A Sensitivity Analysis of a Model for Parenting Risk and Resilience, Social-emotional Readiness, and Reading Achievement in Kindergarten Children from Low-income Families Model by Smith-Adcock, Leite, Kaya and Amatea

Jia Quan (University of Florida) & Huibin Zhang (University of Florida)

2022-07-22

BASED ON PAPER: A Model for Parenting Risk and Resilience, Social-emotional Readiness, and Reading Achievement in Kindergarten Children from Low-income Families Model

Author(s): Sondra Smith-Adcock, Walter Leite, Yasemine Kaya, & Ellen Amatea.

Source: Journal of Child and Family Studies, vol 28(Oct., 2019), pp. 2826-2841

Published by: Springer Nature in Journal of Child and Family studies, doi:10.1007/s10826-019-01462-0

SENSITIVITY ANALYSIS USING SEMsens

This example sensitivity analysis uses the published data and model from Smith-Adcock, Leite, Kaya & Amatea(2019). We use the original data with categorical variables, set up the lavaan models for their original model and the sensitivity model, run the analysis, and view the results.

# Load lavaan and SEMsens packages
require(lavaan)
require(SEMsens)
set.seed(1)

Step 1 : Load data with names and indicate categorical variables

Smith-Adcock et. al (2019) shared the raw data and codebook, so we load the data with their names, and create names for categorical variables.

smith10.use <- data(smith19.use, package = "SEMsens")

#Indicate the ordinal variables and then factorize these variables
factornames <- c("P2BEPARN", "P2CHDOES","P2HRDWRM","P2FLTRAP","P2FEELAN","P2CHHARD",
                 "P2MOREWK", "P2HITCHO","P2HITAPO","P2HITPRV","P2HITWAR","P2ATTENB",
                 "P2ATTENP", "P2PARADV","P2PARGRP","P2ATTENS","P2VOLUNT","P2FUNDRS",
                 "P2TVRULE", "P2TVRUL3","P2TVRUL2","P1TELLST","P1SINGSO","P1HELPAR",
                 "P1CHORES", "P1GAMES","P1NATURE","P1BUILD","P1SPORT","P2LIBRAR",
                 "P2CONCRT", "P2MUSEUM","P2ZOO")

Step 2: Define the models

The SEMsens package requires both an original model and a sensitivity model using the lavaan model syntax. We first mimic the original Mplus model based on the article, and then adding phantom variables (phantom1, phantom2, etc.) for every latent variable into that model to create sensitivity model.

Note: Since we have categorical variables in the model, while the lavaan package did not allow for multiple imputation for missing data with categorical variables, so we have a close mimic model, but not a perfect replication of the model in the original article.

#A model mimicked from the original model in Smith-Adcock et al. (2019). 
model1 <- "   
           # regressions
          C2RSCALE~T2LEARN+T2EXTERN+T2INTERN+T2CONTRO+T2INTERP+f1+f2+f3+f4+f5+f6
          T2LEARN~f1 +f2 +f3 +f4 +f5 +f6
          T2EXTERN~f1 +f2 +f3 +f4 +f5 +f6
          T2INTERN~f1 +f2 +f3 +f4 +f5 +f6
          T2CONTRO~f1 +f2 +f3 +f4 +f5 +f6
          T2INTERP~f1 +f2 +f3 +f4 +f5 +f6

           # latent variables
          f1=~P2BEPARN+P2CHDOES+P2HRDWRM+P2FLTRAP+P2FEELAN+P2CHHARD+P2MOREWK
          f2=~P2HITCHO+P2HITAPO+P2HITPRV+P2HITWAR
          f3=~P2ATTENB+P2ATTENP+P2PARADV+P2PARGRP+P2ATTENS+P2VOLUNT+P2FUNDRS
          f4=~P2TVRULE+P2TVRUL3+P2TVRUL2
          f5=~P1TELLST+P1SINGSO+P1HELPAR+P1CHORES+P1GAMES+P1NATURE+P1BUILD+P1SPORT
          f6=~P2LIBRAR+P2CONCRT+P2MUSEUM+P2ZOO
            
            # residual correlations
          T2LEARN ~~ T2EXTERN+T2INTERN+T2CONTRO+T2INTERP
          T2EXTERN ~~ T2INTERN+T2CONTRO+T2INTERP
          T2INTERN ~~ T2CONTRO+T2INTERP
          T2CONTRO ~~ T2INTERP

          f1 ~~ f2+f3+f4+f5+f6
          f2 ~~ f3+f4+f5+f6
          f3 ~~ f4+f5+f6
          f4 ~~ f5+f6
          f5 ~~ f6
         "

#The sensitivity model 
#This sensitivity model used 6 phantom variables for a quicker result
sens.model1 <- '
            # regressions
          C2RSCALE~T2LEARN+T2EXTERN+T2INTERN+T2CONTRO+T2INTERP+f1+f2+f3+f4+f5+f6
          T2LEARN~f1 +f2 +f3 +f4 +f5 +f6
          T2EXTERN~f1 +f2 +f3 +f4 +f5 +f6
          T2INTERN~f1 +f2 +f3 +f4 +f5 +f6
          T2CONTRO~f1 +f2 +f3 +f4 +f5 +f6
          T2INTERP~f1 +f2 +f3 +f4 +f5 +f6

            # latent variable definitions
          f1=~P2BEPARN+P2CHDOES+P2HRDWRM+P2FLTRAP+P2FEELAN+P2CHHARD+P2MOREWK
          f2=~P2HITCHO+P2HITAPO+P2HITPRV+P2HITWAR
          f3=~P2ATTENB+P2ATTENP+P2PARADV+P2PARGRP+P2ATTENS+P2VOLUNT+P2FUNDRS
          f4=~P2TVRULE+P2TVRUL3+P2TVRUL2
          f5=~P1TELLST+P1SINGSO+P1HELPAR+P1CHORES+P1GAMES+P1NATURE+P1BUILD+P1SPORT
          f6=~P2LIBRAR+P2CONCRT+P2MUSEUM+P2ZOO

            # residual correlations
          T2LEARN ~~ T2EXTERN+T2INTERN+T2CONTRO+T2INTERP
          T2EXTERN ~~ T2INTERN+T2CONTRO+T2INTERP
          T2INTERN ~~ T2CONTRO+T2INTERP
          T2CONTRO ~~ T2INTERP

          f1 ~~ f2+f3+f4+f5+f6
          f2 ~~ f3+f4+f5+f6
          f3 ~~ f4+f5+f6
          f4 ~~ f5+f6
          f5 ~~ f6
          
            # phantom variables 
          T2LEARN ~ phantom1*phantom
          T2EXTERN ~ phantom2*phantom
          C2RSCALE ~ phantom3*phantom
          
          f3 ~ phantom4*phantom
          f4 ~ phantom5*phantom
          f5 ~ phantom6*phantom

          phantom =~ 0   # added for mean of zero
          phantom ~~ 1*phantom   # added for unit variance
          '

Step 3: Identify paths of interest

Before running the analysis, it is recommended to identify the rows in the lavaan parameter table that include the paths we are interested in looking at in the analysis. The rows that we are interested will be used for the next step.

