02 / 0.16 / -0.01 / 0.10 / 0.20 / 0.30 / -0.57 / -0.09 / -0.23 / -0.04 / -0.25 / -0.27
1000 / univariate-r / 0.07 / -0.12 / -0.08 / -0.02 / -0.01 / -0.05 / -0.10 / -0.29 / 0.20 / 0.07 / 0.00 / -0.01 / 0.03
univariate-z / 0.09 / -0.09 / -0.05 / 0.01 / 0.02 / -0.01 / -0.09 / -0.37 / 0.15 / 0.03 / -0.09 / -0.08 / -0.01
GLS / 0.18 / 0.15 / 0.29 / 0.14 / 0.26 / 0.27 / 0.32 / -0.69 / -0.33 / -0.35 / -0.53 / -0.53 / -0.33
TSSEM / 0.07 / -0.02 / 0.04 / 0.01 / 0.07 / 0.05 / -0.08 / -0.29 / 0.02 / -0.06 / -0.09 / -0.16 / -0.08
Note. Values underlined are those greater than 5%.
Full version of Table 6 (continued)
Sample size / Methods / 11 / 21 / 31 / 42 / 52 / 62 / 21 / 11 / 22 / 33 / 44 / 55 / 66Number of studies = 15
50 / univariate-r / 0.21 / -0.78 / -0.63 / -0.14 / -0.43 / -0.84 / 0.65 / -1.90 / 0.85 / 0.19 / -0.67 / 0.18 / 0.49
univariate-z / 0.76 / -0.15 / 0.02 / 0.34 / 0.23 / -0.13 / 0.93 / -3.85 / -0.35 / -0.54 / -2.36 / -1.08 / -0.31
GLS / 3.54 / 4.14 / 6.31 / 3.02 / 4.45 / 6.17 / 10.84 / -13.81 / -8.78 / -7.91 / -11.94 / -9.35 / -7.69
TSSEM / 1.14 / 0.53 / 1.48 / 0.58 / 0.96 / 1.47 / 2.11 / -4.98 / -1.60 / -2.14 / -2.97 / -2.38 / -2.09
100 / univariate-r / 0.08 / -0.27 / 0.03 / -0.06 / -0.18 / -0.34 / 0.01 / -0.82 / 0.22 / -0.29 / -0.33 / 0.05 / 0.15
univariate-z / 0.34 / 0.03 / 0.37 / 0.19 / 0.15 / 0.03 / 0.13 / -1.75 / -0.34 / -0.67 / -1.20 / -0.58 / -0.26
GLS / 1.79 / 1.91 / 3.42 / 1.63 / 2.11 / 3.04 / 4.55 / -6.91 / -3.97 / -4.17 / -6.31 / -4.38 / -3.70
TSSEM / 0.57 / 0.31 / 1.01 / 0.33 / 0.49 / 0.65 / 1.06 / -2.48 / -0.86 / -1.37 / -1.61 / -1.21 / -0.94
200 / univariate-r / -0.06 / 0.15 / -0.18 / -0.05 / 0.06 / -0.23 / 0.00 / -0.04 / -0.43 / 0.08 / -0.07 / -0.26 / 0.15
univariate-z / 0.08 / 0.31 / -0.01 / 0.07 / 0.22 / -0.06 / 0.05 / -0.50 / -0.74 / -0.11 / -0.52 / -0.57 / -0.05
GLS / 0.82 / 1.24 / 1.45 / 0.82 / 1.18 / 1.45 / 1.93 / -3.12 / -2.54 / -1.77 / -3.15 / -2.41 / -1.75
TSSEM / 0.25 / 0.39 / 0.30 / 0.23 / 0.34 / 0.25 / 0.25 / -1.09 / -0.87 / -0.45 / -1.04 / -0.77 / -0.38
500 / univariate-r / 0.03 / -0.13 / 0.06 / 0.19 / -0.10 / -0.11 / -0.16 / -0.21 / 0.18 / -0.12 / -0.78 / 0.13 / 0.08
univariate-z / 0.08 / -0.06 / 0.13 / 0.24 / -0.03 / -0.04 / -0.13 / -0.38 / 0.06 / -0.20 / -0.95 / 0.01 / 0.00
GLS / 0.38 / 0.33 / 0.71 / 0.49 / 0.35 / 0.57 / 0.69 / -1.42 / -0.69 / -0.85 / -1.85 / -0.71 / -0.69
TSSEM / 0.14 / 0.00 / 0.24 / 0.25 / 0.03 / 0.11 / -0.02 / -0.58 / -0.06 / -0.32 / -0.98 / -0.11 / -0.17
1000 / univariate-r / 0.05 / -0.12 / 0.03 / 0.08 / -0.13 / 0.00 / -0.27 / -0.21 / 0.20 / -0.06 / -0.33 / 0.22 / -0.02
univariate-z / 0.07 / -0.09 / 0.07 / 0.10 / -0.10 / 0.04 / -0.26 / -0.31 / 0.14 / -0.10 / -0.41 / 0.15 / -0.06
GLS / 0.20 / 0.11 / 0.35 / 0.23 / 0.11 / 0.31 / 0.20 / -0.75 / -0.23 / -0.41 / -0.87 / -0.23 / -0.37
TSSEM / 0.08 / -0.05 / 0.13 / 0.11 / -0.06 / 0.09 / -0.15 / -0.32 / 0.07 / -0.16 / -0.43 / 0.09 / -0.13
Note. Values underlined are those greater than 5%.
