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 / 66
Number 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 / 66
Number 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 / 66
Number 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 / 66
Number 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 / 66
Number 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 / 66
Number 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