We load the necessary packages as well as the data set for the
example. Because for this example we are using only complete data we
remove the the two studies with NA (i.e., Study 6 and Study
17).
Next, we create a list, which will be imputed in our other functions.
becker09_list <- df_to_corr(becker09,
variables = c('Cognitive_Performance',
'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic'),
ID = 'ID')There are currently three options for the variance-covariance matrix of the correlation matrix (i.e, simple, average, and weighted) for this example we selected the weighted option.
#olkin_siotani(becker09_list, becker09$N, type = 'simple')
#olkin_siotani(becker09_list, becker09$N, type = 'average')
olkin_siotani(becker09_list, becker09$N, type = 'weighted')
#> [[1]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0068964508 0.0034592598 -0.0024249951 -0.0007709388 0.0019806619
#> [2,] 0.0034592598 0.0066061710 -0.0022932962 -0.0002788858 0.0008637677
#> [3,] -0.0024249951 -0.0022932962 0.0053155444 0.0001634926 -0.0001362802
#> [4,] -0.0007709388 -0.0002788858 0.0001634926 0.0037574849 -0.0013337746
#> [5,] 0.0019806619 0.0008637677 -0.0001362802 -0.0013337746 0.0048166300
#> [6,] 0.0010242015 0.0018602041 -0.0005187913 -0.0013441468 0.0021616446
#> [,6]
#> [1,] 0.0010242015
#> [2,] 0.0018602041
#> [3,] -0.0005187913
#> [4,] -0.0013441468
#> [5,] 0.0021616446
#> [6,] 0.0048308442
#>
#> [[2]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.026467460 0.013276078 -0.0093067379 -0.0029587381 0.0076014592
#> [2,] 0.013276078 0.025353413 -0.0088012989 -0.0010703186 0.0033150004
#> [3,] -0.009306738 -0.008801299 0.0204001974 0.0006274581 -0.0005230214
#> [4,] -0.002958738 -0.001070319 0.0006274581 0.0144206177 -0.0051188104
#> [5,] 0.007601459 0.003315000 -0.0005230214 -0.0051188104 0.0184854450
#> [6,] 0.003930719 0.007139162 -0.0019910370 -0.0051586176 0.0082960414
#> [,6]
#> [1,] 0.003930719
#> [2,] 0.007139162
#> [3,] -0.001991037
#> [4,] -0.005158618
#> [5,] 0.008296041
#> [6,] 0.018539997
#>
#> [[3]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.069949715 0.035086777 -0.024596379 -0.007819522 0.020089571
#> [2,] 0.035086777 0.067005449 -0.023260576 -0.002828699 0.008761072
#> [3,] -0.024596379 -0.023260576 0.053914807 0.001658282 -0.001382271
#> [4,] -0.007819522 -0.002828699 0.001658282 0.038111633 -0.013528285
#> [5,] 0.020089571 0.008761072 -0.001382271 -0.013528285 0.048854390
#> [6,] 0.010388330 0.018867784 -0.005262026 -0.013633489 0.021925252
#> [,6]
#> [1,] 0.010388330
#> [2,] 0.018867784
#> [3,] -0.005262026
#> [4,] -0.013633489
#> [5,] 0.021925252
#> [6,] 0.048998563
#>
#> [[4]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.009792960 0.0049121488 -0.0034434930 -0.0010947331 0.0028125399
#> [2,] 0.004912149 0.0093807628 -0.0032564806 -0.0003960179 0.0012265501
#> [3,] -0.003443493 -0.0032564806 0.0075480730 0.0002321595 -0.0001935179
#> [4,] -0.001094733 -0.0003960179 0.0002321595 0.0053356286 -0.0018939599
#> [5,] 0.002812540 0.0012265501 -0.0001935179 -0.0018939599 0.0068396147
#> [6,] 0.001454366 0.0026414898 -0.0007366837 -0.0019086885 0.0030695353
#> [,6]
#> [1,] 0.0014543662
#> [2,] 0.0026414898
#> [3,] -0.0007366837
