This vignette shows examples of multilevel random slopes and intercept models, with both continuous and ordinal data.
slopes_model <- "
X =~ x1 + x2 + x3
Z =~ z1 + z2 + z3
Y =~ y1 + y2 + y3
W =~ w1 + w2 + w3
Y ~ X + Z + (1 + X + Z | cluster)
W ~ X + Z + (1 + X + Z | cluster)
"fit_slopes_cont <- pls(
slopes_model,
data = randomSlopes,
bootstrap = TRUE,
sample = 50
)
summary(fit_slopes_cont)
#> plssem (0.1.0) ended normally after 3 iterations
#>
#> Estimator PLSc-MLM
#> Link LINEAR
#>
#> Number of observations 5000
#> Number of iterations 3
#> Number of latent variables 4
#> Number of observed variables 18
#>
#> R-squared (indicators):
#> x1 0.860
#> x2 0.683
#> x3 0.772
#> z1 0.839
#> z2 0.694
#> z3 0.759
#> y1 0.838
#> y2 0.726
#> y3 0.750
#> w1 0.840
#> w2 0.695
#> w3 0.771
#>
#> R-squared (latents):
#> Y 0.533
#> W 0.547
#>
#> Latent Variables:
#> Estimate Std.Error z.value P(>|z|)
#> X =~
#> x1 0.927 0.009 98.707 0.000
#> x2 0.826 0.010 79.620 0.000
#> x3 0.879 0.008 114.894 0.000
#> Z =~
#> z1 0.916 0.010 87.450 0.000
#> z2 0.833 0.012 71.560 0.000
#> z3 0.871 0.009 94.854 0.000
#> Y =~
#> y1 0.915 0.011 85.376 0.000
#> y2 0.852 0.011 76.649 0.000
#> y3 0.866 0.014 61.430 0.000
#> W =~
#> w1 0.916 0.011 86.168 0.000
#> w2 0.834 0.016 50.799 0.000
#> w3 0.878 0.014 64.442 0.000
#>
#> Regressions:
#> Estimate Std.Error z.value P(>|z|)
#> Y ~
#> X 0.293 0.021 13.836 0.000
#> Z 0.444 0.038 11.540 0.000
#> W ~
#> X 0.393 0.033 11.946 0.000
#> Z 0.248 0.042 5.868 0.000
#>
#> Intercepts:
#> Estimate Std.Error z.value P(>|z|)
#> .Y 0.009 0.005 1.790 0.074
#> .W 0.009 0.008 1.249 0.212
#>
#> Covariances:
#> Estimate Std.Error z.value P(>|z|)
#> X ~~
#> Z 0.175 0.012 14.107 0.000
#> Y~X ~~
#> Y~1 -0.003 0.006 -0.579 0.562
#> Y~Z ~~
#> Y~1 -0.024 0.014 -1.769 0.077
#> Y~X 0.012 0.009 1.422 0.155
#> W~X ~~
#> W~1 0.003 0.012 0.256 0.798
#> W~Z ~~
#> W~1 0.009 0.011 0.815 0.415
#> W~X 0.013 0.012 1.112 0.266
#>
#> Variances:
#> Estimate Std.Error z.value P(>|z|)
#> X 1.000
#> Z 1.000
#> .Y 0.467 0.028 16.699 0.000
#> .W 0.453 0.031 14.606 0.000
#> .x1 0.140 0.017 8.039 0.000
#> .x2 0.317 0.017 18.434 0.000
#> .x3 0.228 0.013 16.940 0.000
#> .z1 0.161 0.019 8.381 0.000
#> .z2 0.306 0.019 15.729 0.000
#> .z3 0.241 0.016 15.072 0.000
#> .y1 0.162 0.020 8.280 0.000
#> .y2 0.274 0.019 14.492 0.000
#> .y3 0.250 0.024 10.343 0.000
#> .w1 0.160 0.020 8.201 0.000
#> .w2 0.305 0.027 11.250 0.000
#> .w3 0.229 0.024 9.599 0.000
#> Y~1 0.079 0.019 4.236 0.000
#> Y~X 0.018 0.004 4.099 0.000
#> Y~Z 0.105 0.017 6.253 0.000
#> W~1 0.054 0.012 4.705 0.000
#> W~X 0.095 0.015 6.326 0.000
#> W~Z 0.144 0.026 5.483 0.000fit_slopes_ord <- pls(
slopes_model,
data = randomSlopesOrdered,
bootstrap = TRUE,
sample = 50,
ordered = colnames(randomSlopesOrdered) # explicitly specify variables as ordered