old.model = model1
old.out  = sem(model = model1, data = smith19.use, estimator="WLSMV",ordered = factornames)
summary(old.out, standardized=TRUE)
## lavaan 0.6-11 ended normally after 213 iterations
## 
##   Estimator                                       DWLS
##   Optimization method                           NLMINB
##   Number of model parameters                       174
##                                                       
##                                                   Used       Total
##   Number of observations                          2466        3444
##                                                                   
## Model Test User Model:
##                                               Standard      Robust
##   Test Statistic                              1250.335    1283.613
##   Degrees of freedom                               642         642
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  1.123
##   Shift parameter                                          170.602
##        simple second-order correction                             
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model        Unstructured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   f1 =~                                                                 
##     P2BEPARN          1.000                               0.544    0.544
##     P2CHDOES          1.267    0.062   20.337    0.000    0.690    0.690
##     P2HRDWRM          0.889    0.059   15.004    0.000    0.484    0.484
##     P2FLTRAP          1.306    0.066   19.707    0.000    0.711    0.711
##     P2FEELAN          1.161    0.062   18.712    0.000    0.632    0.632
##     P2CHHARD          1.353    0.073   18.616    0.000    0.737    0.737
##     P2MOREWK          1.214    0.060   20.309    0.000    0.661    0.661
##   f2 =~                                                                 
##     P2HITCHO          1.000                               0.768    0.768
##     P2HITAPO          0.943    0.062   15.244    0.000    0.724    0.724
##     P2HITPRV          0.775    0.052   14.778    0.000    0.595    0.595
##     P2HITWAR          0.951    0.068   13.961    0.000    0.730    0.730
##   f3 =~                                                                 
##     P2ATTENB          1.000                               0.564    0.564
##     P2ATTENP          0.869    0.075   11.636    0.000    0.490    0.490
##     P2PARADV          0.691    0.096    7.230    0.000    0.390    0.390
##     P2PARGRP          0.669    0.074    9.043    0.000    0.377    0.377
##     P2ATTENS          1.102    0.083   13.305    0.000    0.621    0.621
##     P2VOLUNT          1.110    0.084   13.266    0.000    0.626    0.626
##     P2FUNDRS          0.928    0.077   12.090    0.000    0.523    0.523
##   f4 =~                                                                 
##     P2TVRULE          1.000                               0.831    0.831
##     P2TVRUL3          0.923    0.049   18.812    0.000    0.767    0.767
##     P2TVRUL2          0.969    0.056   17.397    0.000    0.805    0.805
##   f5 =~                                                                 
##     P1TELLST          1.000                               0.585    0.585
##     P1SINGSO          0.849    0.045   18.743    0.000    0.496    0.496
##     P1HELPAR          0.904    0.044   20.671    0.000    0.528    0.528
##     P1CHORES          0.710    0.047   15.210    0.000    0.415    0.415
##     P1GAMES           1.024    0.045   22.755    0.000    0.599    0.599
##     P1NATURE          0.944    0.045   20.986    0.000    0.552    0.552
##     P1BUILD           0.916    0.043   21.075    0.000    0.536    0.536
##     P1SPORT           0.821    0.043   19.015    0.000    0.480    0.480
##   f6 =~                                                                 
##     P2LIBRAR          1.000                               0.593    0.593
##     P2CONCRT          0.936    0.081   11.560    0.000    0.555    0.555
##     P2MUSEUM          1.031    0.085   12.126    0.000    0.611    0.611
##     P2ZOO             0.858    0.077   11.196    0.000    0.508    0.508
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   C2RSCALE ~                                                            
##     T2LEARN           6.046    0.290   20.841    0.000    6.046    0.485
##     T2EXTERN          0.589    0.363    1.623    0.105    0.589    0.045
##     T2INTERN          0.058    0.306    0.190    0.849    0.058    0.004
##     T2CONTRO         -1.077    0.481   -2.237    0.025   -1.077   -0.079
##     T2INTERP         -0.340    0.395   -0.862    0.389   -0.340   -0.025
##     f1               -0.271    0.396   -0.685    0.494   -0.148   -0.017
##     f2               -0.540    0.320   -1.688    0.091   -0.415   -0.048
##     f3                2.306    0.532    4.338    0.000    1.301    0.150
##     f4                0.458    0.278    1.646    0.100    0.381    0.044
##     f5                0.026    0.401    0.064    0.949    0.015    0.002
##     f6               -0.964    0.630   -1.529    0.126   -0.571   -0.066
##   T2LEARN ~                                                             
##     f1               -0.149    0.033   -4.522    0.000   -0.081   -0.116
##     f2               -0.035    0.028   -1.254    0.210   -0.027   -0.038
##     f3                0.137    0.048    2.847    0.004    0.077    0.111
##     f4                0.004    0.025    0.180    0.857    0.004    0.005
##     f5                0.050    0.033    1.506    0.132    0.029    0.042
##     f6               -0.036    0.052   -0.684    0.494   -0.021   -0.031
##   T2EXTERN ~                                                            
##     f1                0.195    0.031    6.260    0.000    0.106    0.158
##     f2                0.030    0.026    1.145    0.252    0.023    0.035
##     f3               -0.148    0.045   -3.268    0.001   -0.084   -0.125
##     f4                0.010    0.024    0.416    0.677    0.008    0.012
##     f5                0.036    0.033    1.093    0.274    0.021    0.031
##     f6                0.032    0.052    0.616    0.538    0.019    0.028
##   T2INTERN ~                                                            
##     f1                0.007    0.026    0.251    0.802    0.004    0.006
##     f2                0.032    0.022    1.448    0.148    0.025    0.045
##     f3               -0.053    0.036   -1.469    0.142   -0.030   -0.055
##     f4                0.009    0.019    0.482    0.630    0.008    0.014
##     f5               -0.001    0.026   -0.054    0.957   -0.001   -0.002
##     f6               -0.030    0.040   -0.757    0.449   -0.018   -0.033
##   T2CONTRO ~                                                            
##     f1               -0.168    0.030   -5.616    0.000   -0.091   -0.145
##     f2               -0.017    0.025   -0.679    0.497   -0.013   -0.021
##     f3                0.134    0.044    3.061    0.002    0.076    0.120
##     f4               -0.000    0.023   -0.005    0.996   -0.000   -0.000
##     f5               -0.004    0.031   -0.125    0.900   -0.002   -0.004
##     f6               -0.057    0.050   -1.147    0.252   -0.034   -0.053
##   T2INTERP ~                                                            
##     f1               -0.160    0.030   -5.351    0.000   -0.087   -0.137
##     f2               -0.020    0.025   -0.814    0.415   -0.016   -0.025
##     f3                0.176    0.043    4.056    0.000    0.100    0.157
##     f4               -0.003    0.023   -0.131    0.896   -0.002   -0.004
##     f5                0.021    0.030    0.675    0.500    0.012    0.019
##     f6               -0.062    0.047   -1.317    0.188   -0.037   -0.058
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##  .T2LEARN ~~                                                            
##    .T2EXTERN         -0.213    0.011  -19.226    0.000   -0.213   -0.474
##    .T2INTERN         -0.126    0.008  -15.626    0.000   -0.126   -0.338
##    .T2CONTRO          0.273    0.013   21.404    0.000    0.273    0.640
##    .T2INTERP          0.294    0.013   22.440    0.000    0.294    0.690
##  .T2EXTERN ~~                                                           
##    .T2INTERN          0.097    0.007   14.364    0.000    0.097    0.271
##    .T2CONTRO         -0.285    0.011  -25.661    0.000   -0.285   -0.700
##    .T2INTERP         -0.235    0.010  -22.582    0.000   -0.235   -0.579
##  .T2INTERN ~~                                                           
##    .T2CONTRO         -0.085    0.007  -11.986    0.000   -0.085   -0.252
##    .T2INTERP         -0.109    0.007  -15.324    0.000   -0.109   -0.323
##  .T2CONTRO ~~                                                           
##    .T2INTERP          0.301    0.012   24.684    0.000    0.301    0.780
##   f1 ~~                                                                 
##     f2                0.038    0.015    2.596    0.009    0.090    0.090
##     f3               -0.048    0.010   -4.903    0.000   -0.156   -0.156
##     f4               -0.015    0.015   -1.005    0.315   -0.033   -0.033
##     f5               -0.064    0.009   -6.772    0.000   -0.201   -0.201
##     f6               -0.038    0.012   -3.128    0.002   -0.119   -0.119
##   f2 ~~                                                                 
##     f3                0.082    0.016    5.055    0.000    0.190    0.190
##     f4                0.112    0.025    4.559    0.000    0.176    0.176
##     f5                0.016    0.014    1.080    0.280    0.035    0.035
##     f6                0.029    0.018    1.639    0.101    0.064    0.064
##   f3 ~~                                                                 
##     f4                0.105    0.018    5.975    0.000    0.224    0.224
##     f5                0.083    0.011    7.360    0.000    0.250    0.250
##     f6                0.171    0.017    9.952    0.000    0.511    0.511
##   f4 ~~                                                                 
##     f5                0.073    0.015    4.763    0.000    0.151    0.151
##     f6                0.142    0.021    6.844    0.000    0.289    0.289
##   f5 ~~                                                                 
##     f6                0.138    0.014    9.651    0.000    0.398    0.398
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .P2BEPARN          0.000                               0.000    0.000
