ตัวอย่างการวิเคราะห์อภิมานด้วยโมเดลสมการเชิงโครงสร้าง (meta-analytic structural equation modelling) ด้วยโปรแกรม R กรณีการสังเคราะห์องค์ประกอบภาวะผู้นำทางการศึกษาจากงานวิจัย 4 งาน

1. > ## 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 <- c(
+1.000,0.721,0.652,0.535,0.468,0.492,0.543,0.547,0.110,0.155,0.477,0.199,0.268,0.414,0.385,0.277,0.369,
+0.721,1.000,0.741,0.594,0.543,0.573,0.637,0.637,0.035,0.090,0.442,0.203,0.250,0.544,0.494,0.398,0.422,
+0.652,0.741,1.000,0.897,0.632,0.588,0.642,0.651,0.008,0.192,0.370,0.257,0.211,0.553,0.501,0.406,0.458,
+0.535,0.594,0.897,1.000,0.594,0.499,0.503,0.551,0.068,0.243,0.310,0.218,0.181,0.478,0.449,0.359,0.401,
+0.468,0.543,0.632,0.594,1.000,0.558,0.509,0.602,0.039,0.147,0.262,0.170,0.144,0.474,0.430,0.350,0.381,
+0.492,0.573,0.588,0.499,0.558,1.000,0.614,0.591,0.055,0.031,0.264,0.167,0.185,0.483,0.427,0.328,0.369,
+0.543,0.637,0.642,0.503,0.509,0.614,1.000,0.632,0.004,0.064,0.345,0.143,0.246,0.531,0.523,0.411,0.472,
+0.547,0.637,0.651,0.551,0.602,0.591,0.632,1.000,0.057,0.129,0.290,0.136,0.127,0.552,0.480,0.435,0.432,
+0.110,0.035,0.008,0.068,0.039,0.055,0.004,0.057,1.000,0.238,0.133,0.141,0.046,0.002,0.006,0.003,0.009,
+0.155,0.090,0.192,0.243,0.147,0.031,0.064,0.129,0.238,1.000,0.138,0.266,0.055,0.046,0.043,0.066,0.049,
+0.477,0.442,0.370,0.310,0.262,0.264,0.345,0.290,0.133,0.138,1.000,0.239,0.762,0.278,0.289,0.243,0.262,
+0.199,0.203,0.257,0.218,0.170,0.167,0.143,0.136,0.141,0.266,0.239,1.000,0.217,0.172,0.180,0.065,0.122,
+0.268,0.250,0.211,0.181,0.144,0.185,0.246,0.127,0.046,0.055,0.762,0.217,1.000,0.173,0.202,0.185,0.158,
+0.414,0.544,0.553,0.478,0.474,0.483,0.531,0.552,0.002,0.046,0.278,0.172,0.173,1.000,0.647,0.431,0.578,
+0.385,0.494,0.501,0.449,0.430,0.427,0.523,0.480,0.006,0.043,0.289,0.180,0.202,0.647,1.000,0.414,0.572,
+0.277,0.398,0.406,0.359,0.350,0.328,0.411,0.435,0.003,0.066,0.243,0.065,0.185,0.431,0.414,1.000,0.499,
+0.369,0.422,0.458,0.401,0.381,0.369,0.472,0.432,0.009,0.049,0.262,0.122,0.158,0.578,0.572,0.499,1.000)
> one <- array(one, dim=c(17,17))
>
> two <- c(
+1.00,0.75,0.81,0.71,0.74,0.70,0.73,0.75,NA,0.16,0.23,NA,0.53,0.66,NA,0.47,0.56,
+0.75,1.00,0.81,0.74,0.74,0.79,0.75,0.73,NA,0.21,0.22,NA,0.57,0.60,NA,0.38,0.58,
+0.81,0.81,1.00,0.78,0.82,0.80,0.83,0.81,NA,0.18,0.22,NA,0.53,0.71,NA,0.47,0.63,
+0.71,0.74,0.78,1.00,0.74,0.72,0.77,0.73,NA,0.18,0.29,NA,0.50,0.60,NA,0.38,0.60,
+0.74,0.74,0.82,0.74,1.00,0.77,0.82,0.81,NA,0.09,0.26,NA,0.54,0.70,NA,0.51,0.66,
+0.70,0.79,0.80,0.72,0.77,1.00,0.82,0.78,NA,0.15,0.22,NA,0.56,0.62,NA,0.39,0.59,
+0.73,0.75,0.83,0.77,0.82,0.82,1.00,0.87,NA,0.11,0.27,NA,0.52,0.65,NA,0.48,0.65,
