Results

Porn use growth specifications with fixed residuals

Model fit
Baseline test
Difference test
  AIC BIC n χ² df p Δχ² Δdf p
Quadratic growth 21034.700 21089.131 1708 39.518 10 < .001  
piecewise growth 21037.900 21092.331 1708 42.718 10 < .001 3.200 0  
Cumulative growth 21041.674 21090.661 1708 48.491 11 < .001 5.773 1 0.016
Linear growth 21055.567 21088.225 1708 68.384 14 < .001 19.893 3 < .001
Note.  some models have the same degrees of freedom

Additional fit measures

Fit indices
Index Linear growth Quadratic growth Cumulative growth piecewise growth
Comparative Fit Index (CFI) 0.989 0.994 0.993 0.994
T-size CFI 0.981 0.988 0.986 0.987
Tucker-Lewis Index (TLI) 0.992 0.994 0.993 0.994
Bentler-Bonett Non-normed Fit Index (NNFI) 0.992 0.994 0.993 0.994
Bentler-Bonett Normed Fit Index (NFI) 0.992 0.992
Parsimony Normed Fit Index (PNFI) 1.381 0.992 1.090 0.992
Bollen's Relative Fit Index (RFI) 0.992 0.992
Bollen's Incremental Fit Index (IFI) 0.989 0.994 0.993 0.994
Relative Noncentrality Index (RNI) 0.989 0.994 0.993 0.994
Note.  T-size CFI is computed for α = 0.05
Note.  The T-size equivalents of the conventional CFI cut-off values (poor < 0.90 < fair < 0.95 < close) are poor < 0.861 < fair < 0.927 < close for model: Linear growth
Note.  The T-size equivalents of the conventional CFI cut-off values (poor < 0.90 < fair < 0.95 < close) are poor < 0.863 < fair < 0.928 < close for model: Cumulative growth
Note.  The T-size equivalents of the conventional CFI cut-off values (poor < 0.90 < fair < 0.95 < close) are poor < 0.863 < fair < 0.928 < close for model: Quadratic growth
Note.  The T-size equivalents of the conventional CFI cut-off values (poor < 0.90 < fair < 0.95 < close) are poor < 0.863 < fair < 0.928 < close for model: piecewise growth
Information criteria
  Linear growth Quadratic growth Cumulative growth piecewise growth
Log-likelihood -10521.783 -10507.350 -10511.837 -10508.950
Number of free parameters 6.000 10.000 9.000 10.000
Akaike (AIC) 21055.567 21034.700 21041.674 21037.900
Bayesian (BIC) 21088.225 21089.131 21090.661 21092.331
Sample-size adjusted Bayesian (SSABIC) 21069.164 21057.362 21062.069 21060.562
Other fit measures
Metric Linear growth Quadratic growth Cumulative growth piecewise growth
Root mean square error of approximation (RMSEA) 0.048 0.042 0.045 0.044
RMSEA 90% CI lower bound 0.037 0.028 0.032 0.031
RMSEA 90% CI upper bound 0.059 0.056 0.058 0.058
RMSEA p-value 0.609 0.830 0.731 0.755
T-size RMSEA 0.059 0.056 0.058 0.058
Standardized root mean square residual (SRMR) 0.029 0.023 0.027 0.018
Hoelter's critical N (α = .05) 592.562 792.253 694.012 732.973
Hoelter's critical N (α = .01) 728.845 1004.133 871.881 928.979
Goodness of fit index (GFI) 0.981 0.985 0.982 0.985
McDonald fit index (MFI) 0.984 0.991 0.989 0.990
Expected cross validation index (ECVI) 0.047 0.035 0.039 0.037
Note.  T-size RMSEA is computed for α = 0.05
Note.  The T-size equivalents of the conventional RMSEA cut-off values (close < 0.05 < fair < 0.08 < poor) are close < 0.061 < fair < 0.09 < poor for model: Linear growth
Note.  The T-size equivalents of the conventional RMSEA cut-off values (close < 0.05 < fair < 0.08 < poor) are close < 0.063 < fair < 0.091 < poor for model: Cumulative growth
Note.  The T-size equivalents of the conventional RMSEA cut-off values (close < 0.05 < fair < 0.08 < poor) are close < 0.064 < fair < 0.092 < poor for model: Quadratic growth
Note.  The T-size equivalents of the conventional RMSEA cut-off values (close < 0.05 < fair < 0.08 < poor) are close < 0.064 < fair < 0.092 < poor for model: piecewise growth

