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I have a conditional quadratic latent growth curve model and am wondering how to interpret the results.

My predictor of interest is significantly associated with the slope factor (B = -0.45, p = .001) and slope2 factor (B = 0.14, p = .002) - what does this suggest?

In case relevant (?) the intercepts for the slope and slope2 are both positive (although not significant).

Output from lavaan:

## lavaan 0.6.14 ended normally after 406 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        55
## 
##   Number of observations                          3939
##   Number of missing patterns                         8
## 
## Model Test User Model:
##                                               Standard      Scaled
##   Test Statistic                                22.228      21.174
##   Degrees of freedom                                15          15
##   P-value (Chi-square)                           0.102       0.131
##   Scaling correction factor                                  1.050
##     Yuan-Bentler correction (Mplus variant)                       
## 
## Model Test Baseline Model:
## 
##   Test statistic                             18195.857   17658.385
##   Degrees of freedom                                62          62
##   P-value                                        0.000       0.000
##   Scaling correction factor                                  1.030
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000       1.000
##   Tucker-Lewis Index (TLI)                       0.998       0.999
##                                                                   
##   Robust Comparative Fit Index (CFI)                         1.000
##   Robust Tucker-Lewis Index (TLI)                            0.999
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -42721.782  -42721.782
##   Scaling correction factor                                  1.033
##       for the MLR correction                                      
##   Loglikelihood unrestricted model (H1)     -42710.667  -42710.667
##   Scaling correction factor                                  1.037
##       for the MLR correction                                      
##                                                                   
##   Akaike (AIC)                               85553.563   85553.563
##   Bayesian (BIC)                             85898.891   85898.891
##   Sample-size adjusted Bayesian (SABIC)      85724.126   85724.126
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.011       0.010
##   90 Percent confidence interval - lower         0.000       0.000
##   90 Percent confidence interval - upper         0.020       0.019
##   P-value H_0: RMSEA <= 0.050                    1.000       1.000
##   P-value H_0: RMSEA >= 0.080                    0.000       0.000
##                                                                   
##   Robust RMSEA                                               0.011
##   90 Percent confidence interval - lower                     0.000
##   90 Percent confidence interval - upper                     0.023
##   P-value H_0: Robust RMSEA <= 0.050                         1.000
##   P-value H_0: Robust RMSEA >= 0.080                         0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.003       0.003
## 
## Parameter Estimates:
## 
##   Standard errors                             Sandwich
##   Information bread                           Observed
##   Observed information based on                Hessian
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   i =~                                                                  
##     Cog_w0           1.000                               1.000    1.000
##     Cog_w1           1.000                               1.000    1.000
##     Cog_w2           1.000                               1.000    1.000
##     Cog_w3           1.000                               1.000    1.000
##   s =~                                                                  
##     Cog_w0           0.000                               0.000    0.000
##     Cog_w1           1.000                               1.000    1.000
##     Cog_w2           2.000                               2.000    2.000
##     Cog_w3           3.000                               3.000    3.000
##   s2 =~                                                                 
##     Cog_w0           0.000                               0.000    0.000
##     Cog_w1           1.000                               1.000    1.000
##     Cog_w2           4.000                               4.000    4.000
##     Cog_w3           9.000                               9.000    9.000
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   i ~                                                                   