+0.75,0.73,0.81,0.73,0.81,0.78,0.87,1.00,NA,0.11,0.26,NA,0.52,0.71,NA,0.47,0.69,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+0.16,0.21,0.18,0.18,0.09,0.15,0.11,0.11,NA,1.00,0.25,NA,0.27,0.15,NA,0.09,0.07,
+0.23,0.22,0.22,0.29,0.26,0.22,0.27,0.26,NA,0.25,1.00,NA,0.21,0.11,NA,0.10,0.18,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+0.53,0.57,0.53,0.50,0.54,0.56,0.52,0.52,NA,0.27,0.21,NA,1.00,0.50,NA,0.43,0.38,
+0.66,0.60,0.71,0.60,0.70,0.62,0.65,0.71,NA,0.15,0.11,NA,0.50,1.00,NA,0.62,0.68,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+0.47,0.38,0.47,0.38,0.51,0.39,0.48,0.47,NA,0.09,0.10,NA,0.43,0.62,NA,1.00,0.62,
+0.56,0.58,0.63,0.60,0.66,0.59,0.65,0.69,NA,0.07,0.18,NA,0.38,0.68,NA,0.62,1.00)
> two <- array(two, dim=c(17,17))
>
>
> three <- c(

2. +NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,1.00,0.83,0.75,NA,0.47,NA,NA,-0.19,0.09,NA,0.13,NA,NA,0.54,NA,NA,
+NA,0.83,1.00,0.77,NA,0.59,NA,NA,-0.10,0.02,NA,0.05,NA,NA,0.68,NA,NA,
+NA,0.75,0.77,1.00,NA,0.63,NA,NA,-0.08,0.02,NA,0.05,NA,NA,0.67,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,0.47,0.59,0.63,NA,1.00,NA,NA,-0.11,-0.08,NA,0.08,NA,NA,0.72,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,-0.19,-0.10,-0.08,NA,-0.11,NA,NA,1.00,-0.20,NA,0.54,NA,NA,-0.08,NA,NA,
+NA,0.09,0.02,0.02,NA,-0.08,NA,NA,-0.20,1.00,NA,-0.15,NA,NA,-0.01,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,0.13,0.05,0.05,NA,0.08,NA,NA,0.54,-0.15,NA,1.00,NA,NA,0.05,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,0.54,0.68,0.67,NA,0.72,NA,NA,-0.08,-0.01,NA,0.05,NA,NA,1.00,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA)
> three <- array(three, dim=c(17,17))
>
> four <- c(
+1.000,0.791,0.703,0.656,NA,NA,0.688,NA,NA,NA,NA,NA,NA,0.557,0.645,NA,0.631,
+0.791,1.000,0.682,0.649,NA,NA,0.664,NA,NA,NA,NA,NA,NA,0.507,0.611,NA,0.636,
+0.703,0.682,1.000,0.681,NA,NA,0.779,NA,NA,NA,NA,NA,NA,0.571,0.663,NA,0.662,
+0.656,0.649,0.681,1.000,NA,NA,0.712,NA,NA,NA,NA,NA,NA,0.466,0.531,NA,0.576,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+0.688,0.664,0.779,0.712,NA,NA,1.000,NA,NA,NA,NA,NA,NA,0.564,0.647,NA,0.640,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+0.557,0.507,0.571,0.466,NA,NA,0.564,NA,NA,NA,NA,NA,NA,1.000,0.774,NA,0.681,
+0.645,0.611,0.663,0.531,NA,NA,0.647,NA,NA,NA,NA,NA,NA,0.774,1.000,NA,0.725,
+NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,NA,
+0.631,0.636,0.662,0.576,NA,NA,0.640,NA,NA,NA,NA,NA,NA,0.681,0.725,NA,1.000)
> four <- array(four, dim=c(17,17))
>
> Pooled <- NULL
> ## Create data list from 4 studies
> Pooled$data <- list('1'=one,'2'=two,'3'=three,'4'=four)
> ## Sample size for each study
> Pooled$n <- c(586,535,660,589)
>
> ##############################################