#> [4,] -0.0019086885
#> [5,] 0.0030695353
#> [6,] 0.0068597988
#>
#> [[5]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.019201883 0.0096316644 -0.0067519471 -0.0021465355 0.0055147841
#> [2,] 0.009631664 0.0183936526 -0.0063852560 -0.0007765056 0.0024050003
#> [3,] -0.006751947 -0.0063852560 0.0148001432 0.0004552147 -0.0003794469
#> [4,] -0.002146536 -0.0007765056 0.0004552147 0.0104620168 -0.0037136468
#> [5,] 0.005514784 0.0024050003 -0.0003794469 -0.0037136468 0.0134110091
#> [6,] 0.002851698 0.0051793917 -0.0014444778 -0.0037425265 0.0060186967
#> [,6]
#> [1,] 0.002851698
#> [2,] 0.005179392
#> [3,] -0.001444478
#> [4,] -0.003742526
#> [5,] 0.006018697
#> [6,] 0.013450586
#>
#> [[6]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0076507501 0.0038376163 -0.0026902289 -0.0008552602 0.0021972968
#> [2,] 0.0038376163 0.0073287209 -0.0025441255 -0.0003093890 0.0009582423
#> [3,] -0.0026902289 -0.0025441255 0.0058969321 0.0001813746 -0.0001511859
#> [4,] -0.0008552602 -0.0003093890 0.0001813746 0.0041684598 -0.0014796561
#> [5,] 0.0021972968 0.0009582423 -0.0001511859 -0.0014796561 0.0053434489
#> [6,] 0.0011362236 0.0020636639 -0.0005755341 -0.0014911629 0.0023980745
#> [,6]
#> [1,] 0.0011362236
#> [2,] 0.0020636639
#> [3,] -0.0005755341
#> [4,] -0.0014911629
#> [5,] 0.0023980745
#> [6,] 0.0053592178
#>
#> [[7]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.013989943 0.0070173555 -0.0049192757 -0.0015639044 0.0040179142
#> [2,] 0.007017355 0.0134010897 -0.0046521151 -0.0005657398 0.0017522145
#> [3,] -0.004919276 -0.0046521151 0.0107829615 0.0003316564 -0.0002764542
#> [4,] -0.001563904 -0.0005657398 0.0003316564 0.0076223265 -0.0027056569
#> [5,] 0.004017914 0.0017522145 -0.0002764542 -0.0027056569 0.0097708781
#> [6,] 0.002077666 0.0037735568 -0.0010524053 -0.0027266979 0.0043850504
#> [,6]
#> [1,] 0.002077666
#> [2,] 0.003773557
#> [3,] -0.001052405
#> [4,] -0.002726698
#> [5,] 0.004385050
#> [6,] 0.009799713
#>
#> [[8]]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.032643200 0.016373829 -0.0114783100 -0.003649110 0.0093751330
#> [2,] 0.016373829 0.031269209 -0.0108549353 -0.001320060 0.0040885004
#> [3,] -0.011478310 -0.010854935 0.0251602435 0.000773865 -0.0006450598
#> [4,] -0.003649110 -0.001320060 0.0007738650 0.017785429 -0.0063131995
#> [5,] 0.009375133 0.004088500 -0.0006450598 -0.006313200 0.0227987155
#> [6,] 0.004847887 0.008804966 -0.0024556123 -0.006362295 0.0102317844
#> [,6]
#> [1,] 0.004847887
#> [2,] 0.008804966
#> [3,] -0.002455612
#> [4,] -0.006362295
#> [5,] 0.010231784
#> [6,] 0.022865996The function below creates and organize elements that are then fitted
internally into the metafor package. Below we fitted fixed
and random-effects models and extracted some more detail information
from objects that are not directly output by the functions. First, we
see results under fixed-effect models.
mars(data = becker09, studyID = 'ID',
effectID = 'numID', sample_size = 'N',
effectsize_type = 'cor',
estimation_method = 'FE',
varcov_type = 'weighted',
variable_names = c('Cognitive_Performance', 'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic')) |>
summary()Now we fit a random-effects model and extract some objects from this output.