Supplementary material for Psychological Methods website
Full version of Table 7
Relative Percentage Bias of Mean Standard Errors of Parameter Estimates in Stage 2 of Study 1 with Homogeneous Case
Sample size / Methods / 11 / 21 / 31 / 42 / 52 / 62 / 21 / 11 / 22 / 33 / 44 / 55 / 66Number of studies = 5
50 / univariate-r / 14.04 / 18.51 / 21.52 / 11.25 / 23.03 / 21.14 / 5.41 / -18.08 / -8.67 / 8.19 / -19.33 / -6.60 / 8.44
univariate-z / 13.28 / 18.50 / 21.47 / 10.37 / 22.14 / 20.57 / 4.52 / -19.23 / -9.40 / 7.22 / -20.76 / -8.08 / 7.20
GLS / -21.89 / -22.72 / -26.03 / -26.02 / -21.60 / -24.35 / -29.28 / -7.32 / -2.33 / -2.98 / -11.52 / -2.86 / -0.72
TSSEM / -5.12 / -10.62 / -3.99 / -11.21 / -7.92 / -6.33 / -9.44 / 9.70 / 9.31 / 22.46 / 2.42 / 11.91 / 19.74
100 / univariate-r / 13.63 / 21.93 / 25.05 / 11.41 / 16.57 / 21.54 / 14.05 / -18.33 / -7.46 / 11.42 / -19.91 / -11.92 / 7.84
univariate-z / 13.47 / 22.02 / 24.63 / 11.45 / 16.18 / 21.34 / 13.52 / -18.97 / -8.03 / 10.88 / -20.27 / -12.57 / 6.78
GLS / -11.55 / -12.83 / -12.72 / -12.99 / -14.26 / -12.42 / -13.47 / 4.16 / 6.65 / 13.04 / 2.66 / 5.49 / 13.39
TSSEM / -3.64 / -1.70 / -1.07 / -5.95 / -5.52 / -2.12 / -1.02 / 12.09 / 18.56 / 26.77 / 9.38 / 14.31 / 25.61
200 / univariate-r / 16.35 / 20.28 / 15.62 / 18.58 / 18.28 / 24.05 / 13.85 / -17.06 / -8.70 / 2.29 / -15.16 / -10.32 / 9.29
univariate-z / 16.40 / 20.34 / 15.93 / 18.31 / 18.01 / 23.75 / 13.85 / -17.09 / -8.91 / 2.06 / -15.36 / -10.52 / 9.05
GLS / -7.39 / -7.00 / -11.36 / -4.39 / -8.60 / -4.75 / -8.20 / 8.27 / 13.61 / 14.32 / 11.59 / 11.76 / 22.68
TSSEM / -3.70 / -2.37 / -7.58 / 0.89 / -3.80 / -0.30 / -2.35 / 11.72 / 18.43 / 18.46 / 16.67 / 16.70 / 27.39
500 / univariate-r / 17.67 / 25.70 / 21.92 / 14.71 / 27.49 / 25.35 / 10.79 / -16.40 / -4.68 / 7.63 / -18.11 / -3.72 / 10.16
univariate-z / 17.67 / 25.70 / 21.92 / 14.71 / 27.49 / 25.35 / 10.79 / -16.40 / -4.68 / 7.63 / -18.11 / -3.73 / 10.16
GLS / -3.65 / -0.96 / -3.74 / -6.64 / 2.49 / -2.37 / -5.78 / 11.61 / 20.55 / 24.03 / 8.54 / 24.38 / 25.49
TSSEM / -1.83 / 1.46 / -1.42 / -4.04 / 3.48 / 0.00 / -2.58 / 13.75 / 22.92 / 26.38 / 11.17 / 25.53 / 27.38
1000 / univariate-r / 19.14 / 21.02 / 25.17 / 14.88 / 24.84 / 22.73 / 10.10 / -15.06 / -8.22 / 9.34 / -18.22 / -6.07 / 8.15