> #### Run fixed-effects model: Stage 1 analysis
> #### to calculate pooled correlation cofficient
> #### FEM - fixed-effects meta-analysis
> ##############################################
> output1<-tssem1(Pooled$data, Pooled$n, method="FEM")
> 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 Std.Error z value Pr(>|z|)
S[1,2] 0.7596738 0.0099726 76.1759 < 2.2e-16 ***
S[1,3] 0.7396249 0.0105187 70.3153 < 2.2e-16 ***
S[1,4] 0.6522624 0.0130981 49.7983 < 2.2e-16 ***
S[1,5] 0.6288517 0.0166507 37.7673 < 2.2e-16 ***
S[1,6] 0.5792238 0.0173216 33.4394 < 2.2e-16 ***
S[1,7] 0.6631129 0.0133503 49.6703 < 2.2e-16 ***
S[1,8] 0.6704674 0.0148463 45.1606 < 2.2e-16 ***
S[1,9] -0.0356534 0.0370966 -0.9611 0.3365044
S[1,10] 0.1099366 0.0260465 4.2208 2.435e-05 ***
S[1,11] 0.3598790 0.0262168 13.7270 < 2.2e-16 ***
S[1,12] 0.1231815 0.0370748 3.3225 0.0008921 ***
S[1,13] 0.4021610 0.0250393 16.0612 < 2.2e-16 ***
S[1,14] 0.5572546 0.0164128 33.9525 < 2.2e-16 ***

3. S[1,15] 0.5848677 0.0165200 35.4036 < 2.2e-16 ***
S[1,16] 0.4100708 0.0235513 17.4118 < 2.2e-16 ***
S[1,17] 0.5354323 0.0170370 31.4276 < 2.2e-16 ***
S[2,3] 0.7721184 0.0083666 92.2862 < 2.2e-16 ***
S[2,4] 0.6903318 0.0108222 63.7882 < 2.2e-16 ***
S[2,5] 0.6367961 0.0162532 39.1797 < 2.2e-16 ***
S[2,6] 0.6070561 0.0144948 41.8809 < 2.2e-16 ***
S[2,7] 0.6813902 0.0124223 54.8522 < 2.2e-16 ***
S[2,8] 0.6702340 0.0147319 45.4955 < 2.2e-16 ***
S[2,9] -0.1338320 0.0298565 -4.4825 7.377e-06 ***
S[2,10] 0.1216304 0.0233116 5.2176 1.813e-07 ***
S[2,11] 0.3408086 0.0264163 12.9014 < 2.2e-16 ***
S[2,12] 0.1528247 0.0298155 5.1257 2.965e-07 ***
S[2,13] 0.4031650 0.0251995 15.9989 < 2.2e-16 ***
S[2,14] 0.5448688 0.0162829 33.4626 < 2.2e-16 ***
S[2,15] 0.5790563 0.0147687 39.2083 < 2.2e-16 ***
S[2,16] 0.4004751 0.0236881 16.9062 < 2.2e-16 ***
S[2,17] 0.5518286 0.0163850 33.6789 < 2.2e-16 ***
S[3,4] 0.7802832 0.0081367 95.8968 < 2.2e-16 ***
S[3,5] 0.7277032 0.0132172 55.0572 < 2.2e-16 ***
S[3,6] 0.6618164 0.0127940 51.7286 < 2.2e-16 ***
S[3,7] 0.7605582 0.0099209 76.6624 < 2.2e-16 ***
S[3,8] 0.7400926 0.0122200 60.5639 < 2.2e-16 ***
S[3,9] -0.0853962 0.0299259 -2.8536 0.0043229 **
S[3,10] 0.1117231 0.0231546 4.8251 1.399e-06 ***
S[3,11] 0.2831830 0.0269023 10.5264 < 2.2e-16 ***
S[3,12] 0.1247131 0.0300662 4.1480 3.355e-05 ***
S[3,13] 0.3570059 0.0257020 13.8902 < 2.2e-16 ***
S[3,14] 0.6255025 0.0141412 44.2326 < 2.2e-16 ***
S[3,15] 0.6562088 0.0127524 51.4576 < 2.2e-16 ***
S[3,16] 0.4650069 0.0218577 21.2743 < 2.2e-16 ***
S[3,17] 0.6000032 0.0150108 39.9716 < 2.2e-16 ***
S[4,5] 0.6735895 0.0146700 45.9162 < 2.2e-16 ***
S[4,6] 0.6217540 0.0138373 44.9332 < 2.2e-16 ***
