Interaction Models with plssem

This vignette shows how to estimate interaction models, with both continuous and ordered (categorical) data.

Model Syntax

m <- '
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  Y ~ X + Z + X:Z
'

Continuous Indicators

fit_cont <- pls(
  m,
  data      = modsem::oneInt,
  bootstrap = TRUE,
  boot.R    = 50
)
summary(fit_cont)
#> plssem (0.1.2) ended normally after 3 iterations
#>   Estimator                                       PLSc
#>   Link                                          LINEAR
#>                                                       
#>   Number of observations                          2000
#>   Number of iterations                               3
#>   Number of latent variables                         3
#>   Number of observed variables                       9
#> 
#> Fit Measures:
#>   Chi-Square                                    56.757
#>   Degrees of Freedom                                24
#>   SRMR                                           0.006
#>   RMSEA                                          0.026
#> 
#> R-squared (indicators):
#>   x1                                             0.863
#>   x2                                             0.819
#>   x3                                             0.809
#>   z1                                             0.830
#>   z2                                             0.827
#>   z3                                             0.843
#>   y1                                             0.934
#>   y2                                             0.919
#>   y3                                             0.923
#> 
#> R-squared (latents):
#>   Y                                              0.604
#> 
#> Latent Variables:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>   X =~          
#>     x1              0.929      0.013   74.030    0.000
#>     x2              0.905      0.014   63.777    0.000
#>     x3              0.899      0.014   66.129    0.000
#>   Z =~          
#>     z1              0.911      0.015   59.585    0.000
#>     z2              0.909      0.019   49.061    0.000
#>     z3              0.918      0.016   55.761    0.000
#>   Y =~          
#>     y1              0.966      0.006  155.072    0.000
#>     y2              0.959      0.007  144.338    0.000
#>     y3              0.961      0.006  161.885    0.000
#> 
#> Regressions:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>   Y ~           
#>     X               0.423      0.015   28.840    0.000
#>     Z               0.361      0.015   24.305    0.000
#>     X:Z             0.452      0.019   24.072    0.000
#> 
#> Covariances:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>   X ~~          
#>     Z               0.201      0.025    8.006    0.000
#>     X:Z             0.018      0.038    0.474    0.635
#>   Z ~~          
#>     X:Z             0.060      0.046    1.304    0.192
#> 
#> Variances:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>     X               1.000      0.026   37.965    0.000
#>     Z               1.000      0.023   43.170    0.000
#>    .Y               0.396      0.015   26.775    0.000
#>     X:Z             1.013      0.069   14.632    0.000
#>    .x1              0.137      0.023    5.892    0.000
#>    .x2              0.181      0.026    7.023    0.000
#>    .x3              0.191      0.024    7.815    0.000
#>    .z1              0.170      0.028    6.131    0.000
#>    .z2              0.173      0.034    5.138    0.000
#>    .z3              0.157      0.030    5.211    0.000
#>    .y1              0.066      0.012    5.496    0.000
#>    .y2              0.081      0.013    6.371    0.000
#>    .y3              0.077      0.011    6.799    0.000

Ordered Indicators

fit_ord <- pls(
  m,
  data      = oneIntOrdered,
  bootstrap = TRUE,
  boot.R    = 50,
  ordered   = colnames(oneIntOrdered) # explicitly specify variables as ordered
)
summary(fit_ord)
#> plssem (0.1.2) ended normally after 53 iterations
#>   Estimator                                  MCOrdPLSc
#>   Link                                          PROBIT
#>                                                       
#>   Number of observations                          2000
#>   Number of iterations                              53
#>   Number of latent variables                         3
#>   Number of observed variables                       9
#> 
#> Fit Measures:
#>   Chi-Square                                    20.754
#>   Degrees of Freedom                                24
#>   SRMR                                           0.012
#>   RMSEA                                          0.000
#> 
#> R-squared (indicators):
#>   x1                                             0.931
#>   x2                                             0.900
#>   x3                                             0.906
#>   z1                                             0.935
#>   z2                                             0.901
#>   z3                                             0.913
#>   y1                                             0.972
#>   y2                                             0.952
#>   y3                                             0.962
#> 
#> R-squared (latents):
#>   Y                                              0.571
#> 
#> Latent Variables:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>   X =~          
#>     x1              0.931      0.007  141.112    0.000
#>     x2              0.900      0.008  119.014    0.000
#>     x3              0.906      0.007  123.232    0.000
#>   Z =~          
#>     z1              0.935      0.006  149.821    0.000
#>     z2              0.901      0.009  102.342    0.000
#>     z3              0.913      0.008  110.558    0.000
#>   Y =~          
#>     y1              0.972      0.004  221.923    0.000
#>     y2              0.952      0.005  187.673    0.000
#>     y3              0.962      0.004  225.935    0.000
#> 
#> Regressions:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>   Y ~           
#>     X               0.417      0.017   24.082    0.000
#>     Z               0.357      0.017   21.191    0.000
#>     X:Z             0.446      0.018   25.221    0.000
#> 
#> Covariances:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>   X ~~          
#>     Z               0.194      0.023    8.254    0.000
#>     X:Z             0.005                             
#>   Z ~~          
#>     X:Z             0.003                             
#> 
#> Variances:
#>                  Estimate  Std.Error  z.value  P(>|z|)
#>     X               1.000                             
#>     Z               1.000                             
#>    .Y               0.429                             
#>     X:Z             1.049                             
#>    .x1              0.069                             
#>    .x2              0.100                             
#>    .x3              0.094                             
#>    .z1              0.065                             
#>    .z2              0.099                             
#>    .z3              0.087                             
#>    .y1              0.028                             
#>    .y2              0.048                             
#>    .y3              0.038