univariate-z / 19.14 / 21.02 / 25.17 / 14.88 / 24.18 / 22.73 / 10.10 / -15.06 / -8.22 / 9.34 / -18.22 / -6.07 / 8.15
GLS / -1.95 / -0.68 / 0.00 / -3.21 / 0.00 / -2.00 / -4.62 / 13.82 / 20.19 / 27.53 / 12.00 / 21.36 / 25.56
TSSEM / -1.31 / 0.00 / 1.37 / -2.56 / 1.37 / -0.67 / -3.61 / 15.16 / 20.77 / 28.98 / 12.40 / 22.55 / 26.82
Note. Values underlined are those greater than 10%.
Full version of Table 7 (continued)
Sample size / Methods / 11 / 21 / 31 / 42 / 52 / 62 / 21 / 11 / 22 / 33 / 44 / 55 / 66Number of studies = 10
50 / univariate-r / 16.69 / 27.00 / 23.54 / 13.94 / 23.52 / 21.01 / 4.61 / -16.05 / -4.19 / 9.34 / -18.03 / -5.57 / 8.83
univariate-z / 15.77 / 25.96 / 23.06 / 13.56 / 22.67 / 20.54 / 3.44 / -17.46 / -6.00 / 8.02 / -19.03 / -7.22 / 7.38
GLS / -22.09 / -23.27 / -23.06 / -22.54 / -25.20 / -25.27 / -28.81 / -10.39 / -8.21 / -4.89 / -11.23 / -10.12 / -7.27
TSSEM / -3.18 / -4.79 / -6.82 / -6.78 / -7.35 / -7.80 / -8.18 / 8.64 / 10.42 / 13.34 / 4.17 / 9.03 / 12.30
100 / univariate-r / 19.09 / 24.10 / 29.52 / 18.86 / 28.43 / 24.45 / 5.62 / -14.99 / -5.69 / 14.68 / -15.13 / -2.85 / 10.02
univariate-z / 18.68 / 24.51 / 29.59 / 18.18 / 28.25 / 23.96 / 5.25 / -15.44 / -5.88 / 14.01 / -15.96 / -3.55 / 9.39
GLS / -5.88 / -12.56 / -8.12 / -13.30 / -13.93 / -14.52 / -14.58 / 6.29 / 3.69 / 12.27 / -1.89 / 1.90 / 5.01
TSSEM / 1.29 / -4.64 / 1.87 / -4.87 / -4.91 / -5.01 / -2.95 / 13.14 / 11.56 / 23.40 / 6.66 / 11.17 / 15.59
200 / univariate-r / 15.72 / 26.92 / 23.37 / 19.48 / 32.97 / 29.14 / 9.55 / -17.29 / -4.00 / 9.20 / -14.98 / 0.52 / 14.46
univariate-z / 15.72 / 26.57 / 23.02 / 19.54 / 32.60 / 29.14 / 9.26 / -17.49 / -4.49 / 8.91 / -15.01 / 0.26 / 13.81
GLS / -5.61 / -5.93 / -8.04 / -3.24 / -2.68 / -5.07 / -5.56 / 6.30 / 10.99 / 12.39 / 8.71 / 14.32 / 16.07
TSSEM / -2.11 / -1.50 / -3.23 / 1.09 / 3.16 / -0.74 / -0.57 / 9.89 / 15.28 / 17.61 / 12.93 / 20.85 / 20.92
500 / univariate-r / 23.40 / 32.37 / 24.73 / 24.06 / 33.14 / 31.98 / 8.71 / -11.96 / 0.00 / 10.09 / -12.00 / 0.00 / 16.50
univariate-z / 23.40 / 32.37 / 24.73 / 23.40 / 33.14 / 31.98 / 8.71 / -12.29 / 0.00 / 9.63 / -12.00 / 0.41 / 16.02
GLS / 0.00 / -1.80 / -3.98 / -2.81 / -2.40 / -0.59 / -3.93 / 12.19 / 15.38 / 17.45 / 9.09 / 14.41 / 20.39
TSSEM / 1.73 / 0.00 / -1.72 / -0.56 / -0.60 / 1.80 / -1.77 / 14.08 / 17.24 / 19.05 / 11.31 / 17.24 / 23.88
