CON & SE

|con_se <- read.csv("con_se.csv")

library("metafor")|

|## Loading required package: Matrix|

|## Loading 'metafor' package (version 2.4-0). For an overview 
## and introduction to the package please type: help(metafor).|

|library("metaSEM")|

|## Loading required package: OpenMx|

|## 
## Attaching package: 'OpenMx'|

|## The following objects are masked from 'package:Matrix':
## 
##     %&%, expm|

|## "SLSQP" is set as the default optimizer in OpenMx.|

|## mxOption(NULL, "Gradient algorithm") is set at "central".|

|## mxOption(NULL, "Optimality tolerance") is set at "6.3e-14".|

|## mxOption(NULL, "Gradient iterations") is set at "2".|


      Moderator analysis

|con_se.mod.fiml <- meta3X(y=y.c, v=v.c, cluster=sample_nr, 
                      x2 = cbind(year, interval.months, idv, class, 
                                 se_academic, se_subject, se_performance,
                                 pers_self, 
                                 pers_retr, pers_prosp), 
                      data=con_se, model.name = "FIML model",
                              intervals.type="z")|

|## Error in running the mxModel:
## <simpleError: The job for model 'FIML model' exited abnormally with the error message: fit is not finite (The continuous part of the model implied covariance (loc2) is not positive definite in data 'FIML model.data' row 6. Detail:
## covariance =  matrix(c(    # 10x10
##  1.81039716046534, 0.314, 17.051, 0.141, 0.342, 0.01, 0.102, -0.089, 0.411, 0.189
## , 0.314, 8.17, -5.33, 0.11, 0.21, 0.39, 0.14, 0.09, 0.04, 0.14
## , 17.051, -5.33, 193.78, 0.18, 2.23, -0.62, 0.04, -2.33, 3.89, 1.34
## , 0.141, 0.11, 0.18, 0.13, 0.09, 0.07, 0.2, 0.09, 0.2, 0.2
## , 0.342, 0.21, 2.23, 0.09, 0.36, -0.02, 0.09, 0.06, 0.14, 0.09
## , 0.01, 0.39, -0.62, 0.07, -0.02, 0.25, -0.04, 0.12, 0.01, 0.01
## , 0.102, 0.14, 0.04, 0.2, 0.09, -0.04, 0.15, 0.2, 0.12, 0.08
## , -0.089, 0.09, -2.33, 0.09, 0.06, 0.12, 0.2, 0.17, 0.04, 0.11
## , 0.411, 0.04, 3.89, 0.2, 0.14, 0.01, 0.12, 0.04, 0.24, -0.04
## , 0.189, 0.14, 1.34, 0.2, 0.09, 0.01, 0.08, 0.11, -0.04, 0.13), byrow=TRUE, nrow=10, ncol=10)
## )>|

|con_se.mod.fiml <- meta3X(y=y.c, v=v.c, cluster=sample_nr, 
                      x2 = c(year, interval.months, idv, class, 
                                 se_academic, se_subject, se_performance,
                                 pers_self, 
                                 pers_retr, pers_prosp), 
                      data=con_se, model.name = "FIML model",
                              intervals.type="z")

summary(rerun(con_se.mod.fiml))|

|## Running FIML model with 7 parameters|

|## 
## Beginning initial fit attempt|

|## Running FIML model with 7 parameters|

|## 
##  Lowest minimum so far:  5985.06351661603|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|##  Not all eigenvalues of the Hessian are positive: 51759023129.2349, 19316432.7768248, 4.95587093264445, 0.0546468696462735, 0.00230661199939619, 3.05880839676697e-09, -0.220238356664249|

|## 
## Beginning fit attempt 1 of at maximum 10 extra tries|

|## Running FIML model with 7 parameters|

|## 
##  Lowest minimum so far:  5869.99881771891|

|## 
## Solution found|

|## 
##  Solution found!  Final fit=5869.9988 (started at 10358.67)  (2 attempt(s): 2 valid, 0 errors)|