model_out_random <- mars(data = becker09, studyID = 'ID',
effectID = 'numID', sample_size = 'N',
effectsize_type = 'cor',
varcov_type = 'weighted',
variable_names = c('Cognitive_Performance', 'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic'))
summary(model_out_random)
#> Results generated with MARS:v 0.2.2
#> Wednesday, March 26, 2025
#>
#> Model Type:
#> multivariate
#>
#> Estimation Method:
#> Restricted Maximum Likelihood
#>
#> Model Formula:
#> NULL
#>
#> Data Summary:
#> Number of Effect Sizes: 48
#> Number of Fixed Effects: 6
#> Number of Random Effects: 6
#>
#> Random Components:
#> ri_1 ri_2 ri_3 ri_4 ri_5 ri_6
#> ri_1 0.13206 0.07632 -0.03147 0.003063 -0.018160 0.0022334
#> ri_2 0.99881 0.04421 -0.01700 0.001536 -0.009868 0.0008382
#> ri_3 -0.42101 -0.39314 0.04231 -0.007312 0.009631 -0.0122626
#> ri_4 0.23221 0.20120 -0.97940 0.001318 -0.001498 0.0022789
#> ri_5 -0.62535 -0.58730 0.58594 -0.516447 0.006385 -0.0024652
#> ri_6 0.09674 0.06275 -0.93846 0.988288 -0.485633 0.0040356
#>
#> Fixed Effects Estimates:
#> attribute estimate SE z_test p_value lower upper
#> ri_1 -0.09772 0.13778 -0.7093 4.782e-01 -0.3678 0.172324
#> ri_2 -0.17554 0.08620 -2.0363 4.172e-02 -0.3445 -0.006584
#> ri_3 0.31868 0.08407 3.7906 1.503e-04 0.1539 0.483463
#> ri_4 0.52719 0.03335 15.8079 2.747e-56 0.4618 0.592552
#> ri_5 -0.41755 0.04590 -9.0963 9.348e-20 -0.5075 -0.327579
#> ri_6 -0.40070 0.04182 -9.5822 9.504e-22 -0.4827 -0.318736
#>
#> Model Fit Statistics:
#> logLik Dev AIC BIC AICc
#> 18.63 -37.25 16.75 63.67 29.48
#>
#> Q Error: 230.642 (42), p < 0.0001
#>
#> I2 (General):
#> names values
#> ri_1 94.53
#> ri_2 85.26
#> ri_3 84.70
#> ri_4 14.70
#> ri_5 45.52
#> ri_6 34.56
#>
#> I2 (Jackson):
#> names values
#> ri_1 90.98
#> ri_2 77.93
#> ri_3 81.33
#> ri_4 16.13
#> ri_5 43.25
#> ri_6 31.42
#>
#> I2 (Between): 83.39602Now, we are ready to input the average correlation matrix and its variance covariance matrix and our own function to appropriate estimate SE via the multivariate delta method.
model <- "## Regression paths
Performance ~ Cognitive + Somatic + Selfconfidence
Selfconfidence ~ Cognitive + Somatic
"
mars(data = becker09, studyID = 'ID',
effectID = 'numID', sample_size = 'N',
effectsize_type = 'cor',
varcov_type = 'weighted',
variable_names = c('Cognitive_Performance', 'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic')) |>
path_model(model = model) |>
summary()
#> Results generated with MARS:v 0.2.2
#> Wednesday, March 26, 2025
#>
#> Model Type:
#> multivariate
#>
#> Average Correlation Matrix:
#> Performance Cognitive Somatic Selfconfidence
#> Performance 1.00000000 -0.09772148 -0.1755405 0.3186829
#> Cognitive -0.09772148 1.00000000 0.5271874 -0.4175481
#> Somatic -0.17554051 0.52718744 1.0000000 -0.4006950
#> Selfconfidence 0.31868294 -0.41754809 -0.4006950 1.0000000
#>
#>
#> Model Fitted:
#> ## Regression paths
#> Performance ~ Cognitive + Somatic + Selfconfidence
#> Selfconfidence ~ Cognitive + Somatic
#>
#>
#> Fixed Effects:
#> predictor outcome estimate
#> Cognitive -> Performance Cognitive Performance 0.08319698
#> Somatic -> Performance Somatic Performance -0.09266449
#> Selfconfidence -> Performance Selfconfidence Performance 0.31629148
#> Cognitive -> Selfconfidence Cognitive Selfconfidence -0.28571432
#> Somatic -> Selfconfidence Somatic Selfconfidence -0.25007001
#> standard_errors test_statistic p_value
#> Cognitive -> Performance 0.15425511 0.5393466 5.896477e-01
#> Somatic -> Performance 0.06354512 -1.4582471 1.447725e-01
#> Selfconfidence -> Performance 0.10216822 3.0957913 1.962884e-03
#> Cognitive -> Selfconfidence 0.03848494 -7.4240552 1.135878e-13
#> Somatic -> Selfconfidence 0.05226454 -4.7846974 1.712452e-06
#>
#>
#> Fit Statistics:
#> Type Value
#> 1 Model Chi-Square 14.23 (2), 8e-04
#> 2 Null Model Chi-Square 642.23 (6)
#> 3 CFI 0.981
#> 4 TLI 0.942
#> 5 RMSEA 0.103 [0.048, 0.166]
#> 6 SRMR 0.232We now subset the data to obtain results only for the studies that reported on Team sports.