1000 / univariate-r / 21.48 / 30.65 / 26.98 / 15.49 / 31.71 / 29.03 / 11.45 / -13.82 / -1.16 / 11.92 / -17.62 / -0.58 / 13.42
univariate-z / 21.48 / 30.65 / 26.98 / 15.49 / 31.71 / 29.03 / 11.45 / -13.82 / -1.16 / 11.92 / -17.62 / -0.58 / 13.42
GLS / -3.13 / -3.31 / -2.42 / -3.88 / -2.52 / 0.00 / 0.00 / 7.77 / 12.94 / 18.12 / 7.25 / 15.66 / 22.22
TSSEM / -1.57 / -2.50 / -1.63 / -3.88 / -1.68 / 1.68 / 1.28 / 9.31 / 14.29 / 19.59 / 8.25 / 15.66 / 23.08
Note. Values underlined are those greater than 10%.
Full version of Table 7 (continued)
Sample size / Methods / 11 / 21 / 31 / 42 / 52 / 62 / 21 / 11 / 22 / 33 / 44 / 55 / 66Number of studies = 15
50 / univariate-r / 14.51 / 25.22 / 23.22 / 13.45 / 26.44 / 31.18 / 0.25 / -17.88 / -3.88 / 10.25 / -18.33 / -3.37 / 17.45
univariate-z / 13.77 / 24.78 / 22.53 / 13.06 / 25.61 / 30.93 / -0.62 / -19.27 / -5.36 / 8.73 / -19.50 / -4.86 / 15.99
GLS / -21.06 / -21.53 / -21.02 / -23.13 / -21.18 / -22.32 / -26.30 / -13.06 / -10.25 / -8.02 / -15.34 / -9.31 / -8.42
TSSEM / -5.07 / -5.93 / -2.55 / -5.80 / -4.64 / -3.24 / -5.64 / 2.69 / 5.52 / 12.22 / 2.07 / 7.95 / 12.76
100 / univariate-r / 17.35 / 31.09 / 24.38 / 16.55 / 31.77 / 31.84 / 1.96 / -15.98 / -0.92 / 9.77 / -16.93 / -0.37 / 17.00
univariate-z / 16.93 / 31.25 / 23.82 / 16.63 / 31.85 / 31.32 / 1.60 / -16.67 / -1.11 / 8.90 / -17.49 / -0.93 / 16.08
GLS / -12.38 / -7.86 / -11.55 / -11.60 / -12.47 / -11.40 / -14.73 / -4.32 / 4.36 / 1.98 / -3.63 / -0.55 / 3.77
TSSEM / -4.95 / -0.55 / -2.32 / -4.03 / -4.11 / -1.64 / -4.29 / 3.23 / 11.35 / 11.91 / 3.91 / 7.96 / 14.51
200 / univariate-r / 23.97 / 32.22 / 26.07 / 17.92 / 31.73 / 32.58 / 7.11 / -11.56 / 0.00 / 11.01 / -15.89 / -0.52 / 17.24
univariate-z / 23.97 / 32.22 / 26.07 / 18.30 / 32.22 / 32.71 / 7.11 / -11.97 / -0.26 / 11.01 / -16.09 / -0.79 / 16.93
GLS / -4.00 / -4.96 / -6.43 / -6.43 / -5.49 / -3.86 / -3.68 / 4.50 / 7.01 / 8.24 / 2.00 / 6.91 / 12.38
TSSEM / 1.49 / 0.39 / -0.74 / -2.53 / -1.98 / 0.39 / 1.16 / 9.72 / 12.57 / 13.46 / 5.62 / 10.39 / 17.05
500 / univariate-r / 26.52 / 29.89 / 23.89 / 23.12 / 40.37 / 29.65 / 1.57 / -9.69 / -2.06 / 9.26 / -12.42 / 5.78 / 14.56
univariate-z / 26.52 / 29.31 / 23.89 / 23.12 / 39.75 / 29.65 / 1.57 / -10.34 / -2.06 / 8.76 / -12.75 / 5.78 / 14.56
