Meta-Analytic SEM a case in Leadership

> ## Meta-Analytic Structural Equation Modeling: > ## A case study in educational leadership > ## synthesized from 4 studies > ## Author: Dr.Twatchai Tangutairuang > ## Load Meta Analytic SEM library > library(metaSEM) > > ## 17 observed variables > ## X1 - Intelligence > ## X2 - Personality > ## X3 - Skill > ## X4 - Charismatic > ## X5 - Work orientation > ## X6 - Relation orientation > ## X7 - Participation > ## X8 - Development orenitation > ## X9 - Age > ## X10 - Education > ## X11 - Teaching/research > ## X12 - Administration > ## X13 - Attitude > ## X14 - Follower > ## X15 - Org structure > ## X16 - Change > ## X17 - Support > ## 4 Latent variables > ## L1 - Trait > ## L2 - Behavior > ## L3 - Background > ## L4 - Situation > > ## define correlation data set > one one > two two > > three three > four four > Pooled ## Create data list from 4 studies > Pooled$data ## Sample size for each study > Pooled$n > ############################################## > #### Run fixed-effects model: Stage 1 analysis > #### to calculate pooled correlation cofficient > #### FEM - fixed-effects meta-analysis > ############################################## > output1 summary(output1) Call: tssem1FEM(my.df = my.df, n = n, cor.analysis = cor.analysis, model.name = model.name, cluster = cluster, suppressWarnings = suppressWarnings, silent = silent, run = run) Coefficients: Estimate S[1,2] 0.7596738 S[1,3] 0.7396249 S[1,4] 0.6522624 S[1,5] 0.6288517 S[1,6] 0.5792238 S[1,7] 0.6631129 S[1,8] 0.6704674 S[1,9] -0.0356534 S[1,10] 0.1099366 S[1,11] 0.3598790 S[1,12] 0.1231815 S[1,13] 0.4021610 S[1,14] 0.5572546

Std.Error 0.0099726 0.0105187 0.0130981 0.0166507 0.0173216 0.0133503 0.0148463 0.0370966 0.0260465 0.0262168 0.0370748 0.0250393 0.0164128

z value 76.1759 70.3153 49.7983 37.7673 33.4394 49.6703 45.1606 -0.9611 4.2208 13.7270 3.3225 16.0612 33.9525

Pr(>|z|) < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 0.3365044 2.435e-05 < 2.2e-16 0.0008921 < 2.2e-16 < 2.2e-16

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S[1,15] S[1,16] S[1,17] S[2,3] S[2,4] S[2,5] S[2,6] S[2,7] S[2,8] S[2,9] S[2,10] S[2,11] S[2,12] S[2,13] S[2,14] S[2,15] S[2,16] S[2,17] S[3,4] S[3,5] S[3,6] S[3,7] S[3,8] S[3,9] S[3,10] S[3,11] S[3,12] S[3,13] S[3,14] S[3,15] S[3,16] S[3,17] S[4,5] S[4,6] S[4,7] S[4,8] S[4,9] S[4,10] S[4,11] S[4,12] S[4,13] S[4,14] S[4,15] S[4,16] S[4,17] S[5,6] S[5,7] S[5,8] S[5,9] S[5,10] S[5,11] S[5,12] S[5,13] S[5,14] S[5,15] S[5,16] S[5,17] S[6,7] S[6,8] S[6,9] S[6,10] S[6,11] S[6,12] S[6,13] S[6,14] S[6,15] S[6,16] S[6,17] S[7,8] S[7,9] S[7,10] S[7,11] S[7,12] S[7,13]