mars(data = becker09_T, studyID = 'ID',
effectID = 'numID', sample_size = 'N',
effectsize_type = 'cor',
varcov_type = 'weighted',
variable_names = c('Cognitive_Performance', 'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic')) |>
summary()
#> Results generated with MARS:v 0.2.2
#> Wednesday, March 26, 2025
#>
#> Model Type:
#> multivariate
#>
#> Estimation Method:
#> Restricted Maximum Likelihood
#>
#> Model Formula:
#> NULL
#>
#> Data Summary:
#> Number of Effect Sizes: 18
#> Number of Fixed Effects: 6
#> Number of Random Effects: 6
#>
#> Random Components:
#> ri_1 ri_2 ri_3 ri_4 ri_5 ri_6
#> ri_1 0.1130 0.07312 0.0092197 0.0012143 -0.0604203 -0.015517
#> ri_2 0.9841 0.04884 0.0003625 -0.0003564 -0.0389002 -0.004652
#> ri_3 0.1885 0.01127 0.0211624 0.0042598 -0.0056167 -0.020890
#> ri_4 0.1231 -0.05496 0.9978056 0.0008612 -0.0007894 -0.004167
#> ri_5 -0.9996 -0.97903 -0.2147559 -0.1496176 0.0323231 0.008956
#> ri_6 -0.3185 -0.14526 -0.9909683 -0.9799149 0.3437839 0.020999
#>
#> Fixed Effects Estimates:
#> attribute estimate SE z_test p_value lower upper
#> ri_1 -0.1245 0.2048 -0.608 5.432e-01 -0.52589 0.27688
#> ri_2 -0.1853 0.1425 -1.300 1.936e-01 -0.46464 0.09408
#> ri_3 0.2329 0.1043 2.232 2.563e-02 0.02837 0.43740
#> ri_4 0.5825 0.0455 12.803 1.581e-37 0.49335 0.67171
#> ri_5 -0.3928 0.1160 -3.385 7.123e-04 -0.62024 -0.16535
#> ri_6 -0.3534 0.1015 -3.482 4.969e-04 -0.55223 -0.15448
#>
#> Model Fit Statistics:
#> logLik Dev AIC BIC AICc
#> 11.04 -22.09 31.91 45 171.9
#>
#> Q Error: 50.049 (12), p < 0.0001
#>
#> I2 (General):
#> names values
#> ri_1 94.43
#> ri_2 88.00
#> ri_3 76.06
#> ri_4 11.45
#> ri_5 82.91
#> ri_6 75.92
#>
#> I2 (Jackson):
#> names values
#> ri_1 90.45
#> ri_2 80.82
#> ri_3 66.53
#> ri_4 14.25
#> ri_5 80.55
#> ri_6 69.67
#>
#> I2 (Between): 85.57973
# random_model2 <- fit_model(data = input_metafor2, effect_size = 'yi',
# var_cor = 'V', moderators = ~ -1 + factor(outcome),
# random_params = ~ factor(outcome) | factor(study))model <- "## Regression paths
Performance ~ Cognitive + Somatic + Selfconfidence
Selfconfidence ~ Cognitive + Somatic
"
mars(data = becker09_T, studyID = 'ID',
effectID = 'numID', sample_size = 'N',
effectsize_type = 'cor',
varcov_type = 'weighted',
variable_names = c('Cognitive_Performance', 'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic')) |>
path_model(model = model) |>
summary()
#> Results generated with MARS:v 0.2.2
#> Wednesday, March 26, 2025
#>
#> Model Type:
#> multivariate
#>
#> Average Correlation Matrix:
#> Performance Cognitive Somatic Selfconfidence
#> Performance 1.0000000 -0.1245064 -0.1852846 0.2328837
#> Cognitive -0.1245064 1.0000000 0.5825298 -0.3927941
#> Somatic -0.1852846 0.5825298 1.0000000 -0.3533528
#> Selfconfidence 0.2328837 -0.3927941 -0.3533528 1.0000000
#>
#>
#> Model Fitted:
#> ## Regression paths