GLS / 0.00 / -5.33 / -3.98 / -3.98 / 0.00 / -3.03 / -6.01 / 8.36 / 6.30 / 9.86 / 4.24 / 13.30 / 13.07
TSSEM / 2.37 / -3.57 / -2.30 / -1.72 / 1.29 / -0.61 / -3.48 / 10.70 / 8.51 / 11.90 / 6.81 / 14.29 / 15.31
1000 / univariate-r / 21.80 / 35.59 / 29.51 / 19.12 / 32.23 / 33.90 / 6.40 / -14.02 / 1.20 / 13.61 / -15.60 / -1.18 / 17.61
univariate-z / 21.80 / 33.61 / 29.51 / 19.12 / 31.40 / 33.90 / 6.40 / -14.02 / 1.20 / 13.61 / -15.60 / -1.18 / 17.61
GLS / -0.81 / 0.00 / 0.00 / -4.76 / -5.17 / 0.88 / -0.64 / 7.11 / 13.21 / 15.28 / 4.48 / 7.36 / 17.65
TSSEM / -0.81 / 1.77 / 1.68 / -3.20 / -4.31 / 0.88 / 0.64 / 7.61 / 13.92 / 16.90 / 5.00 / 8.02 / 18.52
Note. Values underlined are those greater than 10%.
1
Meta-analytic Structural Equation Modeling
Supplementary material for Psychological Methods website
LISREL Code of the First Stage of the TSSEM for the Real Example
! If there are missing data, the values for the variances and covariances of the missing variables should be coded as 1.0 and 0.0, respectively. The stacked correlation matrices are stored in “data.cor”.
TI Stage 1 TSSEM: Study 1
DA NG=11 NI=9 NO=591 MA=CM
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 2
DA NO=656
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 3
DA NO=832
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 4
DA NO=823
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 5
DA NO=581
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 6
DA NO=627
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 7
DA NO=546
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 8
DA NO=463
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 9
DA NO=319
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 10
DA NO=1047
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
OU
TI: Study 11
DA NO=670
CM FU FI=data.cor
MO NX=9 NK=9 LX=DI, FR TD=ZE PH=ST, FR
! Equality constraints on testing the homogeneity of correlation matrices.
EQ PH(1,1,2) PH(2,1,2) PH(3,1,2) PH(4,1,2) PH(5,1,2) PH(6,1,2) PH(7,1,2) PH(8,1,2) PH(9,1,2) PH(10,1,2) PH(11,1,2)
EQ PH(1,1,3) PH(2,1,3) PH(3,1,3) PH(4,1,3) PH(5,1,3) PH(6,1,3) PH(7,1,3) PH(8,1,3) PH(9,1,3) PH(10,1,3) PH(11,1,3)
EQ PH(1,1,4) PH(2,1,4) PH(3,1,4) PH(4,1,4) PH(5,1,4) PH(6,1,4) PH(7,1,4) PH(8,1,4) PH(9,1,4) PH(10,1,4) PH(11,1,4)