Parameter estimates

Linear growth

Factor Loadings
95% Confidence Interval
Standardized
Latent Indicator   Estimate Std. Error z-value p Lower Upper All LV Endo
I a_pornuse 1.000 0.000   1.000 1.000 0.919 2.183 0.919
  b_pornuse 1.000 0.000   1.000 1.000 0.939 2.183 0.939
  c_pornuse 1.000 0.000   1.000 1.000 0.944 2.183 0.944
  d_pornuse 1.000 0.000   1.000 1.000 0.933 2.183 0.933
  e_pornuse 1.000 0.000   1.000 1.000 0.909 2.183 0.909
S a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  b_pornuse 1.000 0.000   1.000 1.000 0.129 0.300 0.129
  c_pornuse 2.000 0.000   2.000 2.000 0.259 0.599 0.259
  d_pornuse 3.000 0.000   3.000 3.000 0.384 0.899 0.384
  e_pornuse 4.000 0.000   4.000 4.000 0.499 1.199 0.499
Factor variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
I 4.764 0.146 32.556 < .001 4.477 5.050 1.000 1.000 1.000
S 0.090 0.013 6.994 < .001 0.065 0.115 1.000 1.000 1.000
Factor covariances
95% Confidence Interval
Standardized
Variables   Estimate Std. Error z-value p Lower Upper All LV Endo
I - S -0.163 0.032 -5.050 < .001 -0.227 -0.100 -0.250 -0.250 -0.250
Residual variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse a 0.876 0.050 17.627 < .001 0.779 0.974 0.155 0.876 0.155
b_pornuse a 0.876 0.050 17.627 < .001 0.779 0.974 0.162 0.876 0.162
c_pornuse a 0.876 0.050 17.627 < .001 0.779 0.974 0.164 0.876 0.164
d_pornuse a 0.876 0.050 17.627 < .001 0.779 0.974 0.160 0.876 0.160
e_pornuse a 0.876 0.050 17.627 < .001 0.779 0.974 0.152 0.876 0.152
Means
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
b_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
c_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
d_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
e_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
I 3.062 0.058 52.405 < .001 2.947 3.177 1.403 1.403 1.403
S 0.025 0.013 1.933 0.053 -3.475×10-4 0.051 0.084 0.084 0.084

Quadratic growth

Factor Loadings
95% Confidence Interval
Standardized
Latent Indicator   Estimate Std. Error z-value p Lower Upper All LV Endo
I a_pornuse 1.000 0.000   1.000 1.000 0.925 2.180 0.925
  b_pornuse 1.000 0.000   1.000 1.000 0.935 2.180 0.935
  c_pornuse 1.000 0.000   1.000 1.000 0.927 2.180 0.927
  d_pornuse 1.000 0.000   1.000 1.000 0.928 2.180 0.928
  e_pornuse 1.000 0.000   1.000 1.000 0.930 2.180 0.930
S_l a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  b_pornuse 1.000 0.000   1.000 1.000 0.286 0.667 0.286
  c_pornuse 2.000 0.000   2.000 2.000 0.568 1.335 0.568
  d_pornuse 3.000 0.000   3.000 3.000 0.853 2.002 0.853
  e_pornuse 4.000 0.000   4.000 4.000 1.139 2.670 1.139
S_q a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  b_pornuse 1.000 0.000   1.000 1.000 0.056 0.131 0.056
  c_pornuse 4.000 0.000   4.000 4.000 0.223 0.524 0.223
  d_pornuse 9.000 0.000   9.000 9.000 0.502 1.179 0.502
  e_pornuse 16.000 0.000   16.000 16.000 0.895 2.096 0.895
Factor variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
I 4.752 0.157 30.306 < .001 4.445 5.060 1.000 1.000 1.000
S_l 0.445 0.121 3.668 < .001 0.207 0.684 1.000 1.000 1.000
S_q 0.017 0.007 2.517 0.012 0.004 0.031 1.000 1.000 1.000
Factor covariances
95% Confidence Interval
Standardized
Variables   Estimate Std. Error z-value p Lower Upper All LV Endo
I - S_l -0.224 0.095 -2.350 0.019 -0.410 -0.037 -0.154 -0.154 -0.154
I - S_q 0.007 0.022 0.333 0.739 -0.036 0.051 0.026 0.026 0.026
S_l - S_q -0.078 0.028 -2.810 0.005 -0.133 -0.024 -0.897 -0.897 -0.897
Residual variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse a 0.807 0.054 14.957 < .001 0.701 0.913 0.145 0.807 0.145
b_pornuse a 0.807 0.054 14.957 < .001 0.701 0.913 0.149 0.807 0.149
c_pornuse a 0.807 0.054 14.957 < .001 0.701 0.913 0.146 0.807 0.146
d_pornuse a 0.807 0.054 14.957 < .001 0.701 0.913 0.146 0.807 0.146
e_pornuse a 0.807 0.054 14.957 < .001 0.701 0.913 0.147 0.807 0.147
Means
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
b_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
c_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
d_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
e_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
I 3.069 0.061 50.643 < .001 2.950 3.188 1.408 1.408 1.408
S_l 0.016 0.037 0.416 0.677 -0.058 0.089 0.023 0.023 0.023
S_q 0.002 0.009 0.267 0.790 -0.015 0.020 0.018 0.018 0.018