#> Performance ~ Cognitive + Somatic + Selfconfidence
#> Selfconfidence ~ Cognitive + Somatic
#>
#>
#> Fixed Effects:
#> predictor outcome estimate
#> Cognitive -> Performance Cognitive Performance 0.0309183
#> Somatic -> Performance Somatic Performance -0.1333659
#> Selfconfidence -> Performance Selfconfidence Performance 0.1979030
#> Cognitive -> Selfconfidence Cognitive Selfconfidence -0.2829834
#> Somatic -> Selfconfidence Somatic Selfconfidence -0.1885065
#> standard_errors test_statistic p_value
#> Cognitive -> Performance 0.25963865 0.1190821 9.052103e-01
#> Somatic -> Performance 0.08357876 -1.5956910 1.105578e-01
#> Selfconfidence -> Performance 0.16482003 1.2007217 2.298592e-01
#> Cognitive -> Selfconfidence 0.06464079 -4.3777839 1.198921e-05
#> Somatic -> Selfconfidence 0.12485886 -1.5097568 1.311055e-01
#>
#>
#> Fit Statistics:
#> Type Value
#> 1 Model Chi-Square 3.541 (2), 0.1703
#> 2 Null Model Chi-Square 320.78 (6)
#> 3 CFI 0.995
#> 4 TLI 0.985
#> 5 RMSEA 0.056 [NA, 0.164]
#> 6 SRMR 0.205Similarly, we now subset the data to obtain results only for the studies that reported on Individual sports.
mars(data = becker09_I, studyID = 'ID',
effectID = 'numID', sample_size = 'N',
effectsize_type = 'cor',
varcov_type = 'weighted',
variable_names = c('Cognitive_Performance', 'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic')) |>
summary()
#> Results generated with MARS:v 0.2.2
#> Wednesday, March 26, 2025
#>
#> Model Type:
#> multivariate
#>
#> Estimation Method:
#> Restricted Maximum Likelihood
#>
#> Model Formula:
#> NULL
#>
#> Data Summary:
#> Number of Effect Sizes: 30
#> Number of Fixed Effects: 6
#> Number of Random Effects: 6
#>
#> Random Components:
#> ri_1 ri_2 ri_3 ri_4 ri_5 ri_6
#> ri_1 0.1947 0.07610 -0.06015 0.0019425 0.013600 0.020942
#> ri_2 0.8003 0.04644 -0.02143 0.0005690 0.004873 0.002169
#> ri_3 -0.5329 -0.38883 0.06542 -0.0073427 0.024498 0.005809
#> ri_4 0.1399 0.08389 -0.91207 0.0009907 -0.004007 -0.001602
#> ri_5 0.2253 0.16531 0.70019 -0.9306298 0.018711 0.009663
#> ri_6 0.5285 0.11209 0.25292 -0.5666477 0.786733 0.008063
#>
#> Fixed Effects Estimates:
#> attribute estimate SE z_test p_value lower upper
#> ri_1 -0.08366 0.20962 -0.3991 6.898e-01 -0.49451 0.32719
#> ri_2 -0.18289 0.11427 -1.6005 1.095e-01 -0.40686 0.04108
#> ri_3 0.33753 0.12615 2.6756 7.460e-03 0.09028 0.58479
#> ri_4 0.49047 0.04562 10.7501 5.922e-27 0.40105 0.57989
#> ri_5 -0.46567 0.07947 -5.8599 4.632e-09 -0.62143 -0.30992
#> ri_6 -0.49761 0.06086 -8.1765 2.921e-16 -0.61689 -0.37833
#>
#> Model Fit Statistics:
#> logLik Dev AIC BIC AICc
#> 11.39 -22.79 31.21 63.02 59.21
#>
#> Q Error: 190.914 (24), p < 0.0001
#>
#> I2 (General):
#> names values
#> ri_1 95.77
#> ri_2 84.36
#> ri_3 88.37
#> ri_4 10.32
#> ri_5 68.49
#> ri_6 48.37
#>
#> I2 (Jackson):
#> names values
#> ri_1 93.28
#> ri_2 78.52
#> ri_3 88.30
#> ri_4 10.40