S[4,7] 0.6861437 0.0121109 56.6551 < 2.2e-16 ***
S[4,8] 0.6617536 0.0144988 45.6419 < 2.2e-16 ***
S[4,9] -0.0351976 0.0297778 -1.1820 0.2372024
S[4,10] 0.1330020 0.0231279 5.7507 8.887e-09 ***
S[4,11] 0.3038593 0.0264550 11.4859 < 2.2e-16 ***
S[4,12] 0.1138995 0.0296195 3.8454 0.0001203 ***
S[4,13] 0.3490439 0.0256052 13.6318 < 2.2e-16 ***
S[4,14] 0.5405339 0.0160556 33.6664 < 2.2e-16 ***
S[4,15] 0.5868355 0.0145555 40.3172 < 2.2e-16 ***
S[4,16] 0.3872551 0.0235371 16.4530 < 2.2e-16 ***
S[4,17] 0.5538009 0.0159968 34.6196 < 2.2e-16 ***
S[5,6] 0.6768490 0.0153075 44.2167 < 2.2e-16 ***
S[5,7] 0.7070118 0.0140386 50.3620 < 2.2e-16 ***
S[5,8] 0.7309575 0.0132829 55.0300 < 2.2e-16 ***
S[5,9] -0.0657110 0.0375229 -1.7512 0.0799075 .
S[5,10] 0.0577106 0.0264345 2.1832 0.0290242 *
S[5,11] 0.2483611 0.0277571 8.9476 < 2.2e-16 ***
S[5,12] 0.0979823 0.0375869 2.6068 0.0091387 **
S[5,13] 0.3476066 0.0263939 13.1700 < 2.2e-16 ***
S[5,14] 0.6095146 0.0172221 35.3914 < 2.2e-16 ***
S[5,15] 0.6375966 0.0183285 34.7872 < 2.2e-16 ***
S[5,16] 0.4586990 0.0227898 20.1274 < 2.2e-16 ***
S[5,17] 0.5792505 0.0179797 32.2170 < 2.2e-16 ***
S[6,7] 0.7286591 0.0130239 55.9478 < 2.2e-16 ***
S[6,8] 0.6927498 0.0146391 47.3219 < 2.2e-16 ***
S[6,9] -0.0823181 0.0306221 -2.6882 0.0071840 **
S[6,10] 0.0262844 0.0236923 1.1094 0.2672555
S[6,11] 0.2080362 0.0284955 7.3007 2.864e-13 ***
S[6,12] 0.1199371 0.0305578 3.9249 8.675e-05 ***
S[6,13] 0.3699745 0.0262397 14.0998 < 2.2e-16 ***
S[6,14] 0.5719998 0.0175968 32.5060 < 2.2e-16 ***
S[6,15] 0.6416751 0.0152573 42.0569 < 2.2e-16 ***
S[6,16] 0.3759546 0.0246526 15.2501 < 2.2e-16 ***
S[6,17] 0.5304775 0.0187401 28.3071 < 2.2e-16 ***
S[7,8] 0.7828048 0.0109129 71.7323 < 2.2e-16 ***
S[7,9] -0.0823120 0.0365971 -2.2491 0.0245035 *
S[7,10] 0.0393762 0.0259847 1.5154 0.1296820
S[7,11] 0.2943974 0.0269887 10.9082 < 2.2e-16 ***
S[7,12] 0.0800677 0.0367991 2.1758 0.0295697 *
S[7,13] 0.3847628 0.0253411 15.1833 < 2.2e-16 ***

4. 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 ‘.’ 0.1 ‘ ’ 1
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 <- create.Fmatrix(c(rep(1,17), rep(0,4)))
>

5. > ## Prepare Smatrix
> ## Factor correlation matrix - 3x3 Latent variables
> Phi <- create.mxMatrix( c("0.3*corf2f1","0.3*corf3f1","0.3*corf4f1","0.3*corf3f2",
+ "0.3*corf4f2","0.3*corf4f3"), type="Stand", as.mxMatrix=FALSE )
>
> ## Error variances matrix - 9x9 error matrix
> Psi <- create.mxMatrix( paste("0.2*e", 1:17, sep=""),
+ type="Diag", as.mxMatrix=FALSE )
>
> ## Create Smatrix
> S1 <- bdiagMat(list(Psi, Phi))
> S1 <- as.mxMatrix(S1)
>
> ## Prepare Amatrix
> ## Factor loadings matrix
> Lambda <- create.mxMatrix(