|## 
## Call:
## meta3X(y = y.c, v = v.c, cluster = sample_nr, x2 = c(year, interval.months, 
##     idv, class, se_academic, se_subject, se_performance, pers_self, 
##     pers_retr, pers_prosp), data = con_se, intervals.type = "z", 
##     model.name = "FIML model")
## 
## 95% confidence intervals: z statistic approximation (robust=FALSE)
## Coefficients:
##              Estimate   Std.Error      lbound      ubound z value Pr(>|z|)
## Intercept  4.2169e-01  6.0243e+01 -1.1765e+02  1.1850e+02   7e-03   0.9944
## SlopeX2_1 -5.7983e-08  3.2281e+05 -6.3270e+05  6.3270e+05   0e+00   1.0000
## Tau2_2     3.0460e-03  6.2811e+03 -1.2311e+04  1.2311e+04   0e+00   1.0000
## Tau2_3     2.0328e-02  2.9129e+02 -5.7089e+02  5.7093e+02   1e-04   0.9999
## 
## Explained variances (R2):
##                          Level 2 Level 3
## Tau2 (no predictor)    3.046e-03  0.0203
## Tau2 (with predictors) 3.046e-03  0.0203
## R2                     1.147e-07  0.0000
## 
## Number of studies (or clusters): 19
## Number of observed statistics: 885
## Number of estimated parameters: 7
## Degrees of freedom: 878
## -2 log likelihood: 5869.999 
## OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
## Other values may indicate problems.)|


  Meta-Regression II: alternative using substitution of median for
  missing moderator values

|# replace missing values in class with median(class)
con_se$class1 <- con_se$class
con_se$class1 <- replmiss(con_se$class1, median(con_se$class1, na.rm = T)) 

# replace missing values in interval with median(interval)
con_se$interval.months1 <- con_se$interval.months
con_se$interval.months1 <- replmiss(con_se$interval.months1, median(con_se$interval.months1, na.rm = T))

# replace missing values in idv
con_se$idv1 <- con_se$idv
con_se$idv1 <- replmiss(con_se$idv1, median(con_se$idv1, na.rm = T)) |

|con_se.mod.subst <- meta3(y=y.c, v=v.c, cluster=sample_nr, 
                      x = cbind(year, interval.months1, idv1, class1, 
                                 se_academic, se_subject, se_performance,
                                 pers_self, 
                                 pers_retr, pers_prosp), 
                      data=con_se, model.name = "FIML model",
                              intervals.type="z")
summary(rerun(rerun(con_se.mod.subst)))|

|## Running FIML model with 13 parameters|

|## 
## Beginning initial fit attempt|

|## Running FIML model with 13 parameters|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|##  Not all eigenvalues of the Hessian are positive: 358619240720.277, 24496071346.3601, 111720578.114342, 480267.338462971, 5899.03975016962, 1212.48325228369, 747.962927881905, 373.565455786753, 360.046714406672, 148.249653291949, 10.2479938872039, -67.6077827467656, -174.742888289843|

|## 
## Beginning fit attempt 1 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
##  Lowest minimum so far:  -86.1755947455597|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 2 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
##  Lowest minimum so far:  -86.1755947455599|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 3 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
##  Lowest minimum so far:  -86.17559474556|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 4 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
##  Fit attempt worse than current best:  3253042.84714927 vs -86.17559474556|

|## 
## Beginning fit attempt 5 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 6 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 7 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
##  Fit attempt worse than current best:  4997581.79361511 vs -86.17559474556|

|## 
## Beginning fit attempt 8 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
## Solution found|

|## 
##  Solution found!  Final fit=-86.175595 (started at 40903961)  (9 attempt(s): 9 valid, 0 errors)|

|## Running FIML model with 13 parameters|

|## 
## Beginning initial fit attempt|

|## Running FIML model with 13 parameters|

|## 
##  Lowest minimum so far:  -86.1755947455597|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 1 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
##  Lowest minimum so far:  -86.1755947455599|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 2 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 3 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 4 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|##  OpenMx status code 6 not in list of acceptable status codes, (0,1)|

|## 
## Beginning fit attempt 5 of at maximum 10 extra tries|

|## Running FIML model with 13 parameters|

|## 
## Solution found|

|## 
##  Solution found!  Final fit=-86.175595 (started at -86.175595)  (6 attempt(s): 6 valid, 0 errors)|

