Examples of Longitudinal Mediation Models

The saved examples below were generated with nlpsem 1.0.0.9006; extdata/REGENERATED.txt records the versions and how the fits compare with the previous ones. They were fitted before version 1.0.0 changed the starting values of the mediation disturbance covariances: with the 1.0.0 starts, the call in Example 1 reaches the same likelihood and estimates (two standard errors differ), and the call in Example 2 reaches the same likelihood (within 0.002) at a point where the numerical Hessian is indefinite and three standard errors are unavailable, so getMediation() issues its diagnostics warning (REGENERATED.txt gives the details). Rendering this guide does not refit its disabled model-fitting chunks. Refit with the current version for a new analysis, use getDiagnostics() to check admissibility and uncertainty, and compare multiple starts for difficult nonlinear or mixture models. These examples are not evidence of numerical qualification.

Load nlpsem package, dependent packages and set CSOLNP as the optimizer

library(nlpsem)
mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)

Load pre-computed models

load(system.file("extdata", "getMediation_examples.RData", package = "nlpsem"))

Load example data and preprocess data

# Load ECLS-K (2011) data
data("RMS_dat")
RMS_dat0 <- RMS_dat
# Re-baseline the data so that the estimated initial status is for the
# starting point of the study
baseT <- RMS_dat0$T1
RMS_dat0$T1 <- RMS_dat0$T1 - baseT
RMS_dat0$T2 <- RMS_dat0$T2 - baseT
RMS_dat0$T3 <- RMS_dat0$T3 - baseT
RMS_dat0$T4 <- RMS_dat0$T4 - baseT
RMS_dat0$T5 <- RMS_dat0$T5 - baseT
RMS_dat0$T6 <- RMS_dat0$T6 - baseT
RMS_dat0$T7 <- RMS_dat0$T7 - baseT
RMS_dat0$T8 <- RMS_dat0$T8 - baseT
RMS_dat0$T9 <- RMS_dat0$T9 - baseT
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
xstarts <- mean(baseT)

Example 1: Fit longitudinal mediation model with a bilinear spline functional form to assess how the baseline teacher-reported approach to learning influences the development of mathematics ability, mediated through the development of reading ability.

Med2_LGCM_BLS <- getMediation(
  dat = RMS_dat0, t_var = rep("T", 2), y_var = "M", m_var = "R",
  x_type = "baseline", x_var = "ex1", curveFun = "bilinear spline",
  records = list(1:9, 1:9), tries = 10,
  paramOut = TRUE
  )

Med2_LGCM_BLS@Estimates
#>           Name      Estimate           SE
#> 1          muX -9.766730e-07  0.044659486
#> 2        phi11  9.979963e-01  0.063067601
#> 3      alphaM1  2.113366e+00  0.024554115
#> 4      alphaMr  1.118319e+02  0.784214604
#> 5      alphaM2  6.877808e-01  0.013437127
#> 6         mugM  2.631100e+01  0.245362966
#> 7    psiM1M1_r  1.934541e-01  0.017323928
#> 8    psiM1Mr_r  4.666079e+00  0.438319029
#> 9    psiM1M2_r -2.783156e-02  0.006671825
#> 10   psiMrMr_r  2.265280e+02 15.395502683
#> 11   psiMrM2_r -1.901147e+00  0.215336019
#> 12   psiM2M2_r  3.411786e-02  0.004499099
#> 13     alphaY1  9.622089e-01  0.069729726
#> 14     alphaYr  1.909048e+01  3.236828680
#> 15     alphaY2  3.802183e-01  0.246286374
#> 16        mugY  3.470409e+01  0.357646351
#> 17   psiY1Y1_r  5.530097e-02  0.006237888
#> 18   psiY1Yr_r  1.781942e+00  0.193468737
#> 19   psiY1Y2_r -7.780311e-03  0.004304679
#> 20   psiYrYr_r  1.042739e+02  7.965204224
#> 21   psiYrY2_r -7.595604e-01  0.158619576
#> 22   psiY2Y2_r  2.345405e-02  0.005214946
#> 23      betaM1  6.230425e-02  0.023133622
#> 24      betaMr  5.547168e+00  0.696475411
#> 25      betaM2 -4.682207e-02  0.011808537
#> 26      betaY1  1.489821e-02  0.013892988
#> 27      betaYr  1.290969e+00  0.513871285
#> 28      betaY2 -2.123731e-02  0.013500876
#> 29    betaM1Y1  3.806581e-01  0.032538416
#> 30    betaM1Yr  1.190299e-01  1.068731861
#> 31    betaM1Y2  5.478122e-02  0.051268165
#> 32    betaMrYr  7.277567e-01  0.031683011
#> 33    betaMrY2 -1.186216e-03  0.002022615
#> 34    betaM2Y2  4.811030e-01  0.145087825
#> 35     muetaM1  2.113366e+00  0.024711733
#> 36     muetaMr  1.118319e+02  0.822427702
#> 37     muetaM2  6.877809e-01  0.013598794
#> 38     muetaY1  1.766679e+00  0.016564995
#> 39     muetaYr  1.007285e+02  0.892430066
#> 40     muetaY2  6.942276e-01  0.017178274
#> 41  Mediator11  2.371662e-02  0.009033392
#> 42  Mediator1r  7.416069e-03  0.066695659
#> 43  Mediator12  3.413103e-03  0.003430562
#> 44  Mediatorrr  4.036989e+00  0.533312095
#> 45  Mediatorr2 -6.580142e-03  0.011246982
#> 46  Mediator22 -2.252624e-02  0.008864215
#> 47      total1  3.861483e-02  0.015576519
#> 48      totalr  5.335374e+00  0.692138153
#> 49      total2 -4.693059e-02  0.013298078
#> 50  residualsM  3.388571e+01  0.872610790
#> 51  residualsY  4.056665e+01  1.061976733
#> 52 residualsYM  6.926780e+00  0.686052327