Cumulative growth

Factor Loadings
95% Confidence Interval
Standardized
Latent Indicator   Estimate Std. Error z-value p Lower Upper All LV Endo
I a_pornuse 1.000 0.000   1.000 1.000 0.921 2.194 0.921
  b_pornuse 1.000 0.000   1.000 1.000 0.948 2.194 0.948
  c_pornuse 1.000 0.000   1.000 1.000 0.949 2.194 0.949
  d_pornuse 1.000 0.000   1.000 1.000 0.927 2.194 0.927
  e_pornuse 1.000 0.000   1.000 1.000 0.921 2.194 0.921
S a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  b_pornuse 0.401 0.080 4.981 < .001 0.243 0.558 0.201 0.464 0.201
  c_pornuse 0.578 0.077 7.514 < .001 0.427 0.729 0.290 0.670 0.290
  d_pornuse 0.950 0.080 11.812 < .001 0.793 1.108 0.465 1.101 0.465
  e_pornuse 1.000 0.000   1.000 1.000 0.487 1.158 0.487
Factor variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
I 4.812 0.151 31.844 < .001 4.516 5.108 1.000 1.000 1.000
S 1.342 0.212 6.337 < .001 0.927 1.757 1.000 1.000 1.000
Factor covariances
95% Confidence Interval
Standardized
Variables   Estimate Std. Error z-value p Lower Upper All LV Endo
I - S -0.675 0.127 -5.328 < .001 -0.923 -0.427 -0.266 -0.266 -0.266
Residual variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse a 0.863 0.049 17.613 < .001 0.767 0.959 0.152 0.863 0.152
b_pornuse a 0.863 0.049 17.613 < .001 0.767 0.959 0.161 0.863 0.161
c_pornuse a 0.863 0.049 17.613 < .001 0.767 0.959 0.162 0.863 0.162
d_pornuse a 0.863 0.049 17.613 < .001 0.767 0.959 0.154 0.863 0.154
e_pornuse a 0.863 0.049 17.613 < .001 0.767 0.959 0.152 0.863 0.152
Means
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
b_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
c_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
d_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
e_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
I 3.048 0.059 51.377 < .001 2.932 3.164 1.390 1.390 1.390
S 0.110 0.049 2.249 0.025 0.014 0.206 0.095 0.095 0.095

piecewise growth

Factor Loadings
95% Confidence Interval
Standardized
Latent Indicator   Estimate Std. Error z-value p Lower Upper All LV Endo
I a_pornuse 1.000 0.000   1.000 1.000 0.914 2.134 0.914
  b_pornuse 1.000 0.000   1.000 1.000 0.895 2.134 0.895
  c_pornuse 1.000 0.000   1.000 1.000 0.931 2.134 0.931
  d_pornuse 1.000 0.000   1.000 1.000 0.916 2.134 0.916
  e_pornuse 1.000 0.000   1.000 1.000 0.887 2.134 0.887
S_a a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  b_pornuse 1.000 0.000   1.000 1.000 0.070 0.167 0.070
  c_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  d_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  e_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
S_b a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  b_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
  c_pornuse 2.000 0.000   2.000 2.000 0.265 0.608 0.265
  d_pornuse 3.000 0.000   3.000 3.000 0.391 0.912 0.391
  e_pornuse 4.000 0.000   4.000 4.000 0.505 1.215 0.505
Factor variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
I 4.552 0.158 28.828 < .001 4.243 4.862 1.000 1.000 1.000
S_a 0.028 0.168 0.166 0.868 -0.302 0.358 1.000 1.000 1.000
S_b 0.092 0.015 6.272 < .001 0.063 0.121 1.000 1.000 1.000
Factor covariances
95% Confidence Interval
Standardized
Variables   Estimate Std. Error z-value p Lower Upper All LV Endo
I - S_a 0.105 0.106 0.986 0.324 -0.103 0.313 0.293 0.293 0.293
I - S_b -0.143 0.035 -4.095 < .001 -0.211 -0.075 -0.221 -0.221 -0.221
S_a - S_b 0.109 0.041 2.674 0.008 0.029 0.188 2.133 2.133 2.133
Residual variances
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse a 0.898 0.062 14.512 < .001 0.777 1.019 0.165 0.898 0.165
b_pornuse a 0.898 0.062 14.512 < .001 0.777 1.019 0.158 0.898 0.158
c_pornuse a 0.898 0.062 14.512 < .001 0.777 1.019 0.171 0.898 0.171
d_pornuse a 0.898 0.062 14.512 < .001 0.777 1.019 0.166 0.898 0.166
e_pornuse a 0.898 0.062 14.512 < .001 0.777 1.019 0.155 0.898 0.155
Means
95% Confidence Interval
Standardized
Variable   Estimate Std. Error z-value p Lower Upper All LV Endo
a_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
b_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
c_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
d_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
e_pornuse 0.000 0.000   0.000 0.000 0.000 0.000 0.000
I 3.021 0.059 50.864 < .001 2.904 3.137 1.416 1.416 1.416
S_a 0.133 0.039 3.389 < .001 0.056 0.211 0.797 0.797 0.797
S_b 0.035 0.014 2.584 0.010 0.009 0.062 0.116 0.116 0.116

Path diagram

Linear growth

Quadratic growth

Cumulative growth

piecewise growth