##    .P2CHDOES          0.000                               0.000    0.000
##    .P2HRDWRM          0.000                               0.000    0.000
##    .P2FLTRAP          0.000                               0.000    0.000
##    .P2FEELAN          0.000                               0.000    0.000
##    .P2CHHARD          0.000                               0.000    0.000
##    .P2MOREWK          0.000                               0.000    0.000
##    .P2HITCHO          0.000                               0.000    0.000
##    .P2HITAPO          0.000                               0.000    0.000
##    .P2HITPRV          0.000                               0.000    0.000
##    .P2HITWAR          0.000                               0.000    0.000
##    .P2ATTENB          0.000                               0.000    0.000
##    .P2ATTENP          0.000                               0.000    0.000
##    .P2PARADV          0.000                               0.000    0.000
##    .P2PARGRP          0.000                               0.000    0.000
##    .P2ATTENS          0.000                               0.000    0.000
##    .P2VOLUNT          0.000                               0.000    0.000
##    .P2FUNDRS          0.000                               0.000    0.000
##    .P2TVRULE          0.000                               0.000    0.000
##    .P2TVRUL3          0.000                               0.000    0.000
##    .P2TVRUL2          0.000                               0.000    0.000
##    .P1TELLST          0.000                               0.000    0.000
##    .P1SINGSO          0.000                               0.000    0.000
##    .P1HELPAR          0.000                               0.000    0.000
##    .P1CHORES          0.000                               0.000    0.000
##    .P1GAMES           0.000                               0.000    0.000
##    .P1NATURE          0.000                               0.000    0.000
##    .P1BUILD           0.000                               0.000    0.000
##    .P1SPORT           0.000                               0.000    0.000
##    .P2LIBRAR          0.000                               0.000    0.000
##    .P2CONCRT          0.000                               0.000    0.000
##    .P2MUSEUM          0.000                               0.000    0.000
##    .P2ZOO             0.000                               0.000    0.000
##    .C2RSCALE         13.381    1.714    7.805    0.000   13.381    1.541
##    .T2LEARN           3.006    0.015  205.268    0.000    3.006    4.313
##    .T2EXTERN          1.716    0.017   99.092    0.000    1.716    2.566
##    .T2INTERN          1.620    0.014  119.690    0.000    1.620    2.958
##    .T2CONTRO          3.102    0.014  229.397    0.000    3.102    4.901
##    .T2INTERP          3.037    0.013  232.253    0.000    3.037    4.787
##     f1                0.000                               0.000    0.000
##     f2                0.000                               0.000    0.000
##     f3                0.000                               0.000    0.000
##     f4                0.000                               0.000    0.000
##     f5                0.000                               0.000    0.000
##     f6                0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     P2BEPARN|t1      -0.642    0.027  -23.588    0.000   -0.642   -0.642
##     P2BEPARN|t2       0.043    0.025    1.691    0.091    0.043    0.043
##     P2BEPARN|t3       0.282    0.026   11.019    0.000    0.282    0.282
##     P2CHDOES|t1      -0.174    0.025   -6.842    0.000   -0.174   -0.174
##     P2CHDOES|t2       1.063    0.031   34.090    0.000    1.063    1.063
##     P2CHDOES|t3       1.392    0.036   38.149    0.000    1.392    1.392
##     P2HRDWRM|t1       0.581    0.027   21.635    0.000    0.581    0.581
##     P2HRDWRM|t2       1.236    0.034   36.709    0.000    1.236    1.236
##     P2HRDWRM|t3       1.634    0.042   38.668    0.000    1.634    1.634
##     P2FLTRAP|t1       0.864    0.029   29.805    0.000    0.864    0.864
##     P2FLTRAP|t2       1.445    0.038   38.437    0.000    1.445    1.445
##     P2FLTRAP|t3       1.713    0.045   38.415    0.000    1.713    1.713
##     P2FEELAN|t1       0.626    0.027   23.082    0.000    0.626    0.626
##     P2FEELAN|t2       1.899    0.051   37.073    0.000    1.899    1.899
##     P2FEELAN|t3       2.352    0.077   30.470    0.000    2.352    2.352
##     P2CHHARD|t1       1.177    0.033   35.937    0.000    1.177    1.177
##     P2CHHARD|t2       1.749    0.046   38.233    0.000    1.749    1.749
##     P2CHHARD|t3       2.110    0.061   34.479    0.000    2.110    2.110
##     P2MOREWK|t1       0.630    0.027   23.199    0.000    0.630    0.630
##     P2MOREWK|t2       1.269    0.034   37.090    0.000    1.269    1.269
##     P2MOREWK|t3       1.558    0.040   38.722    0.000    1.558    1.558
##     P2HITCHO|t1       1.351    0.036   37.852    0.000    1.351    1.351
##     P2HITAPO|t1       0.574    0.027   21.400    0.000    0.574    0.574
##     P2HITPRV|t1       0.439    0.026   16.773    0.000    0.439    0.439
##     P2HITWAR|t1       1.086    0.031   34.509    0.000    1.086    1.086
##     P2ATTENB|t1      -0.159    0.025   -6.279    0.000   -0.159   -0.159
##     P2ATTENP|t1       0.656    0.027   24.015    0.000    0.656    0.656
##     P2PARADV|t1       1.630    0.042   38.675    0.000    1.630    1.630
##     P2PARGRP|t1      -0.666    0.027  -24.324    0.000   -0.666   -0.666
##     P2ATTENS|t1       0.004    0.025    0.161    0.872    0.004    0.004
##     P2VOLUNT|t1       0.610    0.027   22.575    0.000    0.610    0.610
##     P2FUNDRS|t1       0.221    0.025    8.691    0.000    0.221    0.221
##     P2TVRULE|t1      -0.971    0.030  -32.271    0.000   -0.971   -0.971
##     P2TVRUL3|t1      -0.027    0.025   -1.087    0.277   -0.027   -0.027
##     P2TVRUL2|t1      -0.923    0.030  -31.214    0.000   -0.923   -0.923
##     P1TELLST|t1      -1.311    0.035  -37.514    0.000   -1.311   -1.311
##     P1TELLST|t2       0.035    0.025    1.369    0.171    0.035    0.035
##     P1TELLST|t3       0.735    0.028   26.361    0.000    0.735    0.735
##     P1SINGSO|t1      -1.457    0.038  -38.487    0.000   -1.457   -1.457
##     P1SINGSO|t2      -0.464    0.026  -17.687    0.000   -0.464   -0.464
##     P1SINGSO|t3       0.102    0.025    4.026    0.000    0.102    0.102
##     P1HELPAR|t1      -1.181    0.033  -35.995    0.000   -1.181   -1.181
##     P1HELPAR|t2       0.042    0.025    1.651    0.099    0.042    0.042
##     P1HELPAR|t3       0.744    0.028   26.627    0.000    0.744    0.744
##     P1CHORES|t1      -1.608    0.042  -38.709    0.000   -1.608   -1.608
##     P1CHORES|t2      -0.639    0.027  -23.471    0.000   -0.639   -0.639
##     P1CHORES|t3      -0.124    0.025   -4.911    0.000   -0.124   -0.124
##     P1GAMES|t1       -1.512    0.039  -38.659    0.000   -1.512   -1.512
##     P1GAMES|t2       -0.119    0.025   -4.710    0.000   -0.119   -0.119
##     P1GAMES|t3        0.700    0.028   25.327    0.000    0.700    0.700
##     P1NATURE|t1      -0.476    0.026  -18.084    0.000   -0.476   -0.476
##     P1NATURE|t2       0.700    0.028   25.327    0.000    0.700    0.700
##     P1NATURE|t3       1.358    0.036   37.911    0.000    1.358    1.358
##     P1BUILD|t1       -0.763    0.028  -27.158    0.000   -0.763   -0.763
##     P1BUILD|t2        0.358    0.026   13.862    0.000    0.358    0.358
##     P1BUILD|t3        1.022    0.031   33.330    0.000    1.022    1.022
##     P1SPORT|t1       -1.109    0.032  -34.887    0.000   -1.109   -1.109
##     P1SPORT|t2       -0.054    0.025   -2.134    0.033   -0.054   -0.054
##     P1SPORT|t3        0.626    0.027   23.082    0.000    0.626    0.626
##     P2LIBRAR|t1       0.268    0.026   10.497    0.000    0.268    0.268
##     P2CONCRT|t1       0.534    0.027   20.062    0.000    0.534    0.534
##     P2MUSEUM|t1       0.829    0.029   28.920    0.000    0.829    0.829
##     P2ZOO|t1          0.375    0.026   14.461    0.000    0.375    0.375
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .P2BEPARN          0.704                               0.704    0.704
##    .P2CHDOES          0.524                               0.524    0.524
##    .P2HRDWRM          0.766                               0.766    0.766
##    .P2FLTRAP          0.494                               0.494    0.494
##    .P2FEELAN          0.601                               0.601    0.601
##    .P2CHHARD          0.457                               0.457    0.457
##    .P2MOREWK          0.563                               0.563    0.563
##    .P2HITCHO          0.411                               0.411    0.411
##    .P2HITAPO          0.476                               0.476    0.476
##    .P2HITPRV          0.646                               0.646    0.646
##    .P2HITWAR          0.467                               0.467    0.467
##    .P2ATTENB          0.682                               0.682    0.682
##    .P2ATTENP          0.760                               0.760    0.760
##    .P2PARADV          0.848                               0.848    0.848
##    .P2PARGRP          0.858                               0.858    0.858
##    .P2ATTENS          0.614                               0.614    0.614
##    .P2VOLUNT          0.608                               0.608    0.608
##    .P2FUNDRS          0.726                               0.726    0.726
##    .P2TVRULE          0.309                               0.309    0.309
##    .P2TVRUL3          0.412                               0.412    0.412
##    .P2TVRUL2          0.352                               0.352    0.352
##    .P1TELLST          0.658                               0.658    0.658
##    .P1SINGSO          0.754                               0.754    0.754
##    .P1HELPAR          0.721                               0.721    0.721
##    .P1CHORES          0.828                               0.828    0.828
##    .P1GAMES           0.641                               0.641    0.641
##    .P1NATURE          0.696                               0.696    0.696
##    .P1BUILD           0.713                               0.713    0.713
##    .P1SPORT           0.769                               0.769    0.769
##    .P2LIBRAR          0.649                               0.649    0.649
##    .P2CONCRT          0.692                               0.692    0.692
##    .P2MUSEUM          0.626                               0.626    0.626
##    .P2ZOO             0.741                               0.741    0.741
##    .C2RSCALE         60.494    1.537   39.371    0.000   60.494    0.803
##    .T2LEARN           0.470    0.018   26.106    0.000    0.470    0.968
##    .T2EXTERN          0.429    0.013   32.729    0.000    0.429    0.959
##    .T2INTERN          0.298    0.008   38.491    0.000    0.298    0.993
##    .T2CONTRO          0.387    0.014   27.726    0.000    0.387    0.965
##    .T2INTERP          0.385    0.014   27.826    0.000    0.385    0.956
##     f1                0.296    0.024   12.551    0.000    1.000    1.000
##     f2                0.589    0.061    9.696    0.000    1.000    1.000
##     f3                0.318    0.034    9.248    0.000    1.000    1.000
##     f4                0.691    0.049   13.969    0.000    1.000    1.000
##     f5                0.342    0.022   15.270    0.000    1.000    1.000
##     f6                0.351    0.039    8.903    0.000    1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     P2BEPARN          1.000                               1.000    1.000
##     P2CHDOES          1.000                               1.000    1.000
##     P2HRDWRM          1.000                               1.000    1.000
##     P2FLTRAP          1.000                               1.000    1.000
##     P2FEELAN          1.000                               1.000    1.000
##     P2CHHARD          1.000                               1.000    1.000
##     P2MOREWK          1.000                               1.000    1.000
##     P2HITCHO          1.000                               1.000    1.000
##     P2HITAPO          1.000                               1.000    1.000
##     P2HITPRV          1.000                               1.000    1.000
##     P2HITWAR          1.000                               1.000    1.000
##     P2ATTENB          1.000                               1.000    1.000
##     P2ATTENP          1.000                               1.000    1.000
##     P2PARADV          1.000                               1.000    1.000
##     P2PARGRP          1.000                               1.000    1.000
##     P2ATTENS          1.000                               1.000    1.000
##     P2VOLUNT          1.000                               1.000    1.000
##     P2FUNDRS          1.000                               1.000    1.000
##     P2TVRULE          1.000                               1.000    1.000
##     P2TVRUL3          1.000                               1.000    1.000
##     P2TVRUL2          1.000                               1.000    1.000
##     P1TELLST          1.000                               1.000    1.000
##     P1SINGSO          1.000                               1.000    1.000
##     P1HELPAR          1.000                               1.000    1.000
##     P1CHORES          1.000                               1.000    1.000
##     P1GAMES           1.000                               1.000    1.000
##     P1NATURE          1.000                               1.000    1.000
##     P1BUILD           1.000                               1.000    1.000
##     P1SPORT           1.000                               1.000    1.000
##     P2LIBRAR          1.000                               1.000    1.000
##     P2CONCRT          1.000                               1.000    1.000
##     P2MUSEUM          1.000                               1.000    1.000
##     P2ZOO             1.000                               1.000    1.000
old.model.par <- standardizedSolution(old.out,type = "std.all")