|## 
## Call:
## meta3(y = y.c, v = v.c, cluster = sample_nr, x = cbind(year, 
##     interval.months1, idv1, class1, se_academic, se_subject, 
##     se_performance, pers_self, pers_retr, pers_prosp), data = con_se, 
##     intervals.type = "z", model.name = "FIML model")
## 
## 95% confidence intervals: z statistic approximation (robust=FALSE)
## Coefficients:
##              Estimate   Std.Error      lbound      ubound z value Pr(>|z|)   
## Intercept  8.7600e+00  1.8218e+01 -2.6946e+01  4.4467e+01  0.4808 0.630625   
## Slope_1   -3.9181e-03  9.1422e-03 -2.1836e-02  1.4000e-02 -0.4286 0.668231   
## Slope_2   -4.7943e-03  2.3034e-03 -9.3089e-03 -2.7962e-04 -2.0814 0.037401 * 
## Slope_3   -5.6291e-02  1.8162e-01 -4.1225e-01  2.9967e-01 -0.3099 0.756604   
## Slope_4   -5.3043e-02  1.6777e-02 -8.5926e-02 -2.0160e-02 -3.1616 0.001569 **
## Slope_5    9.6157e-03  7.5531e-02 -1.3842e-01  1.5765e-01  0.1273 0.898697   
## Slope_6   -1.2612e-01  7.3864e-02 -2.7090e-01  1.8646e-02 -1.7075 0.087725 . 
## Slope_7   -1.7167e-01  9.2417e-02 -3.5280e-01  9.4673e-03 -1.8575 0.063237 . 
## Slope_8    3.7527e-01  1.5140e-01  7.8546e-02  6.7200e-01  2.4788 0.013183 * 
## Slope_9   -7.1314e-02  4.6549e-02 -1.6255e-01  1.9921e-02 -1.5320 0.125521   
## Slope_10  -8.1544e-02  4.1927e-02 -1.6372e-01  6.3125e-04 -1.9449 0.051786 . 
## Tau2_2     3.2940e-03  1.6166e-03  1.2557e-04  6.4624e-03  2.0376 0.041586 * 
## Tau2_3     1.5797e-03  2.6992e-03 -3.7107e-03  6.8702e-03  0.5852 0.558380   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Q statistic on the homogeneity of effect sizes: 501.8658
## Degrees of freedom of the Q statistic: 44
## P value of the Q statistic: 0
## 
## Explained variances (R2):
##                          Level 2 Level 3
## Tau2 (no predictor)    0.0053749  0.0116
## Tau2 (with predictors) 0.0032940  0.0016
## R2                     0.3871531  0.8643
## 
## Number of studies (or clusters): 19
## Number of observed statistics: 45
## Number of estimated parameters: 13
## Degrees of freedom: 32
## -2 log likelihood: -86.17559 
## OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
## Other values may indicate problems.)|

|rma.mv(y.c, v.c, 
        random = ~ 1 | sample_nr/effect_nr, 
        mods=~ year + interval.months1 + idv1 + class1 +                        
                        se + pers_rater + pers_retro, 
        data= con_se)|

|## 
## Multivariate Meta-Analysis Model (k = 45; method: REML)
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed               factor 
## sigma^2.1  0.0073  0.0857     19     no            sample_nr 
## sigma^2.2  0.0037  0.0605     45     no  sample_nr/effect_nr 
## 
## Test for Residual Heterogeneity:
## QE(df = 34) = 153.7273, p-val < .0001
## 
## Test of Moderators (coefficients 2:11):
## QM(df = 10) = 26.7261, p-val = 0.0029
## 
## Model Results:
## 
##                           estimate       se     zval    pval     ci.lb    ci.ub 
## intrcpt                     7.5785  24.0262   0.3154  0.7524  -39.5120  54.6691 
## year                       -0.0032   0.0120  -0.2654  0.7907   -0.0268   0.0204 
## interval.months1           -0.0047   0.0025  -1.9140  0.0556   -0.0095   0.0001 
## idv1                       -0.1208   0.2322  -0.5201  0.6030   -0.5758   0.3343 
## class1                     -0.0424   0.0160  -2.6424  0.0082   -0.0738  -0.0109 
## segeneral SE                0.0041   0.0960   0.0426  0.9660   -0.1841   0.1923 
## seperformance SE           -0.1841   0.0851  -2.1637  0.0305   -0.3508  -0.0173 
## sesubject SE               -0.1304   0.0668  -1.9533  0.0508   -0.2613   0.0004 
## pers_raterself-rated        0.2907   0.1685   1.7245  0.0846   -0.0397   0.6210 
## pers_retropers -> se/ach   -0.0758   0.0502  -1.5085  0.1314   -0.1742   0.0227 
## pers_retrose/ach -> pers   -0.0764   0.0470  -1.6274  0.1037   -0.1685   0.0156 
##  
## intrcpt 
## year 
## interval.months1           . 
## idv1 
## class1                    ** 
## segeneral SE 
## seperformance SE           * 
## sesubject SE               . 
## pers_raterself-rated       . 
## pers_retropers -> se/ach     
## pers_retrose/ach -> pers     
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1|