)
summary(fit_slopes_ord)
#> plssem (0.1.0) ended normally after 3 iterations
#>
#> Estimator OrdPLSc-MLM
#> Link PROBIT
#>
#> Number of observations 5000
#> Number of iterations 3
#> Number of latent variables 4
#> Number of observed variables 18
#>
#> R-squared (indicators):
#> x1 0.870
#> x2 0.669
#> x3 0.789
#> z1 0.841
#> z2 0.714
#> z3 0.758
#> y1 0.844
#> y2 0.711
#> y3 0.754
#> w1 0.835
#> w2 0.681
#> w3 0.785
#>
#> R-squared (latents):
#> Y 0.531
#> W 0.544
#>
#> Latent Variables:
#> Estimate Std.Error z.value P(>|z|)
#> X =~
#> x1 0.933 0.011 87.644 0.000
#> x2 0.818 0.011 72.002 0.000
#> x3 0.888 0.010 86.496 0.000
#> Z =~
#> z1 0.917 0.009 100.749 0.000
#> z2 0.845 0.013 66.353 0.000
#> z3 0.871 0.010 83.421 0.000
#> Y =~
#> y1 0.918 0.009 97.607 0.000
#> y2 0.843 0.012 71.023 0.000
#> y3 0.869 0.014 62.273 0.000
#> W =~
#> w1 0.914 0.013 69.631 0.000
#> w2 0.825 0.014 57.186 0.000
#> w3 0.886 0.016 56.953 0.000
#>
#> Regressions:
#> Estimate Std.Error z.value P(>|z|)
#> Y ~
#> X 0.290 0.022 13.000 0.000
#> Z 0.451 0.033 13.676 0.000
#> W ~
#> X 0.391 0.033 11.720 0.000
#> Z 0.245 0.052 4.729 0.000
#>
#> Intercepts:
#> Estimate Std.Error z.value P(>|z|)
#> .Y 0.011 0.005 2.204 0.028
#> .W 0.009 0.008 1.045 0.296
#>
#> Covariances:
#> Estimate Std.Error z.value P(>|z|)
#> X ~~
#> Z 0.168 0.014 11.947 0.000
#> Y~X ~~
#> Y~1 -0.006 0.005 -1.401 0.161
#> Y~Z ~~
#> Y~1 -0.024 0.013 -1.825 0.068
#> Y~X 0.012 0.009 1.400 0.161
#> W~X ~~
#> W~1 0.004 0.011 0.335 0.738
#> W~Z ~~
#> W~1 0.009 0.011 0.874 0.382
#> W~X 0.016 0.013 1.305 0.192
#>
#> Variances:
#> Estimate Std.Error z.value P(>|z|)
#> X 1.000
#> Z 1.000
#> .Y 0.469 0.028 16.941 0.000
#> .W 0.456 0.035 12.917 0.000
#> .x1 0.130 0.020 6.552 0.000
#> .x2 0.331 0.019 17.840 0.000
#> .x3 0.211 0.018 11.629 0.000
#> .z1 0.159 0.017 9.487 0.000
#> .z2 0.286 0.021 13.325 0.000
#> .z3 0.242 0.018 13.359 0.000
#> .y1 0.156 0.017 9.075 0.000
#> .y2 0.289 0.020 14.466 0.000
#> .y3 0.246 0.024 10.183 0.000
#> .w1 0.165 0.024 6.885 0.000
#> .w2 0.319 0.024 13.424 0.000
#> .w3 0.215 0.027 7.858 0.000
#> Y~1 0.076 0.018 4.329 0.000
#> Y~X 0.018 0.005 3.726 0.000
#> Y~Z 0.101 0.014 7.370 0.000
#> W~1 0.052 0.012 4.550 0.000
#> W~X 0.099 0.016 6.141 0.000
#> W~Z 0.142 0.027 5.336 0.000intercepts_model <- '
f =~ y1 + y2 + y3
f ~ x1 + x2 + x3 + w1 + w2 + (1 | cluster)
'fit_intercepts_cont <- pls(
intercepts_model,
data = randomIntercepts,
bootstrap = TRUE,
sample = 50
)
summary(fit_intercepts_cont)
#> plssem (0.1.0) ended normally after 2 iterations
#>
#> Estimator PLSc-MLM
#> Link LINEAR
#>
#> Number of observations 10000
#> Number of iterations 2
#> Number of latent variables 1
#> Number of observed variables 9
#>
#> R-squared (indicators):
#> y1 0.891
#> y2 0.785
#> y3 0.814
#>