old.model.par
##          lhs  op      rhs est.std    se       z pvalue ci.lower ci.upper
## 1   C2RSCALE   ~  T2LEARN   0.485 0.023  21.425  0.000    0.441    0.530
## 2   C2RSCALE   ~ T2EXTERN   0.045 0.028   1.622  0.105   -0.009    0.100
## 3   C2RSCALE   ~ T2INTERN   0.004 0.019   0.190  0.849   -0.034    0.042
## 4   C2RSCALE   ~ T2CONTRO  -0.079 0.035  -2.226  0.026   -0.148   -0.009
## 5   C2RSCALE   ~ T2INTERP  -0.025 0.029  -0.862  0.388   -0.081    0.032
## 6   C2RSCALE   ~       f1  -0.017 0.025  -0.685  0.493   -0.066    0.032
## 7   C2RSCALE   ~       f2  -0.048 0.028  -1.692  0.091   -0.103    0.008
## 8   C2RSCALE   ~       f3   0.150 0.033   4.478  0.000    0.084    0.215
## 9   C2RSCALE   ~       f4   0.044 0.027   1.651  0.099   -0.008    0.096
## 10  C2RSCALE   ~       f5   0.002 0.027   0.064  0.949   -0.051    0.055
## 11  C2RSCALE   ~       f6  -0.066 0.043  -1.535  0.125   -0.150    0.018
## 12   T2LEARN   ~       f1  -0.116 0.025  -4.636  0.000   -0.165   -0.067
## 13   T2LEARN   ~       f2  -0.038 0.030  -1.255  0.210   -0.098    0.022
## 14   T2LEARN   ~       f3   0.111 0.038   2.901  0.004    0.036    0.185
## 15   T2LEARN   ~       f4   0.005 0.030   0.180  0.857   -0.053    0.063
## 16   T2LEARN   ~       f5   0.042 0.028   1.506  0.132   -0.013    0.097
## 17   T2LEARN   ~       f6  -0.031 0.045  -0.685  0.493   -0.118    0.057
## 18  T2EXTERN   ~       f1   0.158 0.024   6.518  0.000    0.111    0.206
## 19  T2EXTERN   ~       f2   0.035 0.030   1.146  0.252   -0.025    0.094
## 20  T2EXTERN   ~       f3  -0.125 0.038  -3.336  0.001   -0.199   -0.052
## 21  T2EXTERN   ~       f4   0.012 0.029   0.416  0.677   -0.046    0.070
## 22  T2EXTERN   ~       f5   0.031 0.028   1.096  0.273   -0.025    0.087
## 23  T2EXTERN   ~       f6   0.028 0.046   0.617  0.538   -0.062    0.118
## 24  T2INTERN   ~       f1   0.006 0.026   0.251  0.802   -0.044    0.057
## 25  T2INTERN   ~       f2   0.045 0.031   1.452  0.147   -0.016    0.105
## 26  T2INTERN   ~       f3  -0.055 0.037  -1.476  0.140   -0.127    0.018
## 27  T2INTERN   ~       f4   0.014 0.029   0.482  0.630   -0.042    0.070
## 28  T2INTERN   ~       f5  -0.002 0.028  -0.054  0.957   -0.057    0.054
## 29  T2INTERN   ~       f6  -0.033 0.043  -0.758  0.449   -0.118    0.052
## 30  T2CONTRO   ~       f1  -0.145 0.025  -5.826  0.000   -0.193   -0.096
## 31  T2CONTRO   ~       f2  -0.021 0.030  -0.679  0.497   -0.080    0.039
## 32  T2CONTRO   ~       f3   0.120 0.038   3.130  0.002    0.045    0.195
## 33  T2CONTRO   ~       f4   0.000 0.030  -0.005  0.996   -0.059    0.059
## 34  T2CONTRO   ~       f5  -0.004 0.029  -0.125  0.900   -0.060    0.053
## 35  T2CONTRO   ~       f6  -0.053 0.046  -1.150  0.250   -0.144    0.038
## 36  T2INTERP   ~       f1  -0.137 0.025  -5.529  0.000   -0.186   -0.089
## 37  T2INTERP   ~       f2  -0.025 0.030  -0.814  0.416   -0.084    0.035
## 38  T2INTERP   ~       f3   0.157 0.037   4.210  0.000    0.084    0.230
## 39  T2INTERP   ~       f4  -0.004 0.030  -0.131  0.896   -0.062    0.055
## 40  T2INTERP   ~       f5   0.019 0.028   0.675  0.500   -0.036    0.074
## 41  T2INTERP   ~       f6  -0.058 0.044  -1.324  0.185   -0.144    0.028
## 42        f1  =~ P2BEPARN   0.544 0.022  25.101  0.000    0.502    0.587
## 43        f1  =~ P2CHDOES   0.690 0.019  36.425  0.000    0.653    0.727
## 44        f1  =~ P2HRDWRM   0.484 0.026  18.369  0.000    0.433    0.536
## 45        f1  =~ P2FLTRAP   0.711 0.023  30.642  0.000    0.666    0.757
## 46        f1  =~ P2FEELAN   0.632 0.023  27.515  0.000    0.587    0.677
## 47        f1  =~ P2CHHARD   0.737 0.026  28.233  0.000    0.686    0.788
## 48        f1  =~ P2MOREWK   0.661 0.022  30.009  0.000    0.618    0.704
## 49        f2  =~ P2HITCHO   0.768 0.040  19.391  0.000    0.690    0.845
## 50        f2  =~ P2HITAPO   0.724 0.026  27.769  0.000    0.673    0.775
## 51        f2  =~ P2HITPRV   0.595 0.028  21.461  0.000    0.541    0.650
## 52        f2  =~ P2HITWAR   0.730 0.034  21.364  0.000    0.663    0.797
## 53        f3  =~ P2ATTENB   0.564 0.030  18.497  0.000    0.504    0.624
## 54        f3  =~ P2ATTENP   0.490 0.033  14.971  0.000    0.426    0.554
## 55        f3  =~ P2PARADV   0.390 0.049   7.947  0.000    0.293    0.486
## 56        f3  =~ P2PARGRP   0.377 0.036  10.349  0.000    0.306    0.449
## 57        f3  =~ P2ATTENS   0.621 0.029  21.247  0.000    0.564    0.679
## 58        f3  =~ P2VOLUNT   0.626 0.031  20.400  0.000    0.566    0.686
## 59        f3  =~ P2FUNDRS   0.523 0.031  17.105  0.000    0.463    0.583
## 60        f4  =~ P2TVRULE   0.831 0.030  27.938  0.000    0.773    0.889
## 61        f4  =~ P2TVRUL3   0.767 0.025  30.268  0.000    0.717    0.817
## 62        f4  =~ P2TVRUL2   0.805 0.030  26.967  0.000    0.747    0.864
## 63        f5  =~ P1TELLST   0.585 0.019  30.540  0.000    0.547    0.622
## 64        f5  =~ P1SINGSO   0.496 0.021  23.154  0.000    0.454    0.538
## 65        f5  =~ P1HELPAR   0.528 0.020  26.965  0.000    0.490    0.567
## 66        f5  =~ P1CHORES   0.415 0.023  17.675  0.000    0.369    0.461
## 67        f5  =~  P1GAMES   0.599 0.019  31.491  0.000    0.562    0.636
## 68        f5  =~ P1NATURE   0.552 0.020  27.965  0.000    0.513    0.590
## 69        f5  =~  P1BUILD   0.536 0.019  27.846  0.000    0.498    0.573
## 70        f5  =~  P1SPORT   0.480 0.020  23.556  0.000    0.440    0.520
## 71        f6  =~ P2LIBRAR   0.593 0.033  17.806  0.000    0.528    0.658
## 72        f6  =~ P2CONCRT   0.555 0.034  16.295  0.000    0.488    0.621
## 73        f6  =~ P2MUSEUM   0.611 0.034  17.999  0.000    0.545    0.678
## 74        f6  =~    P2ZOO   0.508 0.033  15.355  0.000    0.444    0.573
## 75   T2LEARN  ~~ T2EXTERN  -0.474 0.015 -31.483  0.000   -0.503   -0.444
## 76   T2LEARN  ~~ T2INTERN  -0.338 0.017 -19.877  0.000   -0.371   -0.305
## 77   T2LEARN  ~~ T2CONTRO   0.640 0.012  53.526  0.000    0.617    0.664
## 78   T2LEARN  ~~ T2INTERP   0.690 0.011  63.190  0.000    0.669    0.712
## 79  T2EXTERN  ~~ T2INTERN   0.271 0.016  16.707  0.000    0.239    0.303
## 80  T2EXTERN  ~~ T2CONTRO  -0.700 0.010 -71.226  0.000   -0.719   -0.680
## 81  T2EXTERN  ~~ T2INTERP  -0.579 0.013 -44.553  0.000   -0.605   -0.554
## 82  T2INTERN  ~~ T2CONTRO  -0.252 0.019 -13.476  0.000   -0.289   -0.215
## 83  T2INTERN  ~~ T2INTERP  -0.323 0.017 -18.685  0.000   -0.357   -0.290
## 84  T2CONTRO  ~~ T2INTERP   0.780 0.008  99.334  0.000    0.765    0.795
## 85        f1  ~~       f2   0.090 0.034   2.647  0.008    0.023    0.157
## 86        f1  ~~       f3  -0.156 0.031  -5.120  0.000   -0.216   -0.096
## 87        f1  ~~       f4  -0.033 0.033  -1.006  0.314   -0.099    0.032
## 88        f1  ~~       f5  -0.201 0.028  -7.248  0.000   -0.255   -0.147
## 89        f1  ~~       f6  -0.119 0.037  -3.170  0.002   -0.192   -0.045
## 90        f2  ~~       f3   0.190 0.035   5.347  0.000    0.120    0.259
## 91        f2  ~~       f4   0.176 0.037   4.773  0.000    0.103    0.248
## 92        f2  ~~       f5   0.035 0.032   1.084  0.278   -0.028    0.098
## 93        f2  ~~       f6   0.064 0.039   1.648  0.099   -0.012    0.141
## 94        f3  ~~       f4   0.224 0.034   6.586  0.000    0.157    0.290
## 95        f3  ~~       f5   0.250 0.030   8.359  0.000    0.192    0.309
## 96        f3  ~~       f6   0.511 0.035  14.490  0.000    0.442    0.580
## 97        f4  ~~       f5   0.151 0.031   4.892  0.000    0.090    0.211
## 98        f4  ~~       f6   0.289 0.038   7.524  0.000    0.214    0.364
## 99        f5  ~~       f6   0.398 0.033  12.069  0.000    0.333    0.462
## 100 P2BEPARN   |       t1  -0.642 0.027 -23.588  0.000   -0.696   -0.589
## 101 P2BEPARN   |       t2   0.043 0.025   1.691  0.091   -0.007    0.092
## 102 P2BEPARN   |       t3   0.282 0.026  11.019  0.000    0.232    0.332
## 103 P2CHDOES   |       t1  -0.174 0.025  -6.842  0.000   -0.223   -0.124
## 104 P2CHDOES   |       t2   1.063 0.031  34.090  0.000    1.002    1.124
## 105 P2CHDOES   |       t3   1.392 0.036  38.149  0.000    1.321    1.464
## 106 P2HRDWRM   |       t1   0.581 0.027  21.635  0.000    0.528    0.634
## 107 P2HRDWRM   |       t2   1.236 0.034  36.709  0.000    1.170    1.302
## 108 P2HRDWRM   |       t3   1.634 0.042  38.668  0.000    1.551    1.717
## 109 P2FLTRAP   |       t1   0.864 0.029  29.805  0.000    0.807    0.921
## 110 P2FLTRAP   |       t2   1.445 0.038  38.437  0.000    1.371    1.519
## 111 P2FLTRAP   |       t3   1.713 0.045  38.415  0.000    1.625    1.800
## 112 P2FEELAN   |       t1   0.626 0.027  23.082  0.000    0.573    0.679
## 113 P2FEELAN   |       t2   1.899 0.051  37.073  0.000    1.798    1.999
## 114 P2FEELAN   |       t3   2.352 0.077  30.470  0.000    2.201    2.504
## 115 P2CHHARD   |       t1   1.177 0.033  35.937  0.000    1.113    1.241
## 116 P2CHHARD   |       t2   1.749 0.046  38.233  0.000    1.659    1.839
## 117 P2CHHARD   |       t3   2.110 0.061  34.479  0.000    1.990    2.230
## 118 P2MOREWK   |       t1   0.630 0.027  23.199  0.000    0.577    0.683
## 119 P2MOREWK   |       t2   1.269 0.034  37.090  0.000    1.202    1.336
## 120 P2MOREWK   |       t3   1.558 0.040  38.722  0.000    1.479    1.637
## 121 P2HITCHO   |       t1   1.351 0.036  37.852  0.000    1.281    1.421
## 122 P2HITAPO   |       t1   0.574 0.027  21.400  0.000    0.521    0.626
## 123 P2HITPRV   |       t1   0.439 0.026  16.773  0.000    0.387    0.490
## 124 P2HITWAR   |       t1   1.086 0.031  34.509  0.000    1.025    1.148
## 125 P2ATTENB   |       t1  -0.159 0.025  -6.279  0.000   -0.209   -0.110
## 126 P2ATTENP   |       t1   0.656 0.027  24.015  0.000    0.603    0.710
## 127 P2PARADV   |       t1   1.630 0.042  38.675  0.000    1.548    1.713
## 128 P2PARGRP   |       t1  -0.666 0.027 -24.324  0.000   -0.720   -0.613
## 129 P2ATTENS   |       t1   0.004 0.025   0.161  0.872   -0.045    0.054
## 130 P2VOLUNT   |       t1   0.610 0.027  22.575  0.000    0.557    0.663
## 131 P2FUNDRS   |       t1   0.221 0.025   8.691  0.000    0.171    0.271
## 132 P2TVRULE   |       t1  -0.971 0.030 -32.271  0.000   -1.030   -0.912
## 133 P2TVRUL3   |       t1  -0.027 0.025  -1.087  0.277   -0.077    0.022
## 134 P2TVRUL2   |       t1  -0.923 0.030 -31.214  0.000   -0.981   -0.865
## 135 P1TELLST   |       t1  -1.311 0.035 -37.514  0.000   -1.380   -1.243
## 136 P1TELLST   |       t2   0.035 0.025   1.369  0.171   -0.015    0.084
## 137 P1TELLST   |       t3   0.735 0.028  26.361  0.000    0.680    0.790
## 138 P1SINGSO   |       t1  -1.457 0.038 -38.487  0.000   -1.531   -1.383
## 139 P1SINGSO   |       t2  -0.464 0.026 -17.687  0.000   -0.516   -0.413
## 140 P1SINGSO   |       t3   0.102 0.025   4.026  0.000    0.052    0.151
## 141 P1HELPAR   |       t1  -1.181 0.033 -35.995  0.000   -1.245   -1.117
## 142 P1HELPAR   |       t2   0.042 0.025   1.651  0.099   -0.008    0.091
## 143 P1HELPAR   |       t3   0.744 0.028  26.627  0.000    0.690    0.799
## 144 P1CHORES   |       t1  -1.608 0.042 -38.709  0.000   -1.689   -1.526
## 145 P1CHORES   |       t2  -0.639 0.027 -23.471  0.000   -0.692   -0.585
## 146 P1CHORES   |       t3  -0.124 0.025  -4.911  0.000   -0.174   -0.075
## 147  P1GAMES   |       t1  -1.512 0.039 -38.659  0.000   -1.588   -1.435
## 148  P1GAMES   |       t2  -0.119 0.025  -4.710  0.000   -0.169   -0.070
## 149  P1GAMES   |       t3   0.700 0.028  25.327  0.000    0.645    0.754
## 150 P1NATURE   |       t1  -0.476 0.026 -18.084  0.000   -0.527   -0.424
## 151 P1NATURE   |       t2   0.700 0.028  25.327  0.000    0.645    0.754
## 152 P1NATURE   |       t3   1.358 0.036  37.911  0.000    1.288    1.429
## 153  P1BUILD   |       t1  -0.763 0.028 -27.158  0.000   -0.818   -0.708
## 154  P1BUILD   |       t2   0.358 0.026  13.862  0.000    0.308    0.409
## 155  P1BUILD   |       t3   1.022 0.031  33.330  0.000    0.962    1.083
## 156  P1SPORT   |       t1  -1.109 0.032 -34.887  0.000   -1.171   -1.046
## 157  P1SPORT   |       t2  -0.054 0.025  -2.134  0.033   -0.103   -0.004
## 158  P1SPORT   |       t3   0.626 0.027  23.082  0.000    0.573    0.679
## 159 P2LIBRAR   |       t1   0.268 0.026  10.497  0.000    0.218    0.319
## 160 P2CONCRT   |       t1   0.534 0.027  20.062  0.000    0.481    0.586
## 161 P2MUSEUM   |       t1   0.829 0.029  28.920  0.000    0.773    0.885
## 162    P2ZOO   |       t1   0.375 0.026  14.461  0.000    0.324    0.425
## 163 P2BEPARN  ~~ P2BEPARN   0.704 0.024  29.802  0.000    0.657    0.750
## 164 P2CHDOES  ~~ P2CHDOES   0.524 0.026  20.052  0.000    0.473    0.575
## 165 P2HRDWRM  ~~ P2HRDWRM   0.766 0.026  29.988  0.000    0.716    0.816
## 166 P2FLTRAP  ~~ P2FLTRAP   0.494 0.033  14.970  0.000    0.430    0.559
## 167 P2FEELAN  ~~ P2FEELAN   0.601 0.029  20.680  0.000    0.544    0.657
## 168 P2CHHARD  ~~ P2CHHARD   0.457 0.038  11.897  0.000    0.382    0.533
## 169 P2MOREWK  ~~ P2MOREWK   0.563 0.029  19.344  0.000    0.506    0.620
## 170 P2HITCHO  ~~ P2HITCHO   0.411 0.061   6.756  0.000    0.292    0.530
## 171 P2HITAPO  ~~ P2HITAPO   0.476 0.038  12.623  0.000    0.402    0.550
## 172 P2HITPRV  ~~ P2HITPRV   0.646 0.033  19.545  0.000    0.581    0.710
## 173 P2HITWAR  ~~ P2HITWAR   0.467 0.050   9.355  0.000    0.369    0.565
## 174 P2ATTENB  ~~ P2ATTENB   0.682 0.034  19.823  0.000    0.614    0.749
## 175 P2ATTENP  ~~ P2ATTENP   0.760 0.032  23.689  0.000    0.697    0.823
## 176 P2PARADV  ~~ P2PARADV   0.848 0.038  22.217  0.000    0.773    0.923
## 177 P2PARGRP  ~~ P2PARGRP   0.858 0.028  31.179  0.000    0.804    0.912
## 178 P2ATTENS  ~~ P2ATTENS   0.614 0.036  16.884  0.000    0.543    0.685
## 179 P2VOLUNT  ~~ P2VOLUNT   0.608 0.038  15.819  0.000    0.533    0.683
## 180 P2FUNDRS  ~~ P2FUNDRS   0.726 0.032  22.685  0.000    0.663    0.789
## 181 P2TVRULE  ~~ P2TVRULE   0.309 0.049   6.252  0.000    0.212    0.406
## 182 P2TVRUL3  ~~ P2TVRUL3   0.412 0.039  10.602  0.000    0.336    0.488
## 183 P2TVRUL2  ~~ P2TVRUL2   0.352 0.048   7.320  0.000    0.258    0.446
## 184 P1TELLST  ~~ P1TELLST   0.658 0.022  29.408  0.000    0.614    0.702
## 185 P1SINGSO  ~~ P1SINGSO   0.754 0.021  35.457  0.000    0.712    0.796
## 186 P1HELPAR  ~~ P1HELPAR   0.721 0.021  34.842  0.000    0.680    0.762
## 187 P1CHORES  ~~ P1CHORES   0.828 0.019  42.483  0.000    0.790    0.866
## 188  P1GAMES  ~~  P1GAMES   0.641 0.023  28.149  0.000    0.597    0.686
## 189 P1NATURE  ~~ P1NATURE   0.696 0.022  31.941  0.000    0.653    0.738
## 190  P1BUILD  ~~  P1BUILD   0.713 0.021  34.595  0.000    0.673    0.753
## 191  P1SPORT  ~~  P1SPORT   0.769 0.020  39.295  0.000    0.731    0.808
## 192 P2LIBRAR  ~~ P2LIBRAR   0.649 0.039  16.427  0.000    0.571    0.726
## 193 P2CONCRT  ~~ P2CONCRT   0.692 0.038  18.333  0.000    0.618    0.766
## 194 P2MUSEUM  ~~ P2MUSEUM   0.626 0.042  15.095  0.000    0.545    0.708
## 195    P2ZOO  ~~    P2ZOO   0.741 0.034  22.019  0.000    0.675    0.807
## 196 C2RSCALE  ~~ C2RSCALE   0.803 0.014  57.073  0.000    0.775    0.830
## 197  T2LEARN  ~~  T2LEARN   0.968 0.009 107.076  0.000    0.950    0.985
## 198 T2EXTERN  ~~ T2EXTERN   0.959 0.010  95.652  0.000    0.939    0.978
## 199 T2INTERN  ~~ T2INTERN   0.993 0.005 216.996  0.000    0.984    1.002
## 200 T2CONTRO  ~~ T2CONTRO   0.965 0.010  99.939  0.000    0.946    0.984
## 201 T2INTERP  ~~ T2INTERP   0.956 0.011  88.494  0.000    0.935    0.977
## 202       f1  ~~       f1   1.000 0.000      NA     NA    1.000    1.000
## 203       f2  ~~       f2   1.000 0.000      NA     NA    1.000    1.000
## 204       f3  ~~       f3   1.000 0.000      NA     NA    1.000    1.000
## 205       f4  ~~       f4   1.000 0.000      NA     NA    1.000    1.000
## 206       f5  ~~       f5   1.000 0.000      NA     NA    1.000    1.000
## 207       f6  ~~       f6   1.000 0.000      NA     NA    1.000    1.000
## 208 P2BEPARN ~*~ P2BEPARN   1.000 0.000      NA     NA    1.000    1.000
## 209 P2CHDOES ~*~ P2CHDOES   1.000 0.000      NA     NA    1.000    1.000
## 210 P2HRDWRM ~*~ P2HRDWRM   1.000 0.000      NA     NA    1.000    1.000
## 211 P2FLTRAP ~*~ P2FLTRAP   1.000 0.000      NA     NA    1.000    1.000
## 212 P2FEELAN ~*~ P2FEELAN   1.000 0.000      NA     NA    1.000    1.000
## 213 P2CHHARD ~*~ P2CHHARD   1.000 0.000      NA     NA    1.000    1.000
## 214 P2MOREWK ~*~ P2MOREWK   1.000 0.000      NA     NA    1.000    1.000
## 215 P2HITCHO ~*~ P2HITCHO   1.000 0.000      NA     NA    1.000    1.000
## 216 P2HITAPO ~*~ P2HITAPO   1.000 0.000      NA     NA    1.000    1.000
## 217 P2HITPRV ~*~ P2HITPRV   1.000 0.000      NA     NA    1.000    1.000
## 218 P2HITWAR ~*~ P2HITWAR   1.000 0.000      NA     NA    1.000    1.000
## 219 P2ATTENB ~*~ P2ATTENB   1.000 0.000      NA     NA    1.000    1.000
## 220 P2ATTENP ~*~ P2ATTENP   1.000 0.000      NA     NA    1.000    1.000
## 221 P2PARADV ~*~ P2PARADV   1.000 0.000      NA     NA    1.000    1.000
## 222 P2PARGRP ~*~ P2PARGRP   1.000 0.000      NA     NA    1.000    1.000
## 223 P2ATTENS ~*~ P2ATTENS   1.000 0.000      NA     NA    1.000    1.000
## 224 P2VOLUNT ~*~ P2VOLUNT   1.000 0.000      NA     NA    1.000    1.000
## 225 P2FUNDRS ~*~ P2FUNDRS   1.000 0.000      NA     NA    1.000    1.000
## 226 P2TVRULE ~*~ P2TVRULE   1.000 0.000      NA     NA    1.000    1.000
## 227 P2TVRUL3 ~*~ P2TVRUL3   1.000 0.000      NA     NA    1.000    1.000
## 228 P2TVRUL2 ~*~ P2TVRUL2   1.000 0.000      NA     NA    1.000    1.000
## 229 P1TELLST ~*~ P1TELLST   1.000 0.000      NA     NA    1.000    1.000
## 230 P1SINGSO ~*~ P1SINGSO   1.000 0.000      NA     NA    1.000    1.000
## 231 P1HELPAR ~*~ P1HELPAR   1.000 0.000      NA     NA    1.000    1.000
## 232 P1CHORES ~*~ P1CHORES   1.000 0.000      NA     NA    1.000    1.000
## 233  P1GAMES ~*~  P1GAMES   1.000 0.000      NA     NA    1.000    1.000
## 234 P1NATURE ~*~ P1NATURE   1.000 0.000      NA     NA    1.000    1.000
## 235  P1BUILD ~*~  P1BUILD   1.000 0.000      NA     NA    1.000    1.000
## 236  P1SPORT ~*~  P1SPORT   1.000 0.000      NA     NA    1.000    1.000
## 237 P2LIBRAR ~*~ P2LIBRAR   1.000 0.000      NA     NA    1.000    1.000
## 238 P2CONCRT ~*~ P2CONCRT   1.000 0.000      NA     NA    1.000    1.000
## 239 P2MUSEUM ~*~ P2MUSEUM   1.000 0.000      NA     NA    1.000    1.000
## 240    P2ZOO ~*~    P2ZOO   1.000 0.000      NA     NA    1.000    1.000
## 241 P2BEPARN  ~1            0.000 0.000      NA     NA    0.000    0.000
## 242 P2CHDOES  ~1            0.000 0.000      NA     NA    0.000    0.000
## 243 P2HRDWRM  ~1            0.000 0.000      NA     NA    0.000    0.000
## 244 P2FLTRAP  ~1            0.000 0.000      NA     NA    0.000    0.000
## 245 P2FEELAN  ~1            0.000 0.000      NA     NA    0.000    0.000
## 246 P2CHHARD  ~1            0.000 0.000      NA     NA    0.000    0.000
## 247 P2MOREWK  ~1            0.000 0.000      NA     NA    0.000    0.000
## 248 P2HITCHO  ~1            0.000 0.000      NA     NA    0.000    0.000
## 249 P2HITAPO  ~1            0.000 0.000      NA     NA    0.000    0.000
## 250 P2HITPRV  ~1            0.000 0.000      NA     NA    0.000    0.000
## 251 P2HITWAR  ~1            0.000 0.000      NA     NA    0.000    0.000
## 252 P2ATTENB  ~1            0.000 0.000      NA     NA    0.000    0.000
## 253 P2ATTENP  ~1            0.000 0.000      NA     NA    0.000    0.000
## 254 P2PARADV  ~1            0.000 0.000      NA     NA    0.000    0.000
## 255 P2PARGRP  ~1            0.000 0.000      NA     NA    0.000    0.000
## 256 P2ATTENS  ~1            0.000 0.000      NA     NA    0.000    0.000
## 257 P2VOLUNT  ~1            0.000 0.000      NA     NA    0.000    0.000
## 258 P2FUNDRS  ~1            0.000 0.000      NA     NA    0.000    0.000
## 259 P2TVRULE  ~1            0.000 0.000      NA     NA    0.000    0.000
## 260 P2TVRUL3  ~1            0.000 0.000      NA     NA    0.000    0.000
## 261 P2TVRUL2  ~1            0.000 0.000      NA     NA    0.000    0.000
## 262 P1TELLST  ~1            0.000 0.000      NA     NA    0.000    0.000
## 263 P1SINGSO  ~1            0.000 0.000      NA     NA    0.000    0.000
## 264 P1HELPAR  ~1            0.000 0.000      NA     NA    0.000    0.000
## 265 P1CHORES  ~1            0.000 0.000      NA     NA    0.000    0.000
## 266  P1GAMES  ~1            0.000 0.000      NA     NA    0.000    0.000
## 267 P1NATURE  ~1            0.000 0.000      NA     NA    0.000    0.000
## 268  P1BUILD  ~1            0.000 0.000      NA     NA    0.000    0.000
## 269  P1SPORT  ~1            0.000 0.000      NA     NA    0.000    0.000
## 270 P2LIBRAR  ~1            0.000 0.000      NA     NA    0.000    0.000
## 271 P2CONCRT  ~1            0.000 0.000      NA     NA    0.000    0.000
## 272 P2MUSEUM  ~1            0.000 0.000      NA     NA    0.000    0.000
## 273    P2ZOO  ~1            0.000 0.000      NA     NA    0.000    0.000
## 274 C2RSCALE  ~1            1.541 0.202   7.623  0.000    1.145    1.938
## 275  T2LEARN  ~1            4.313 0.079  54.326  0.000    4.158    4.469
## 276 T2EXTERN  ~1            2.566 0.058  43.978  0.000    2.451    2.680
## 277 T2INTERN  ~1            2.958 0.056  52.695  0.000    2.848    3.068
## 278 T2CONTRO  ~1            4.901 0.083  58.795  0.000    4.737    5.064
## 279 T2INTERP  ~1            4.787 0.084  57.248  0.000    4.623    4.950
## 280       f1  ~1            0.000 0.000      NA     NA    0.000    0.000
## 281       f2  ~1            0.000 0.000      NA     NA    0.000    0.000
## 282       f3  ~1            0.000 0.000      NA     NA    0.000    0.000
## 283       f4  ~1            0.000 0.000      NA     NA    0.000    0.000
## 284       f5  ~1            0.000 0.000      NA     NA    0.000    0.000
## 285       f6  ~1            0.000 0.000      NA     NA    0.000    0.000
#The lines that we are interested are line 1 to line 11

