ramLCM: Conduct growth curve analysis

Description Usage Arguments Value References Examples

Description

Conduct growth curve analysis

Usage

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ramLCM(data, outcome, model = c("all", "no", "linear", "quadratic", "latent"), 
basis = 0:(length(outcome) - 1), predictor, equal.var = TRUE, digits = 3, 
ram.out = FALSE, ...)

Arguments

data

Data

outcome

Outcome variable indices

model

Models to fit

basis

Basis coefficients

predictor

Covariates as predictors

equal.var

Set residual variances to be equal

digits

Print digits

ram.out

Print ram matrices

...

Options can be used for lavaan

Value

model

The lavaan model specification of the bivariate latent change score model

lavaan

The lavaan output

ram

Output in terms of RAM matrices

fit

Model fit

References

Zhang, Z., Hamagami, F., Grimm, K. J., & McArdle, J. J. (2013). Using R Package RAMpath for Tracing SEM Path Diagrams and Conducting Complex Longitudinal Data Analysis. Structural Equation Modeling.

Examples

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data(ex3)
## Example 3. Growth curve models
gcm.all<-ramLCM(ex3, 1:6, ram.out=TRUE)
## plot the path diagram
bridge<-ramPathBridge(gcm.all$ram$latent, FALSE, FALSE)
plot(bridge, 'latent')

##unequal variance
gcm.all<-ramLCM(ex3, 1:6, ram.out=TRUE, equal.var=FALSE)

## missing data
gcm.all<-ramLCM(ex3, c(1,2,4,6), basis=c(1,2,4,6), ram.out=TRUE)

gcm.l<-ramLCM(ex3, 1:6, model='linear', ram.out=TRUE)

## with a predictor
gcm.pred<-ramLCM(ex3, c(1,2,4,6), model='linear', basis=c(1,2,4,6), 
                 predictor=c(3,5), ram.out=TRUE)
bridge3<-ramPathBridge(gcm.pred$ram$linear)
plot(bridge3, 'gcmlinear')

Example output

Loading required package: lavaan
This is lavaan 0.6-3
lavaan is BETA software! Please report any bugs.
Loading required package: ellipse

Attaching package: 'ellipse'

The following object is masked from 'package:graphics':

    pairs

Loading required package: MASS


======================================
Results from the no growth curve model
======================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level
X1     0  0  0  0  0  0     1
X2     0  0  0  0  0  0     1
X3     0  0  0  0  0  0     1
X4     0  0  0  0  0  0     1
X5     0  0  0  0  0  0     1
X6     0  0  0  0  0  0     1
level  0  0  0  0  0  0     0

Matrix S

       X1  X2  X3  X4  X5  X6 level
X1    347   0   0   0   0   0     0
X2      0 347   0   0   0   0     0
X3      0   0 347   0   0   0     0
X4      0   0   0 347   0   0     0
X5      0   0   0   0 347   0     0
X6      0   0   0   0   0 347     0
level   0   0   0   0   0   0   -29

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level
X1     0  0  0  0  0  0     0
X2     0  0  0  0  0  0     0
X3     0  0  0  0  0  0     0
X4     0  0  0  0  0  0     0
X5     0  0  0  0  0  0     0
X6     0  0  0  0  0  0     0
level  0  0  0  0  0  0     0

Matrix S

       X1  X2  X3  X4  X5  X6 level
X1    9.8   0   0   0   0   0     0
X2      0 9.8   0   0   0   0     0
X3      0   0 9.8   0   0   0     0
X4      0   0   0 9.8   0   0     0
X5      0   0   0   0 9.8   0     0
X6      0   0   0   0   0 9.8     0
level   0   0   0   0   0   0   2.5


lavaan 0.6-3 ended normally after 36 iterations

  Optimization method                           NLMINB
  Number of free parameters                          8
  Number of equality constraints                     5

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                    8847.234
  Degrees of freedom                                24
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.000
  Tucker-Lewis Index (TLI)                      -1.433

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)             -12859.453
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                          3
  Akaike (AIC)                               25724.906
  Bayesian (BIC)                             25737.550
  Sample-size adjusted Bayesian (BIC)        25728.028