#> R-squared (latents):
#> f 0.705
#>
#> Latent Variables:
#> Estimate Std.Error z.value P(>|z|)
#> f =~
#> y1 0.944 0.008 120.524 0.000
#> y2 0.886 0.009 96.581 0.000
#> y3 0.902 0.010 87.518 0.000
#>
#> Regressions:
#> Estimate Std.Error z.value P(>|z|)
#> f ~
#> x1 0.238 0.007 32.191 0.000
#> x2 0.162 0.007 23.900 0.000
#> x3 0.077 0.005 15.071 0.000
#> w1 0.128 0.032 4.024 0.000
#> w2 0.091 0.037 2.486 0.013
#>
#> Intercepts:
#> Estimate Std.Error z.value P(>|z|)
#> .f -0.012 0.008 -1.617 0.106
#>
#> Covariances:
#> Estimate Std.Error z.value P(>|z|)
#> x1 ~~
#> x2 0.104 0.009 11.591 0.000
#> x3 0.004 0.012 0.352 0.725
#> w1 0.000
#> w2 0.000
#> x2 ~~
#> x3 0.097 0.013 7.568 0.000
#> w1 0.000
#> w2 0.000
#> x3 ~~
#> w1 0.000
#> w2 0.000
#> w1 ~~
#> w2 -0.041 0.044 -0.923 0.356
#>
#> Variances:
#> Estimate Std.Error z.value P(>|z|)
#> .f 0.295 0.015 19.227 0.000
#> x1 1.000
#> x2 1.000
#> x3 1.000
#> w1 1.000
#> w2 1.000
#> .y1 0.109 0.015 7.343 0.000
#> .y2 0.215 0.016 13.196 0.000
#> .y3 0.186 0.019 10.018 0.000
#> f~1 0.582 0.021 28.051 0.000fit_intercepts_ord <- pls(
intercepts_model,
data = randomInterceptsOrdered,
bootstrap = TRUE,
sample = 50,
ordered = colnames(randomInterceptsOrdered) # explicitly specify variables as ordered
)
summary(fit_intercepts_ord)
#> plssem (0.1.0) ended normally after 2 iterations
#>
#> Estimator OrdPLSc-MLM
#> Link PROBIT
#>
#> Number of observations 10000
#> Number of iterations 2
#> Number of latent variables 1
#> Number of observed variables 9
#>
#> R-squared (indicators):
#> y1 0.885
#> y2 0.788
#> y3 0.809
#>
#> R-squared (latents):
#> f 0.684
#>
#> Latent Variables:
#> Estimate Std.Error z.value P(>|z|)
#> f =~
#> y1 0.941 0.011 83.225 0.000
#> y2 0.888 0.014 64.791 0.000
#> y3 0.899 0.012 73.257 0.000
#>
#> Regressions:
#> Estimate Std.Error z.value P(>|z|)
#> f ~
#> x1 0.241 0.008 30.016 0.000
#> x2 0.158 0.009 18.199 0.000
#> x3 0.080 0.007 12.154 0.000
#> w1 0.121 0.049 2.480 0.013
#> w2 0.081 0.044 1.861 0.063
#>
#> Intercepts:
#> Estimate Std.Error z.value P(>|z|)
#> .f -0.011 0.005 -2.184 0.029
#>
#> Covariances:
#> Estimate Std.Error z.value P(>|z|)
#> x1 ~~
#> x2 0.110 0.011 9.693 0.000
#> x3 0.012 0.011 1.124 0.261
#> w1 0.001 0.004 0.186 0.853
#> w2 0.001 0.004 0.279 0.781
#> x2 ~~
#> x3 0.099 0.012 7.955 0.000
#> w1 -0.003 0.003 -1.097 0.273
#> w2 -0.001 0.003 -0.464 0.643
#> x3 ~~
#> w1 -0.003 0.003 -0.873 0.382
#> w2 0.003 0.003 0.961 0.337
#> w1 ~~
#> w2 -0.025 0.058 -0.430 0.667
#>
#> Variances:
#> Estimate Std.Error z.value P(>|z|)
#> .f 0.316 0.014 22.558 0.000
#> x1 1.000
#> x2 1.000
#> x3 1.000
#> w1 1.000
#> w2 1.000
#> .y1 0.115 0.021 5.405 0.000
#> .y2 0.212 0.024 8.651 0.000
#> .y3 0.191 0.022 8.696 0.000
#> f~1 0.562 0.021 27.261 0.000
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