Step 4: Run sensitivity analysis with the SEMsen package

In the SEMsen package, the sa.aco function is used to run the sensitivity analysis. The original model is complicated, and for illustration purpose, we analyzed 6 phantom variables, and paths for the C2RSCALE.

my.sa1 <- sa.aco(data= smith19.use,
                 model = model1,
                 sens.model = sens.model1,
                 k = 10,
                 opt.fun = quote(1/abs(new.par$pvalue[9]-0.05)),
                 rate.of.conv = .05,
                 paths = c(1:11),
                 seed=119,
                 max.iter = 100,
                 estimator="WLSMV",
                 ordered = factornames)
#15 out of 175 evaluations converged. 

In the sa.aco function, we specified the data(data) we are using, original model (model1), the sensitivity model (sens.model1), the optimization function (opt.fun), the convergence rate threshold (rate.of.conv)the paths that we are interested from the previous step (paths), a seed for reproducibility (seed), the estimator we used to conduct the analysis (estimator;using the lavaan package format), and the variables that are ordinal(ordered; using the lavaan package format).

Note: We only used k = 10 and max.iter = 100 so the analysis would run quickly for illustration purposes. For actual analyses, please specify these parameters as larger numbers (e.g., default value of k = 100 and max.iter = 1000). In addition, the convergence rate is set to be (rate.of.conv = .05) in this example as the model is complicated. An error message may show up like below:

#error message 
# Error in sa.aco(data= smith19.use,
#                  model = model1,
#                  sens.model = sens.model1,
#                  k = 10,rate.of.conv = .1, : 
#                   
#                 Sensitivity analysis models do not reach the specified convergence rate. 
#                 Please set a lower convergence rate threshold (i.e., rate. of. conv) or 
#                 reduce model complexicity)

Step 5: Results

The sens.tables function helps summarize the results of a sensitivity analysis.

my.sa.table = sens.tables(my.sa1) # get results

The sens.summary table provides estimates and p-values for each path in the original model. The phan.paths table provides the minimum, mean and maximum value of sensitivity parameters that we described in our sensitivity model at Step 2. The phan.min table provides the sensitivity parameters lead to the minimum coefficient for each path from sa.aco. The phan.max table provides the sensitivity parameters lead to the maximum coefficient for each path estimates from sa.aco. The p.paths table provides sensitivity parameters lead to change in significance foe each path. The NA indicates there is no change in p-value and meaningful sensitivity parameters that can change p-value.