#> ri_5 65.30
#> ri_6 49.12
#>
#> I2 (Between): 86.61981
# random_model3 <- fit_model(data = input_metafor3, effect_size = 'yi',
# var_cor = 'V', moderators = ~ -1 + factor(outcome),
# random_params = ~ factor(outcome) | factor(study))model <- "## Regression paths
Performance ~ Cognitive + Somatic + Selfconfidence
Selfconfidence ~ Cognitive + Somatic
"
mars(data = becker09_I, studyID = 'ID',
effectID = 'numID', sample_size = 'N',
effectsize_type = 'cor',
varcov_type = 'weighted',
variable_names = c('Cognitive_Performance', 'Somatic_Performance',
'Selfconfidence_Performance',
'Somatic_Cognitive',
'Selfconfidence_Cognitive',
'Selfconfidence_Somatic')) |>
path_model(model = model) |>
summary()
#> Results generated with MARS:v 0.2.2
#> Wednesday, March 26, 2025
#>
#> Model Type:
#> multivariate
#>
#> Average Correlation Matrix:
#> Performance Cognitive Somatic Selfconfidence
#> Performance 1.00000000 -0.08366225 -0.1828908 0.3375302
#> Cognitive -0.08366225 1.00000000 0.4904679 -0.4656716
#> Somatic -0.18289084 0.49046789 1.0000000 -0.4976085
#> Selfconfidence 0.33753017 -0.46567157 -0.4976085 1.0000000
#>
#>
#> Model Fitted:
#> ## Regression paths
#> Performance ~ Cognitive + Somatic + Selfconfidence
#> Selfconfidence ~ Cognitive + Somatic
#>
#>
#> Fixed Effects:
#> predictor outcome estimate
#> Cognitive -> Performance Cognitive Performance 0.11330325
#> Somatic -> Performance Somatic Performance -0.05881252
#> Selfconfidence -> Performance Selfconfidence Performance 0.36102667
#> Cognitive -> Selfconfidence Cognitive Selfconfidence -0.29180740
#> Somatic -> Selfconfidence Somatic Selfconfidence -0.35448633
#> standard_errors test_statistic p_value
#> Cognitive -> Performance 0.23313037 0.4860081 6.269614e-01
#> Somatic -> Performance 0.13568155 -0.4334599 6.646807e-01
#> Selfconfidence -> Performance 0.14686285 2.4582573 1.396131e-02
#> Cognitive -> Selfconfidence 0.06212853 -4.6968345 2.642244e-06
#> Somatic -> Selfconfidence 0.08749797 -4.0513664 5.091940e-05
#>
#>
#> Fit Statistics:
#> Type Value
#> 1 Model Chi-Square 19.292 (2), 1e-04
#> 2 Null Model Chi-Square 427.836 (6)
#> 3 CFI 0.959
#> 4 TLI 0.877
#> 5 RMSEA 0.164 [0.09, 0.247]
#> 6 SRMR 0.27Here we compute the synthetic partial correlation from the average correlation matrix.
Here we work with partial correlation for each study and then synthesize that information.
#---------------------------------------------------------------------
# Create a data set with 8 complete studies
#---------------------------------------------------------------------
R <- becker09_list
R$"6" <- NULL
R$"17" <- NULL
n <- becker09$N[c(-3, -5)]
#------------------------------------------------------------------
# first replace NA by zeros
RR <- R # redifine list
PR <- lapply(RR, cor2pcor)
pr <- unlist(lapply(PR, '[[', 4))
var_pr <- (1-pr^2)^2 / (n - 3 -1)
rma.uni(pr, var_pr)