0.5848677 0.4100708 0.5354323 0.7721184 0.6903318 0.6367961 0.6070561 0.6813902 0.6702340 -0.1338320 0.1216304 0.3408086 0.1528247 0.4031650 0.5448688 0.5790563 0.4004751 0.5518286 0.7802832 0.7277032 0.6618164 0.7605582 0.7400926 -0.0853962 0.1117231 0.2831830 0.1247131 0.3570059 0.6255025 0.6562088 0.4650069 0.6000032 0.6735895 0.6217540 0.6861437 0.6617536 -0.0351976 0.1330020 0.3038593 0.1138995 0.3490439 0.5405339 0.5868355 0.3872551 0.5538009 0.6768490 0.7070118 0.7309575 -0.0657110 0.0577106 0.2483611 0.0979823 0.3476066 0.6095146 0.6375966 0.4586990 0.5792505 0.7286591 0.6927498 -0.0823181 0.0262844 0.2080362 0.1199371 0.3699745 0.5719998 0.6416751 0.3759546 0.5304775 0.7828048 -0.0823120 0.0393762 0.2943974 0.0800677 0.3847628

0.0165200 0.0235513 0.0170370 0.0083666 0.0108222 0.0162532 0.0144948 0.0124223 0.0147319 0.0298565 0.0233116 0.0264163 0.0298155 0.0251995 0.0162829 0.0147687 0.0236881 0.0163850 0.0081367 0.0132172 0.0127940 0.0099209 0.0122200 0.0299259 0.0231546 0.0269023 0.0300662 0.0257020 0.0141412 0.0127524 0.0218577 0.0150108 0.0146700 0.0138373 0.0121109 0.0144988 0.0297778 0.0231279 0.0264550 0.0296195 0.0256052 0.0160556 0.0145555 0.0235371 0.0159968 0.0153075 0.0140386 0.0132829 0.0375229 0.0264345 0.0277571 0.0375869 0.0263939 0.0172221 0.0183285 0.0227898 0.0179797 0.0130239 0.0146391 0.0306221 0.0236923 0.0284955 0.0305578 0.0262397 0.0175968 0.0152573 0.0246526 0.0187401 0.0109129 0.0365971 0.0259847 0.0269887 0.0367991 0.0253411

35.4036 17.4118 31.4276 92.2862 63.7882 39.1797 41.8809 54.8522 45.4955 -4.4825 5.2176 12.9014 5.1257 15.9989 33.4626 39.2083 16.9062 33.6789 95.8968 55.0572 51.7286 76.6624 60.5639 -2.8536 4.8251 10.5264 4.1480 13.8902 44.2326 51.4576 21.2743 39.9716 45.9162 44.9332 56.6551 45.6419 -1.1820 5.7507 11.4859 3.8454 13.6318 33.6664 40.3172 16.4530 34.6196 44.2167 50.3620 55.0300 -1.7512 2.1832 8.9476 2.6068 13.1700 35.3914 34.7872 20.1274 32.2170 55.9478 47.3219 -2.6882 1.1094 7.3007 3.9249 14.0998 32.5060 42.0569 15.2501 28.3071 71.7323 -2.2491 1.5154 10.9082 2.1758 15.1833

< 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 7.377e-06 1.813e-07 < 2.2e-16 2.965e-07 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 0.0043229 1.399e-06 < 2.2e-16 3.355e-05 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 0.2372024 8.887e-09 < 2.2e-16 0.0001203 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 0.0799075 0.0290242 < 2.2e-16 0.0091387 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 0.0071840 0.2672555 2.864e-13 8.675e-05 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 < 2.2e-16 0.0245035 0.1296820 < 2.2e-16 0.0295697 < 2.2e-16