EQ PH(1,1,5) PH(2,1,5) PH(3,1,5) PH(4,1,5) PH(5,1,5) PH(6,1,5) PH(7,1,5) PH(8,1,5) PH(9,1,5) PH(10,1,5) PH(11,1,5)
EQ PH(1,1,6) PH(2,1,6) PH(3,1,6) PH(4,1,6) PH(5,1,6) PH(6,1,6) PH(7,1,6) PH(8,1,6) PH(9,1,6) PH(10,1,6) PH(11,1,6)
EQ PH(1,1,7) PH(2,1,7) PH(3,1,7) PH(4,1,7) PH(5,1,7) PH(6,1,7) PH(7,1,7) PH(8,1,7) PH(9,1,7) PH(10,1,7) PH(11,1,7)
EQ PH(1,1,8) PH(2,1,8) PH(3,1,8) PH(4,1,8) PH(5,1,8) PH(6,1,8) PH(7,1,8) PH(8,1,8) PH(9,1,8) PH(10,1,8) PH(11,1,8)
EQ PH(1,1,9) PH(2,1,9) PH(3,1,9) PH(4,1,9) PH(5,1,9) PH(6,1,9) PH(7,1,9) PH(8,1,9) PH(9,1,9) PH(10,1,9) PH(11,1,9)
EQ PH(1,2,3) PH(2,2,3) PH(3,2,3) PH(4,2,3) PH(5,2,3) PH(6,2,3) PH(7,2,3) PH(8,2,3) PH(9,2,3) PH(10,2,3) PH(11,2,3)
EQ PH(1,2,4) PH(2,2,4) PH(3,2,4) PH(4,2,4) PH(5,2,4) PH(6,2,4) PH(7,2,4) PH(8,2,4) PH(9,2,4) PH(10,2,4) PH(11,2,4)
EQ PH(1,2,5) PH(2,2,5) PH(3,2,5) PH(4,2,5) PH(5,2,5) PH(6,2,5) PH(7,2,5) PH(8,2,5) PH(9,2,5) PH(10,2,5) PH(11,2,5)
EQ PH(1,2,6) PH(2,2,6) PH(3,2,6) PH(4,2,6) PH(5,2,6) PH(6,2,6) PH(7,2,6) PH(8,2,6) PH(9,2,6) PH(10,2,6) PH(11,2,6)
EQ PH(1,2,7) PH(2,2,7) PH(3,2,7) PH(4,2,7) PH(5,2,7) PH(6,2,7) PH(7,2,7) PH(8,2,7) PH(9,2,7) PH(10,2,7) PH(11,2,7)
EQ PH(1,2,8) PH(2,2,8) PH(3,2,8) PH(4,2,8) PH(5,2,8) PH(6,2,8) PH(7,2,8) PH(8,2,8) PH(9,2,8) PH(10,2,8) PH(11,2,8)
EQ PH(1,2,9) PH(2,2,9) PH(3,2,9) PH(4,2,9) PH(5,2,9) PH(6,2,9) PH(7,2,9) PH(8,2,9) PH(9,2,9) PH(10,2,9) PH(11,2,9)
EQ PH(1,3,4) PH(2,3,4) PH(3,3,4) PH(4,3,4) PH(5,3,4) PH(6,3,4) PH(7,3,4) PH(8,3,4) PH(9,3,4) PH(10,3,4) PH(11,3,4)
EQ PH(1,3,5) PH(2,3,5) PH(3,3,5) PH(4,3,5) PH(5,3,5) PH(6,3,5) PH(7,3,5) PH(8,3,5) PH(9,3,5) PH(10,3,5) PH(11,3,5)
EQ PH(1,3,6) PH(2,3,6) PH(3,3,6) PH(4,3,6) PH(5,3,6) PH(6,3,6) PH(7,3,6) PH(8,3,6) PH(9,3,6) PH(10,3,6) PH(11,3,6)
EQ PH(1,3,7) PH(2,3,7) PH(3,3,7) PH(4,3,7) PH(5,3,7) PH(6,3,7) PH(7,3,7) PH(8,3,7) PH(9,3,7) PH(10,3,7) PH(11,3,7)
EQ PH(1,3,8) PH(2,3,8) PH(3,3,8) PH(4,3,8) PH(5,3,8) PH(6,3,8) PH(7,3,8) PH(8,3,8) PH(9,3,8) PH(10,3,8) PH(11,3,8)
EQ PH(1,3,9) PH(2,3,9) PH(3,3,9) PH(4,3,9) PH(5,3,9) PH(6,3,9) PH(7,3,9) PH(8,3,9) PH(9,3,9) PH(10,3,9) PH(11,3,9)
EQ PH(1,4,5) PH(2,4,5) PH(3,4,5) PH(4,4,5) PH(5,4,5) PH(6,4,5) PH(7,4,5) PH(8,4,5) PH(9,4,5) PH(10,4,5) PH(11,4,5)
EQ PH(1,4,6) PH(2,4,6) PH(3,4,6) PH(4,4,6) PH(5,4,6) PH(6,4,6) PH(7,4,6) PH(8,4,6) PH(9,4,6) PH(10,4,6) PH(11,4,6)