##     Predictor         0.110    0.142    0.775    0.438   -0.168    0.388
##     Covariate1      -16.186   13.635   -1.187    0.235  -42.911   10.538
##     Covariate2       18.645   12.963    1.438    0.150   -6.762   44.052
##     Covariate3      -14.014   13.707   -1.022    0.307  -40.879   12.851
##     Covariate4      -24.058   13.026   -1.847    0.065  -49.588    1.473
##     Covariate5      -16.204   12.205   -1.328    0.184  -40.125    7.716
##     Covariate6      -16.086   12.777   -1.259    0.208  -41.128    8.955
##     Covariate7       -0.423    0.034  -12.489    0.000   -0.489   -0.357
##     Covariate8        0.466    0.312    1.493    0.135   -0.146    1.077
##     Covariate9        1.398    0.100   14.035    0.000    1.203    1.594
##     Covariate10      -0.647    0.791   -0.818    0.414   -2.198    0.904
##     Covariate11      -0.514    0.904   -0.569    0.570   -2.285    1.258
##     Covariate12       0.226    0.959    0.236    0.814   -1.653    2.105
##     Covariate13      -5.703    2.616   -2.180    0.029  -10.829   -0.576
##   s ~                                                                   
##     Predictor        -0.454    0.138   -3.289    0.001   -0.724   -0.183
##     Covariate1       -0.456   12.995   -0.035    0.972  -25.926   25.015
##     Covariate2        7.446   12.364    0.602    0.547  -16.787   31.679
##     Covariate3        6.285   11.488    0.547    0.584  -16.230   28.800
##     Covariate4        0.323   12.500    0.026    0.979  -24.177   24.823
##     Covariate5        8.817   13.105    0.673    0.501  -16.870   34.503
##     Covariate6       -9.180   11.445   -0.802    0.422  -31.611   13.251
##     Covariate7       -0.033    0.029   -1.140    0.254   -0.089    0.024
##     Covariate8        0.799    0.306    2.613    0.009    0.200    1.398
##     Covariate9        0.215    0.100    2.151    0.031    0.019    0.410
##     Covariate10      -0.204    0.846   -0.241    0.810   -1.862    1.455
##     Covariate11      -0.627    0.967   -0.648    0.517   -2.523    1.269
##     Covariate12      -0.473    0.993   -0.477    0.633   -2.420    1.473
##     Covariate13      -2.020    2.862   -0.706    0.480   -7.629    3.589
##   s2 ~                                                                  
##     Predictor         0.135    0.043    3.138    0.002    0.051    0.219
##     Covariate1        1.269    4.224    0.300    0.764   -7.011    9.548
##     Covariate2       -2.259    4.088   -0.553    0.580  -10.271    5.752
##     Covariate3       -3.537    3.810   -0.928    0.353  -11.004    3.931
##     Covariate4        0.234    3.968    0.059    0.953   -7.543    8.011
##     Covariate5       -3.636    4.123   -0.882    0.378  -11.718    4.445
##     Covariate6        4.409    3.546    1.243    0.214   -2.541   11.359
##     Covariate7       -0.003    0.009   -0.383    0.702   -0.021    0.014
##     Covariate8       -0.142    0.097   -1.464    0.143   -0.331    0.048
##     Covariate9       -0.054    0.031   -1.748    0.080   -0.115    0.007
##     Covariate10      -0.038    0.259   -0.146    0.884   -0.545    0.469
##     Covariate11       0.021    0.298    0.070    0.944   -0.564    0.606
##     Covariate12       0.029    0.304    0.097    0.923   -0.566    0.625
##     Covariate13       0.224    0.822    0.272    0.785   -1.388    1.836
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##  .i ~~                                                                  
##    .s                -0.438    4.074   -0.108    0.914   -8.423    7.547
##    .s2                0.248    1.016    0.244    0.807   -1.743    2.239
##  .s ~~                                                                  
##    .s2               -2.170    1.021   -2.126    0.034   -4.172   -0.169
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .Cog_w0           0.000                               0.000    0.000
##    .Cog_w1           0.000                               0.000    0.000
##    .Cog_w2           0.000                               0.000    0.000
##    .Cog_w3           0.000                               0.000    0.000
##    .i                54.717    2.527   21.656    0.000   49.765   59.670
##    .s                 3.234    2.226    1.453    0.146   -1.129    7.597
##    .s2                0.212    0.696    0.305    0.761   -1.153    1.577
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .Cog_w0          22.794    3.581    6.365    0.000   15.775   29.813
##    .Cog_w1          20.891    1.311   15.936    0.000   18.321   23.460
##    .Cog_w2          19.891    1.377   14.450    0.000   17.193   22.589
##    .Cog_w3          18.455    4.119    4.480    0.000   10.382   26.528
##    .i               55.545    3.707   14.986    0.000   48.280   62.810
##    .s                9.668    4.312    2.242    0.025    1.216   18.120
##    .s2               0.546    0.302    1.806    0.071   -0.047    1.138
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1 Answer 1

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I would plot the model-implied/predicted growth curves for different values of the predictor to examine this effect in detail. That way, you could see in which way the trajectories differ across different levels of the predictor.

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