+ c(".3*f1x1",".3*f1x2",".3*f1x3",rep(0,17),
+ ".3*f2x4",".3*f2x5",".3*f2x6",".3*f2x7",".3*f2x8", rep(0,17),
+ ".3*f3x9",".3*f3x10",".3*f3x11",".3*f3x12",".3*f3x13", rep(0,17),
+ ".3*f4x14",".3*f4x15",".3*f4x16",".3*f4x17"), type="Full",
+ ncol=4, nrow=17, as.mxMatrix=FALSE )
>
> ## Create asymetric matrix
> Zero1 <- matrix(0, nrow=17, ncol=17)
> Zero2 <- matrix(0, nrow=4, ncol=21)
> A1 <- rbind( cbind(Zero1, Lambda), Zero2 )
> A1 <- as.mxMatrix(A1)
>
> ###############################################
> #### Fixed-effects model: Stage 2 analysis
> #### to fit the model
> #### output1 - pooled correlation coefficient
> #### Amatrix - asymmetric matrix
> #### Smatrix - symmetric matrix
> #### Fmatrix - filtered matrix
> #### Likehood-based confidence intervals at 95%
> ###############################################
> output2<-tssem2(output1, Amatrix=A1, Smatrix=S1, Fmatrix=F1, intervals.type="LB")
> summary(output2)
Call:
wls(Cov = pooledS, asyCov = tssem1.obj$acovS, n = sum(tssem1.obj$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,
silent = silent, run = run)
95% confidence intervals: Likelihood-based statistic
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
f1x1 0.87565 NA 0.86097 0.89024 NA NA
f1x2 0.88742 NA 0.87566 0.89911 NA NA
f1x3 0.93858 NA 0.93002 0.94711 NA NA
f2x4 0.87274 NA 0.85941 0.88602 NA NA
f2x5 0.86548 NA 0.84762 0.88324 NA NA
f2x6 0.82937 NA 0.81159 0.84705 NA NA
f2x7 0.90482 NA 0.89267 0.91690 NA NA
f2x8 0.90222 NA 0.88792 0.91644 NA NA
f3x9 0.32494 NA 0.25673 0.39005 NA NA
f3x10 0.16750 NA 0.11630 0.21875 NA NA
f3x11 0.68010 NA 0.63519 0.72557 NA NA
f3x12 0.57470 NA 0.51424 0.63247 NA NA
f3x13 0.82647 NA 0.78021 0.87400 NA NA
f4x14 0.86434 NA 0.84736 0.88124 NA NA
f4x15 0.90130 NA 0.88605 0.91651 NA NA
f4x16 0.69961 NA 0.66450 0.73447 NA NA
f4x17 0.84685 NA 0.82804 0.86554 NA NA
corf2f1 0.97310 NA 0.96358 0.98268 NA NA
corf3f1 0.56667 NA 0.51622 0.61746 NA NA
corf3f2 0.55656 NA 0.50706 0.60650 NA NA
corf4f1 0.84880 NA 0.83032 0.86722 NA NA
corf4f2 0.87282 NA 0.85625 0.88930 NA NA
corf4f3 0.51141 NA 0.45819 0.56508 NA NA

6. Goodness-of-fit indices:
Value
Sample size 2370.0000
Chi-square of target model 781.7033
DF of target model 113.0000
p value of target model 0.0000
Number of constraints imposed on "Smatrix" 0.0000
DF manually adjusted 0.0000
Chi-square of independence model 25323.6306
DF of independence model 136.0000
RMSEA 0.0500
SRMR 0.1187
TLI 0.9680
CFI 0.9735
AIC 555.7033
BIC 96.3796

7. Correlation Matrix
1.000
0.721 1.000
0.652 0.741 1.000
0.535 0.594 0.897 1.000
0.468 0.543 0.632 0.594 1.000
0.492 0.573 0.588 0.499 0.558 1.000
0.543 0.637 0.642 0.503 0.509 0.614 1.000