EQ PH(1,4,7) PH(2,4,7) PH(3,4,7) PH(4,4,7) PH(5,4,7) PH(6,4,7) PH(7,4,7) PH(8,4,7) PH(9,4,7) PH(10,4,7) PH(11,4,7)
EQ PH(1,4,8) PH(2,4,8) PH(3,4,8) PH(4,4,8) PH(5,4,8) PH(6,4,8) PH(7,4,8) PH(8,4,8) PH(9,4,8) PH(10,4,8) PH(11,4,8)
EQ PH(1,4,9) PH(2,4,9) PH(3,4,9) PH(4,4,9) PH(5,4,9) PH(6,4,9) PH(7,4,9) PH(8,4,9) PH(9,4,9) PH(10,4,9) PH(11,4,9)
EQ PH(1,5,6) PH(2,5,6) PH(3,5,6) PH(4,5,6) PH(5,5,6) PH(6,5,6) PH(7,5,6) PH(8,5,6) PH(9,5,6) PH(10,5,6) PH(11,5,6)
EQ PH(1,5,7) PH(2,5,7) PH(3,5,7) PH(4,5,7) PH(5,5,7) PH(6,5,7) PH(7,5,7) PH(8,5,7) PH(9,5,7) PH(10,5,7) PH(11,5,7)
EQ PH(1,5,8) PH(2,5,8) PH(3,5,8) PH(4,5,8) PH(5,5,8) PH(6,5,8) PH(7,5,8) PH(8,5,8) PH(9,5,8) PH(10,5,8) PH(11,5,8)
EQ PH(1,5,9) PH(2,5,9) PH(3,5,9) PH(4,5,9) PH(5,5,9) PH(6,5,9) PH(7,5,9) PH(8,5,9) PH(9,5,9) PH(10,5,9) PH(11,5,9)
EQ PH(1,6,7) PH(2,6,7) PH(3,6,7) PH(4,6,7) PH(5,6,7) PH(6,6,7) PH(7,6,7) PH(8,6,7) PH(9,6,7) PH(10,6,7) PH(11,6,7)
EQ PH(1,6,8) PH(2,6,8) PH(3,6,8) PH(4,6,8) PH(5,6,8) PH(6,6,8) PH(7,6,8) PH(8,6,8) PH(9,6,8) PH(10,6,8) PH(11,6,8)
EQ PH(1,6,9) PH(2,6,9) PH(3,6,9) PH(4,6,9) PH(5,6,9) PH(6,6,9) PH(7,6,9) PH(8,6,9) PH(9,6,9) PH(10,6,9) PH(11,6,9)
EQ PH(1,7,8) PH(2,7,8) PH(3,7,8) PH(4,7,8) PH(5,7,8) PH(6,7,8) PH(7,7,8) PH(8,7,8) PH(9,7,8) PH(10,7,8) PH(11,7,8)
EQ PH(1,7,9) PH(2,7,9) PH(3,7,9) PH(4,7,9) PH(5,7,9) PH(6,7,9) PH(7,7,9) PH(8,7,9) PH(9,7,9) PH(10,7,9) PH(11,7,9)
EQ PH(1,8,9) PH(2,8,9) PH(3,8,9) PH(4,8,9) PH(5,8,9) PH(6,8,9) PH(7,8,9) PH(8,8,9) PH(9,8,9) PH(10,8,9) PH(11,8,9)
OU PH='stage1.cor' EC='stage1.ack'
! The pooled correlation matrix and its asymptotic covariance matrix are stored in “Stage1.cor” and “Stage1.ack”, respectively. Note that they also include parameter estimates of the “standard deviations.”
LISREL Code of the Second Stage of the TSSEM for the Real Example
! Some data manipulations are required to convert the outputs from Stage1.cor and Stage1.ack before they are submitted to Stage 2 analysis. Specifically, duplicated elements in Stage1.cor and Stage1.ack have to be removed and the total sample size is multiplied into the elements of Stage1.ack.
TI: Stage 2 TSSEM
DA NI=9 NO=7155 MA=KM
KM='stage2.cor' SY
AC='stage2.ack' SY
MO NX=9 NK=3 PH=ST, FR
PA LX
3*(1 0 0)
4*(0 1 0)
2*(0 0 1)
OU ME=WL
! Request ADF (WLS in LISREL) as the estimation method