my.sa.table$sens.summary
##                       model.est model.pvalue mean.est.sens  min.est.sens
## T2CONTRO~f1       -0.1445446263 5.672534e-09 -0.1445445513 -0.1445453225
## T2INTERP~f1       -0.1372948697 3.220701e-08 -0.1372944661 -0.1372950392
## T2LEARN~f1        -0.1161465928 3.557464e-06 -0.1110832468 -0.2609898707
## C2RSCALE~T2CONTRO -0.0785269002 2.599748e-02 -0.0753318919 -0.1004213881
## C2RSCALE~f6       -0.0658091048 1.247915e-01 -0.0593832142 -0.1107343431
## T2INTERP~f6       -0.0582568971 1.854210e-01 -0.0582647493 -0.0583085157
## T2INTERN~f3       -0.0546445782 1.400257e-01 -0.0546438300 -0.0546451212
## T2CONTRO~f6       -0.0533439553 2.502683e-01 -0.0533369842 -0.0533699567
## C2RSCALE~f2       -0.0478053252 9.044476e-02 -0.0469410164 -0.0650719618
## T2EXTERN~f6        0.0283456107 5.375607e-01 -0.0452896434 -0.8440902468
## T2LEARN~f4         0.0053384171 8.568420e-01 -0.0422538655 -0.6815210545
## T2LEARN~f6        -0.0305375590 4.931428e-01 -0.0397184257 -0.8642471071
## T2LEARN~f2        -0.0382625825 2.096279e-01 -0.0376372197 -0.2273087662
## T2INTERN~f6       -0.0327797770 4.486623e-01 -0.0327804185 -0.0327849972
## T2INTERP~f2       -0.0246496948 4.157732e-01 -0.0246527957 -0.0246712634
## C2RSCALE~T2INTERP -0.0248810443 3.884874e-01 -0.0237905506 -0.0557040649
## T2EXTERN~f3       -0.1251606892 8.509256e-04 -0.0220709380 -0.5981441959
## T2CONTRO~f2       -0.0207138567 4.969758e-01 -0.0207105641 -0.0207202900
## C2RSCALE~f1       -0.0169880165 4.933816e-01 -0.0195577234 -0.0388915254
## C2RSCALE~f5        0.0017189063 9.492271e-01 -0.0113484705 -0.0989397759
## T2INTERP~f4       -0.0039044391 8.959249e-01 -0.0039022435 -0.0039045852
## T2CONTRO~f5       -0.0036095049 9.003702e-01 -0.0036100114 -0.0036175548
## T2INTERN~f5       -0.0015122973 9.570646e-01 -0.0015122455 -0.0015127834
## T2CONTRO~f4       -0.0001404092 9.962962e-01 -0.0001425849 -0.0001592474
## C2RSCALE~T2INTERN  0.0036770123 8.490658e-01  0.0030015383 -0.0072204190
## T2INTERN~f1        0.0064944410 8.020084e-01  0.0064945100  0.0064943042
## T2EXTERN~f2        0.0347198310 2.518782e-01  0.0103434105 -0.1631032684
## T2INTERN~f4        0.0137869556 6.299069e-01  0.0137871852  0.0137867874
## T2INTERP~f5        0.0188911241 4.996183e-01  0.0188921184  0.0188908153
## C2RSCALE~f4        0.0438501902 9.878833e-02  0.0418164692 -0.0350299147
## T2INTERN~f2        0.0447558098 1.466241e-01  0.0447555307  0.0447537609
## C2RSCALE~T2EXTERN  0.0454009043 1.047413e-01  0.0490681985  0.0268152023
## T2LEARN~f5         0.0421933914 1.319447e-01  0.0498815401 -0.5054167960
## T2EXTERN~f4        0.0122678817 6.774808e-01  0.0507932861 -0.5303015652
## T2EXTERN~f5        0.0311271634 2.730746e-01  0.0650823756 -0.2997877071
## T2CONTRO~f3        0.1197561322 1.749667e-03  0.1197477775  0.1196844296
## C2RSCALE~f3        0.1498234539 7.525736e-06  0.1480770913  0.0657390418
## T2LEARN~f3         0.1106045344 3.715749e-03  0.1506356077 -0.4881633895
## T2INTERP~f3        0.1568265729 2.557126e-05  0.1568349314  0.1568259576
## T2EXTERN~f1        0.1583809130 7.146328e-11  0.1760751862  0.0439651742
## C2RSCALE~T2LEARN   0.4853128580 0.000000e+00  0.4828125863  0.4318415842
##                    max.est.sens
## T2CONTRO~f1       -0.1445425972
## T2INTERP~f1       -0.1372919437
## T2LEARN~f1         0.1419114735
## C2RSCALE~T2CONTRO -0.0348539196
## C2RSCALE~f6        0.0078880074
## T2INTERP~f6       -0.0582561794
## T2INTERN~f3       -0.0546391116
## T2CONTRO~f6       -0.0532773618
## C2RSCALE~f2       -0.0224232440
## T2EXTERN~f6        0.5336562364
## T2LEARN~f4         0.4278551493
## T2LEARN~f6         0.6091549553
## T2LEARN~f2         0.1825455390
## T2INTERN~f6       -0.0327783434
## T2INTERP~f2       -0.0246493892
## C2RSCALE~T2INTERP  0.0016133701
## T2EXTERN~f3        0.4450368117
## T2CONTRO~f2       -0.0206871256
## C2RSCALE~f1       -0.0079199773
## C2RSCALE~f5        0.0509632547
## T2INTERP~f4       -0.0038897621
## T2CONTRO~f5       -0.0036036597
## T2INTERN~f5       -0.0015116692
## T2CONTRO~f4       -0.0001353881
## C2RSCALE~T2INTERN  0.0128769548
## T2INTERN~f1        0.0064948260
## T2EXTERN~f2        0.2091424014
## T2INTERN~f4        0.0137885043
## T2INTERP~f5        0.0188972207
## C2RSCALE~f4        0.0985734639
## T2INTERN~f2        0.0447559818
## C2RSCALE~T2EXTERN  0.0991216923
## T2LEARN~f5         1.2390163456
## T2EXTERN~f4        0.5835144174
## T2EXTERN~f5        1.2834450825
## T2CONTRO~f3        0.1197768658
## C2RSCALE~f3        0.1985251435
## T2LEARN~f3         1.0027244773
## T2INTERP~f3        0.1568834567
## T2EXTERN~f1        0.4284066793
## C2RSCALE~T2LEARN   0.5530986059
my.sa.table$phan.paths
##                    mean.phan   min.phan  max.phan
## T2EXTERN~phantom -0.23241566 -1.3517301 0.5478649
## T2LEARN~phantom  -0.17684069 -1.2918587 0.6248955
## f5~phantom       -0.02110502 -0.3992532 0.7794786
## C2RSCALE~phantom  0.00684393 -0.1119661 0.1082448
## f4~phantom        0.13047824 -0.7186094 0.5766870
## f3~phantom        0.27881719 -0.5192671 0.6243018
my.sa.table$phan.min
##                   T2LEARN~phantom T2EXTERN~phantom C2RSCALE~phantom  f3~phantom
## C2RSCALE~T2LEARN       0.55218125       -0.4747524     0.0525956099 -0.07833205
## C2RSCALE~T2EXTERN     -0.04070211       -0.2690685    -0.0468532735  0.30651642
## C2RSCALE~T2INTERN      0.55218125       -0.4747524     0.0525956099 -0.07833205
## C2RSCALE~T2CONTRO     -1.05580059        0.1057519     0.0990550986  0.57939657
## C2RSCALE~T2INTERP     -1.05580059        0.1057519     0.0990550986  0.57939657
## C2RSCALE~f1           -1.29185870       -1.3517301     0.1082448198  0.33840983
## C2RSCALE~f2           -0.24734577        0.3501010     0.0719601880 -0.51926712
## C2RSCALE~f3           -1.05580059        0.1057519     0.0990550986  0.57939657
## C2RSCALE~f4           -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## C2RSCALE~f5           -1.29185870       -1.3517301     0.1082448198  0.33840983
## C2RSCALE~f6           -0.24734577        0.3501010     0.0719601880 -0.51926712
## T2LEARN~f1            -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## T2LEARN~f2            -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2LEARN~f3            -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## T2LEARN~f4            -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## T2LEARN~f5            -1.05580059        0.1057519     0.0990550986  0.57939657
## T2LEARN~f6            -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2EXTERN~f1           -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## T2EXTERN~f2           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2EXTERN~f3           -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## T2EXTERN~f4           -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## T2EXTERN~f5           -0.97205864       -0.7678565    -0.1119660675 -0.47950875
## T2EXTERN~f6           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2INTERN~f1           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2INTERN~f2           -0.31730618        0.3385820     0.0005171162  0.20901534
## T2INTERN~f3           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2INTERN~f4           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2INTERN~f5           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2INTERN~f6           -0.31730618        0.3385820     0.0005171162  0.20901534
## T2CONTRO~f1           -0.31730618        0.3385820     0.0005171162  0.20901534
## T2CONTRO~f2           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2CONTRO~f3           -0.31730618        0.3385820     0.0005171162  0.20901534
## T2CONTRO~f4           -0.31730618        0.3385820     0.0005171162  0.20901534
## T2CONTRO~f5           -0.31730618        0.3385820     0.0005171162  0.20901534
## T2CONTRO~f6           -1.29185870       -1.3517301     0.1082448198  0.33840983
## T2INTERP~f1           -0.37615240       -0.2219899    -0.0342680283  0.58754335
## T2INTERP~f2           -0.31730618        0.3385820     0.0005171162  0.20901534
## T2INTERP~f3            0.55218125       -0.4747524     0.0525956099 -0.07833205
## T2INTERP~f4            0.62489554       -0.9184887     0.0904980088  0.45849095
## T2INTERP~f5           -0.04070211       -0.2690685    -0.0468532735  0.30651642
## T2INTERP~f6           -0.31730618        0.3385820     0.0005171162  0.20901534
##                    f4~phantom  f5~phantom
## C2RSCALE~T2LEARN  -0.26408850  0.20684082
## C2RSCALE~T2EXTERN -0.05317235 -0.34366777
## C2RSCALE~T2INTERN -0.26408850  0.20684082
## C2RSCALE~T2CONTRO  0.04555417 -0.39925324
## C2RSCALE~T2INTERP  0.04555417 -0.39925324
## C2RSCALE~f1        0.34219070  0.77947860
## C2RSCALE~f2       -0.71860936 -0.22442134
## C2RSCALE~f3        0.04555417 -0.39925324
## C2RSCALE~f4       -0.67428477 -0.39220692
## C2RSCALE~f5        0.34219070  0.77947860
## C2RSCALE~f6       -0.71860936 -0.22442134
## T2LEARN~f1        -0.67428477 -0.39220692
## T2LEARN~f2         0.34219070  0.77947860
## T2LEARN~f3        -0.67428477 -0.39220692
## T2LEARN~f4        -0.67428477 -0.39220692
## T2LEARN~f5         0.04555417 -0.39925324
## T2LEARN~f6         0.34219070  0.77947860
## T2EXTERN~f1       -0.67428477 -0.39220692
## T2EXTERN~f2        0.34219070  0.77947860
## T2EXTERN~f3       -0.67428477 -0.39220692
## T2EXTERN~f4       -0.67428477 -0.39220692
## T2EXTERN~f5       -0.67428477 -0.39220692
## T2EXTERN~f6        0.34219070  0.77947860
## T2INTERN~f1        0.34219070  0.77947860
## T2INTERN~f2        0.20038571  0.18558215
## T2INTERN~f3        0.34219070  0.77947860
## T2INTERN~f4        0.34219070  0.77947860
## T2INTERN~f5        0.34219070  0.77947860
## T2INTERN~f6        0.20038571  0.18558215
## T2CONTRO~f1        0.20038571  0.18558215
## T2CONTRO~f2        0.34219070  0.77947860
## T2CONTRO~f3        0.20038571  0.18558215
## T2CONTRO~f4        0.20038571  0.18558215
## T2CONTRO~f5        0.20038571  0.18558215
## T2CONTRO~f6        0.34219070  0.77947860
## T2INTERP~f1        0.26334431 -0.04515809
## T2INTERP~f2        0.20038571  0.18558215
## T2INTERP~f3       -0.26408850  0.20684082
## T2INTERP~f4        0.57668697 -0.18007001
## T2INTERP~f5       -0.05317235 -0.34366777
## T2INTERP~f6        0.20038571  0.18558215
my.sa.table$phan.max