0.547 0.637 0.651 0.551 0.602 0.591 0.632 1.000
0.110 0.035 0.008 0.068 0.039 0.055 0.004 0.057 1.000
0.155 0.090 0.192 0.243 0.147 0.031 0.064 0.129 0.238 1.000
0.477 0.442 0.370 0.310 0.262 0.264 0.345 0.290 0.133 0.138 1.000
0.199 0.203 0.257 0.218 0.170 0.167 0.143 0.136 0.141 0.266 0.239 1.000
0.268 0.250 0.211 0.181 0.144 0.185 0.246 0.127 0.046 0.055 0.762 0.217 1.000
0.414 0.544 0.553 0.478 0.474 0.483 0.531 0.552 0.002 0.046 0.278 0.172 0.173 1.000
0.385 0.494 0.501 0.449 0.430 0.427 0.523 0.480 0.006 0.043 0.289 0.180 0.202 0.647 1.000
0.277 0.398 0.406 0.359 0.350 0.328 0.411 0.435 0.003 0.066 0.243 0.065 0.185 0.431 0.414 1.000
0.369 0.422 0.458 0.401 0.381 0.369 0.472 0.432 0.009 0.049 0.262 0.122 0.158 0.578 0.572 0.499 1.000
1.000
0.750 1.000
0.810 0.810 1.000
0.710 0.740 0.780 1.000
0.740 0.740 0.820 0.740 1.000
0.700 0.790 0.800 0.720 0.770 1.000
0.730 0.750 0.830 0.770 0.820 0.820 1.000
0.750 0.730 0.810 0.730 0.810 0.780 0.870 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.160 0.210 0.180 0.180 0.090 0.150 0.114 0.110 0.000 1.000
0.230 0.220 0.220 0.290 0.260 0.220 0.270 0.260 0.000 0.250 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.530 0.570 0.530 0.500 0.540 0.560 0.520 0.520 0.000 0.270 0.210 0.000 1.000
0.660 0.600 0.710 0.600 0.700 0.620 0.650 0.710 0.000 0.150 0.110 0.000 0.500 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.470 0.380 0.470 0.380 0.510 0.390 0.480 0.470 0.000 0.090 0.100 0.000 0.430 0.620 0.000 1.000
0.560 0.580 0.630 0.600 0.660 0.590 0.650 0.690 0.000 0.070 0.180 0.000 0.380 0.680 0.000 0.620 1.000
1.000
0.000 1.000
0.000 0.830 1.000
0.000 0.750 0.770 1.000
0.000 0.000 0.000 0.000 1.000
0.000 0.470 0.590 0.630 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 -0.190 -0.100 -0.080 0.000 -0.110 0.000 0.000 1.000
0.000 0.090 0.020 0.020 0.000 -0.080 0.000 0.000 -0.200 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.130 0.050 0.050 0.000 0.080 0.000 0.000 0.540 -0.150 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.540 0.680 0.670 0.000 0.720 0.000 0.000 -0.080 -0.010 0.000 0.050 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
1.000
0.791 1.000
0.703 0.682 1.000
0.656 0.649 0.681 1.000
0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 1.000
0.688 0.664 0.779 0.712 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.557 0.507 0.571 0.466 0.000 0.000 0.564 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.645 0.611 0.663 0.531 0.000 0.000 0.647 0.000 0.000 0.000 0.000 0.000 0.000 0.774 1.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.000
0.631 0.636 0.662 0.576 0.000 0.000 0.640 0.000 0.000 0.000 0.000 0.000 0.000 0.681 0.725 0.000 1.000