Example 2: Fit longitudinal mediation model with a bilinear spline functional form to assess how the development of reading ability influences the development of science ability, mediated through the development of mathematics ability.

set.seed(20191029)
Med3_LGCM_BLS <- getMediation(
  dat = RMS_dat0, t_var = rep("T", 3), y_var = "S", m_var = "M", x_type = "longitudinal",
  x_var = "R", curveFun = "bilinear spline", records = list(2:9, 1:9, 1:9),
  tries = 10, paramOut = TRUE
  )

Med3_LGCM_BLS@Estimates
#>           Name      Estimate           SE
#> 1      muetaX1  2.113461e+00  0.024463187
#> 2      muetaXr  1.118428e+02  0.826779517
#> 3      muetaX2  6.873752e-01  0.013546743
#> 4         mugX  2.631556e+01  0.248781669
#> 5      psiX1X1  1.894248e-01  0.017600091
#> 6      psiX1Xr  5.032575e+00  0.469665404
#> 7      psiX1X2 -2.735054e-02  0.006534708
#> 8      psiXrXr  2.583072e+02 17.376671959
#> 9      psiXrX2 -2.152757e+00  0.226104688
#> 10     psiX2X2  3.406075e-02  0.004444882
#> 11     alphaM1  9.248644e-01  0.067103593
#> 12     alphaMr  1.593221e+01  3.059394855
#> 13     alphaM2  4.586478e-01  0.320465732
#> 14        mugM  3.463420e+01  0.357438052
#> 15   psiM1M1_r  5.441177e-02  0.006219918
#> 16   psiM1Mr_r  1.766659e+00  0.192670626
#> 17   psiM1M2_r -7.266545e-03  0.004211347
#> 18   psiMrMr_r  1.044943e+02  7.975560048
#> 19   psiMrM2_r -7.655868e-01  0.155781875
#> 20   psiM2M2_r  2.325785e-02  0.005183435
#> 21     alphaY1  4.313663e-02  0.070372652
#> 22     alphaYr  5.940067e-01  1.506418168
#> 23     alphaY2 -1.150213e+00  0.314149207
#> 24        mugY  3.368094e+01  1.003692837
#> 25   psiY1Y1_r  1.945689e-02  0.004126769
#> 26   psiY1Yr_r  5.091720e-01  0.100101792
#> 27   psiY1Y2_r -9.642075e-04  0.002837145
#> 28   psiYrYr_r  3.665495e+01  3.445173005
#> 29   psiYrY2_r -3.654724e-01  0.084213601
#> 30   psiY2Y2_r  7.930385e-03  0.004366445
#> 31    betaX1Y1  3.987623e-01  0.031347715
#> 32    betaX1Yr  6.690534e-01  1.095564944
#> 33    betaX1Y2  6.538787e-02  0.058294341
#> 34    betaXrYr  7.446452e-01  0.030914504
#> 35    betaXrY2 -2.032093e-03  0.002563359
#> 36    betaX2Y2  4.753052e-01  0.189917023
#> 37    betaX1M1  1.540497e-01  0.039781802
#> 38    betaX1Mr  4.451749e+00  1.346400691
#> 39    betaX1M2 -2.000375e-01  0.079828894
#> 40    betaXrMr  1.960615e-01  0.033999056
#> 41    betaXrM2  9.015947e-03  0.003365725
#> 42    betaX2M2  8.529928e-01  0.230998312
#> 43    betaM1Y1  2.718526e-01  0.054733417
#> 44    betaM1Yr -2.625031e+00  1.857629568
#> 45    betaM1Y2  9.006190e-03  0.102850159
#> 46    betaMrYr  2.927027e-01  0.039540828
#> 47    betaMrY2  2.805934e-03  0.002709719
#> 48    betaM2Y2  3.743428e-01  0.177590073
#> 49     muetaM1  1.767633e+00  0.016545054
#> 50     muetaMr  1.006294e+02  0.892396668
#> 51     muetaM2  6.962805e-01  0.017145668
#> 52     muetaY1  8.492502e-01  0.013125248
#> 53     muetaYr  5.674509e+01  0.903442092
#> 54     muetaY2  5.806370e-01  0.012985970
#> 55 mediator111  1.084046e-01  0.023262604
#> 56 mediator11r -1.046764e+00  0.741988748
#> 57 mediator112  3.591329e-03  0.041013689
#> 58 mediator1rr  1.958337e-01  0.311534689
#> 59 mediator1r2  1.877319e-03  0.004170095
#> 60 mediator122  2.447748e-02  0.028646054
#> 61 mediatorrrr  2.179596e-01  0.032336526
#> 62 mediatorrr2  2.089425e-03  0.001997517
#> 63 mediatorr22 -7.606996e-04  0.001199964
#> 64 mediator222  1.779271e-01  0.070384641
#> 65     total11  2.624542e-01  0.029304906
#> 66     total1r  3.600819e+00  1.160547193
#> 67     total12 -1.700913e-01  0.071862183
#> 68     totalrr  4.140211e-01  0.030946049
#> 69     totalr2  1.034467e-02  0.002902466
#> 70     total22  1.030920e+00  0.224142158
#> 71  residualsX  4.117715e+01  1.087857122
#> 72  residualsM  1.944187e+01  0.553516949
#> 73  residualsY  3.396886e+01  0.891650380
#> 74 residualsMX  7.007795e+00  0.746608061
#> 75 residualsYX  1.831448e+00  0.694328488
#> 76 residualsYM  2.568343e+00  0.557334388