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S[7,14] 0.6000357 0.0150202 39.9486 < 2.2e-16 S[7,15] 0.6648262 0.0140516 47.3131 < 2.2e-16 S[7,16] 0.4650718 0.0221844 20.9639 < 2.2e-16 S[7,17] 0.6092580 0.0148812 40.9414 < 2.2e-16 S[8,9] -0.0574504 0.0379520 -1.5138 0.1300856 S[8,10] 0.0656193 0.0262821 2.4967 0.0125344 S[8,11] 0.2617323 0.0276255 9.4743 < 2.2e-16 S[8,12] 0.0762592 0.0380878 2.0022 0.0452641 S[8,13] 0.3309157 0.0267133 12.3877 < 2.2e-16 S[8,14] 0.6476125 0.0155792 41.5690 < 2.2e-16 S[8,15] 0.6637709 0.0170217 38.9956 < 2.2e-16 S[8,16] 0.4718486 0.0223420 21.1193 < 2.2e-16 S[8,17] 0.6186388 0.0164076 37.7043 < 2.2e-16 S[9,10] -0.0156279 0.0288737 -0.5412 0.5883359 S[9,11] 0.1659605 0.0438270 3.7867 0.0001526 S[9,12] 0.3700308 0.0259014 14.2861 < 2.2e-16 S[9,13] -0.1012142 0.0440931 -2.2955 0.0217063 S[9,14] -0.0862498 0.0401763 -2.1468 0.0318104 S[9,15] -0.0812015 0.0306349 -2.6506 0.0080343 S[9,16] -0.0786775 0.0444120 -1.7715 0.0764715 S[9,17] -0.0680072 0.0380171 -1.7889 0.0736380 S[10,11] 0.1411700 0.0294061 4.8007 1.581e-06 S[10,12] 0.0510440 0.0288523 1.7691 0.0768690 S[10,13] 0.1338480 0.0291321 4.5945 4.338e-06 S[10,14] 0.0591632 0.0270491 2.1873 0.0287242 S[10,15] 0.0468185 0.0254635 1.8387 0.0659662 S[10,16] 0.0610955 0.0288749 2.1159 0.0343562 S[10,17] 0.0311119 0.0273439 1.1378 0.2552042 S[11,12] 0.2328087 0.0435643 5.3440 9.091e-08 S[11,13] 0.5243843 0.0237504 22.0790 < 2.2e-16 S[11,14] 0.1803909 0.0288366 6.2556 3.959e-10 S[11,15] 0.2144721 0.0322019 6.6602 2.734e-11 S[11,16] 0.1746783 0.0291684 5.9886 2.116e-09 S[11,17] 0.2328267 0.0282322 8.2468 2.220e-16 S[12,13] 0.1132415 0.0440740 2.5693 0.0101890 S[12,14] 0.0719117 0.0406103 1.7708 0.0765984 S[12,15] 0.0960223 0.0307939 3.1182 0.0018194 S[12,16] -0.0084252 0.0448643 -0.1878 0.8510387 S[12,17] 0.0716383 0.0381830 1.8762 0.0606302 S[13,14] 0.3392767 0.0265588 12.7745 < 2.2e-16 S[13,15] 0.3735918 0.0290731 12.8501 < 2.2e-16 S[13,16] 0.3136114 0.0270953 11.5744 < 2.2e-16 S[13,17] 0.2910990 0.0270990 10.7421 < 2.2e-16 S[14,15] 0.7535376 0.0120095 62.7454 < 2.2e-16 S[14,16] 0.5500434 0.0204542 26.8915 < 2.2e-16 S[14,17] 0.6584273 0.0135766 48.4971 < 2.2e-16 S[15,16] 0.5205212 0.0249199 20.8877 < 2.2e-16 S[15,17] 0.6878869 0.0142196 48.3760 < 2.2e-16 S[16,17] 0.5814717 0.0194839 29.8437 < 2.2e-16 --Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 Goodness-of-fit indices: Value Sample size 2370.0000 Chi-square of target model 1920.5123 DF of target model 147.0000 p value of target model 0.0000 Chi-square of independence model 18946.5638 DF of independence model 283.0000 RMSEA 0.1427 SRMR 0.0860 TLI 0.8171 CFI 0.9050 AIC 1626.5123 BIC 778.2275 > > > > > > >

################################# ## Prepare a model implied matrix ################################# ## Prepare Fmatrix F1 > > + > > > + > > > > > > > > + + + + + > > > > > > > > > > > > > > > > > >

## Prepare Smatrix ## Factor correlation matrix - 3x3 Latent variables Phi