##                   T2LEARN~phantom T2EXTERN~phantom C2RSCALE~phantom  f3~phantom
## C2RSCALE~T2LEARN       -1.0558006        0.1057519     0.0990550986  0.57939657
## C2RSCALE~T2EXTERN       0.6248955       -0.9184887     0.0904980088  0.45849095
## C2RSCALE~T2INTERN      -1.0558006        0.1057519     0.0990550986  0.57939657
## C2RSCALE~T2CONTRO       0.6248955       -0.9184887     0.0904980088  0.45849095
## C2RSCALE~T2INTERP       0.5521812       -0.4747524     0.0525956099 -0.07833205
## C2RSCALE~f1            -0.2473458        0.3501010     0.0719601880 -0.51926712
## C2RSCALE~f2            -0.9720586       -0.7678565    -0.1119660675 -0.47950875
## C2RSCALE~f3            -0.2473458        0.3501010     0.0719601880 -0.51926712
## C2RSCALE~f4            -0.2473458        0.3501010     0.0719601880 -0.51926712
## C2RSCALE~f5            -1.0558006        0.1057519     0.0990550986  0.57939657
## C2RSCALE~f6            -0.9720586       -0.7678565    -0.1119660675 -0.47950875
## T2LEARN~f1             -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2LEARN~f2             -0.9720586       -0.7678565    -0.1119660675 -0.47950875
## T2LEARN~f3             -1.0558006        0.1057519     0.0990550986  0.57939657
## T2LEARN~f4             -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2LEARN~f5             -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2LEARN~f6             -0.9720586       -0.7678565    -0.1119660675 -0.47950875
## T2EXTERN~f1            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2EXTERN~f2            -0.9720586       -0.7678565    -0.1119660675 -0.47950875
## T2EXTERN~f3            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2EXTERN~f4             0.6248955       -0.9184887     0.0904980088  0.45849095
## T2EXTERN~f5            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2EXTERN~f6            -0.9720586       -0.7678565    -0.1119660675 -0.47950875
## T2INTERN~f1            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERN~f2            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2INTERN~f3            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERN~f4            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERN~f5            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERN~f6            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2CONTRO~f1            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2CONTRO~f2            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2CONTRO~f3            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2CONTRO~f4            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2CONTRO~f5            -1.2918587       -1.3517301     0.1082448198  0.33840983
## T2CONTRO~f6            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERP~f1            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERP~f2             0.5521812       -0.4747524     0.0525956099 -0.07833205
## T2INTERP~f3            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERP~f4            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERP~f5            -0.3173062        0.3385820     0.0005171162  0.20901534
## T2INTERP~f6             0.2764462        0.3808589     0.0499169125  0.23533817
##                    f4~phantom f5~phantom
## C2RSCALE~T2LEARN   0.04555417 -0.3992532
## C2RSCALE~T2EXTERN  0.57668697 -0.1800700
## C2RSCALE~T2INTERN  0.04555417 -0.3992532
## C2RSCALE~T2CONTRO  0.57668697 -0.1800700
## C2RSCALE~T2INTERP -0.26408850  0.2068408
## C2RSCALE~f1       -0.71860936 -0.2244213
## C2RSCALE~f2       -0.67428477 -0.3922069
## C2RSCALE~f3       -0.71860936 -0.2244213
## C2RSCALE~f4       -0.71860936 -0.2244213
## C2RSCALE~f5        0.04555417 -0.3992532
## C2RSCALE~f6       -0.67428477 -0.3922069
## T2LEARN~f1         0.34219070  0.7794786
## T2LEARN~f2        -0.67428477 -0.3922069
## T2LEARN~f3         0.04555417 -0.3992532
## T2LEARN~f4         0.34219070  0.7794786
## T2LEARN~f5         0.34219070  0.7794786
## T2LEARN~f6        -0.67428477 -0.3922069
## T2EXTERN~f1        0.34219070  0.7794786
## T2EXTERN~f2       -0.67428477 -0.3922069
## T2EXTERN~f3        0.34219070  0.7794786
## T2EXTERN~f4        0.57668697 -0.1800700
## T2EXTERN~f5        0.34219070  0.7794786
## T2EXTERN~f6       -0.67428477 -0.3922069
## T2INTERN~f1        0.20038571  0.1855821
## T2INTERN~f2        0.34219070  0.7794786
## T2INTERN~f3        0.20038571  0.1855821
## T2INTERN~f4        0.20038571  0.1855821
## T2INTERN~f5        0.20038571  0.1855821
## T2INTERN~f6        0.34219070  0.7794786
## T2CONTRO~f1        0.34219070  0.7794786
## T2CONTRO~f2        0.20038571  0.1855821
## T2CONTRO~f3        0.34219070  0.7794786
## T2CONTRO~f4        0.34219070  0.7794786
## T2CONTRO~f5        0.34219070  0.7794786
## T2CONTRO~f6        0.20038571  0.1855821
## T2INTERP~f1        0.20038571  0.1855821
## T2INTERP~f2       -0.26408850  0.2068408
## T2INTERP~f3        0.20038571  0.1855821
## T2INTERP~f4        0.20038571  0.1855821
## T2INTERP~f5        0.20038571  0.1855821
## T2INTERP~f6        0.46095003  0.5284704
my.sa.table$p.paths
##                        p.value    p.changed T2LEARN~phantom T2EXTERN~phantom
## C2RSCALE~f5       9.492271e-01 0.0002804033      -1.2918587     -1.351730085
## C2RSCALE~T2EXTERN 1.047413e-01 0.0075055104       0.2699275      0.547864851
## T2LEARN~f5        1.319447e-01 0.0105797885       0.1868681      0.004585214
## T2EXTERN~f6       5.375607e-01 0.0128454029      -0.3173062      0.338581972
## T2EXTERN~f5       2.730746e-01 0.0137743468      -0.2454073     -0.546981432
## T2LEARN~f6        4.931428e-01 0.0199000254       0.2764462      0.380858850
## T2EXTERN~f4       6.774808e-01 0.0227129668      -0.3761524     -0.221989930
## T2LEARN~f4        8.568420e-01 0.0236271337       0.1868681      0.004585214
## T2LEARN~f2        2.096279e-01 0.0373372490      -0.3173062      0.338581972
## C2RSCALE~f2       9.044476e-02 0.0460107125       0.1868681      0.004585214
## C2RSCALE~f6       1.247915e-01 0.0489983864       0.2699275      0.547864851
## C2RSCALE~f4       9.878833e-02 0.0492902306      -0.3761524     -0.221989930
## T2EXTERN~f2       2.518782e-01 0.0494754271       0.5521812     -0.474752423
## C2RSCALE~f3       7.525736e-06 0.0512910622      -1.0558006      0.105751894
## C2RSCALE~T2CONTRO 2.599748e-02 0.0717371949       0.2699275      0.547864851
## T2EXTERN~f3       8.509256e-04 0.1433011796      -0.3761524     -0.221989930
## T2LEARN~f3        3.715749e-03 0.1633065843      -0.2473458      0.350101035
## T2EXTERN~f1       7.146328e-11 0.2607842095      -0.9720586     -0.767856540
## C2RSCALE~T2LEARN  0.000000e+00           NA              NA               NA
## C2RSCALE~T2INTERN 8.490658e-01           NA              NA               NA
## C2RSCALE~T2INTERP 3.884874e-01           NA              NA               NA
## C2RSCALE~f1       4.933816e-01           NA              NA               NA
## T2LEARN~f1        3.557464e-06           NA              NA               NA
## T2INTERN~f1       8.020084e-01           NA              NA               NA
## T2INTERN~f2       1.466241e-01           NA              NA               NA
## T2INTERN~f3       1.400257e-01           NA              NA               NA
## T2INTERN~f4       6.299069e-01           NA              NA               NA
## T2INTERN~f5       9.570646e-01           NA              NA               NA
## T2INTERN~f6       4.486623e-01           NA              NA               NA
## T2CONTRO~f1       5.672534e-09           NA              NA               NA
## T2CONTRO~f2       4.969758e-01           NA              NA               NA
## T2CONTRO~f3       1.749667e-03           NA              NA               NA
## T2CONTRO~f4       9.962962e-01           NA              NA               NA
## T2CONTRO~f5       9.003702e-01           NA              NA               NA
## T2CONTRO~f6       2.502683e-01           NA              NA               NA
## T2INTERP~f1       3.220701e-08           NA              NA               NA
## T2INTERP~f2       4.157732e-01           NA              NA               NA
## T2INTERP~f3       2.557126e-05           NA              NA               NA
## T2INTERP~f4       8.959249e-01           NA              NA               NA
## T2INTERP~f5       4.996183e-01           NA              NA               NA
## T2INTERP~f6       1.854210e-01           NA              NA               NA
##                   C2RSCALE~phantom  f3~phantom  f4~phantom  f5~phantom
## C2RSCALE~f5           0.1082448198  0.33840983  0.34219070  0.77947860
## C2RSCALE~T2EXTERN    -0.0800522058  0.42483437  0.49088616 -0.34633287
## T2LEARN~f5           -0.0471767154  0.57246992  0.38514600 -0.09567508
## T2EXTERN~f6           0.0005171162  0.20901534  0.20038571  0.18558215
## T2EXTERN~f5          -0.0192800832  0.58987744  0.44088352 -0.13340756
## T2LEARN~f6            0.0499169125  0.23533817  0.46095003  0.52847043
## T2EXTERN~f4          -0.0342680283  0.58754335  0.26334431 -0.04515809
## T2LEARN~f4           -0.0471767154  0.57246992  0.38514600 -0.09567508
## T2LEARN~f2            0.0005171162  0.20901534  0.20038571  0.18558215
## C2RSCALE~f2          -0.0471767154  0.57246992  0.38514600 -0.09567508
## C2RSCALE~f6          -0.0800522058  0.42483437  0.49088616 -0.34633287
## C2RSCALE~f4          -0.0342680283  0.58754335  0.26334431 -0.04515809
## T2EXTERN~f2           0.0525956099 -0.07833205 -0.26408850  0.20684082
## C2RSCALE~f3           0.0990550986  0.57939657  0.04555417 -0.39925324
## C2RSCALE~T2CONTRO    -0.0800522058  0.42483437  0.49088616 -0.34633287
## T2EXTERN~f3          -0.0342680283  0.58754335  0.26334431 -0.04515809
## T2LEARN~f3            0.0719601880 -0.51926712 -0.71860936 -0.22442134
## T2EXTERN~f1          -0.1119660675 -0.47950875 -0.67428477 -0.39220692
## C2RSCALE~T2LEARN                NA          NA          NA          NA
## C2RSCALE~T2INTERN               NA          NA          NA          NA
## C2RSCALE~T2INTERP               NA          NA          NA          NA
## C2RSCALE~f1                     NA          NA          NA          NA
## T2LEARN~f1                      NA          NA          NA          NA
## T2INTERN~f1                     NA          NA          NA          NA
## T2INTERN~f2                     NA          NA          NA          NA
## T2INTERN~f3                     NA          NA          NA          NA
## T2INTERN~f4                     NA          NA          NA          NA
## T2INTERN~f5                     NA          NA          NA          NA
## T2INTERN~f6                     NA          NA          NA          NA
## T2CONTRO~f1                     NA          NA          NA          NA
## T2CONTRO~f2                     NA          NA          NA          NA
## T2CONTRO~f3                     NA          NA          NA          NA
## T2CONTRO~f4                     NA          NA          NA          NA
## T2CONTRO~f5                     NA          NA          NA          NA
## T2CONTRO~f6                     NA          NA          NA          NA
## T2INTERP~f1                     NA          NA          NA          NA
## T2INTERP~f2                     NA          NA          NA          NA
## T2INTERP~f3                     NA          NA          NA          NA
## T2INTERP~f4                     NA          NA          NA          NA
## T2INTERP~f5                     NA          NA          NA          NA
## T2INTERP~f6                     NA          NA          NA          NA

References

Leite, W., Shen, Z., Marcoulides, K., Fish, C., & Harring, J. (2022). Using ant colony optimization for sensitivity analysis in structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 29 (1), 47-56.