Root Mean Square Error of Approximation:

  RMSEA                                          0.857
  90 Percent Confidence Interval          0.843  0.873
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           6.420

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            41.818    0.242  173.057    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)  346.873    9.811   35.355    0.000
   .X2      (vare)  346.873    9.811   35.355    0.000
   .X3      (vare)  346.873    9.811   35.355    0.000
   .X4      (vare)  346.873    9.811   35.355    0.000
   .X5      (vare)  346.873    9.811   35.355    0.000
   .X6      (vare)  346.873    9.811   35.355    0.000
    level           -28.617    2.466  -11.603    0.000



==========================================
Results from the linear growth curve model
==========================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     1     0
X2     0  0  0  0  0  0     1     1
X3     0  0  0  0  0  0     1     2
X4     0  0  0  0  0  0     1     3
X5     0  0  0  0  0  0     1     4
X6     0  0  0  0  0  0     1     5
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

      X1 X2 X3 X4 X5 X6 level slope
X1    15  0  0  0  0  0     0     0
X2     0 15  0  0  0  0     0     0
X3     0  0 15  0  0  0     0     0
X4     0  0  0 15  0  0     0     0
X5     0  0  0  0 15  0     0     0
X6     0  0  0  0  0 15     0     0
level  0  0  0  0  0  0  0.17   2.3
slope  0  0  0  0  0  0  2.31   2.4

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     0     0
X2     0  0  0  0  0  0     0     0
X3     0  0  0  0  0  0     0     0
X4     0  0  0  0  0  0     0     0
X5     0  0  0  0  0  0     0     0
X6     0  0  0  0  0  0     0     0
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

        X1   X2   X3   X4   X5   X6 level slope
X1    0.47    0    0    0    0    0     0     0
X2       0 0.47    0    0    0    0     0     0
X3       0    0 0.47    0    0    0     0     0
X4       0    0    0 0.47    0    0     0     0
X5       0    0    0    0 0.47    0     0     0
X6       0    0    0    0    0 0.47     0     0
level    0    0    0    0    0    0  0.56  0.24
slope    0    0    0    0    0    0  0.24  0.21


lavaan 0.6-3 ended normally after 53 iterations

  Optimization method                           NLMINB
  Number of free parameters                         11
  Number of equality constraints                     5

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                     978.024
  Degrees of freedom                                21
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.578
  Tucker-Lewis Index (TLI)                       0.698

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8924.848
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                          6
  Akaike (AIC)                               17861.696
  Bayesian (BIC)                             17886.984
  Sample-size adjusted Bayesian (BIC)        17867.940

Root Mean Square Error of Approximation:

  RMSEA                                          0.302
  90 Percent Confidence Interval          0.286  0.318
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           0.203

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                0.000                           
    X2                1.000                           
    X3                2.000                           
    X4                3.000                           
    X5                4.000                           
    X6                5.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             2.307    0.237    9.751    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            17.776    0.126  141.288    0.000
    slope             9.617    0.081  119.306    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)   14.779    0.467   31.623    0.000
   .X2      (vare)   14.779    0.467   31.623    0.000
   .X3      (vare)   14.779    0.467   31.623    0.000
   .X4      (vare)   14.779    0.467   31.623    0.000
   .X5      (vare)   14.779    0.467   31.623    0.000
   .X6      (vare)   14.779    0.467   31.623    0.000
    level             0.173    0.557    0.311    0.756
    slope             2.404    0.207   11.603    0.000



==========================================
Results from the latent growth curve model
==========================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     1     0
X2     0  0  0  0  0  0     1   0.7
X3     0  0  0  0  0  0     1   1.6
X4     0  0  0  0  0  0     1   2.5
X5     0  0  0  0  0  0     1   3.6
X6     0  0  0  0  0  0     1   5.0
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

       X1  X2  X3  X4  X5  X6 level slope
X1    9.1   0   0   0   0   0     0     0
X2      0 9.1   0   0   0   0     0     0
X3      0   0 9.1   0   0   0     0     0
X4      0   0   0 9.1   0   0     0     0
X5      0   0   0   0 9.1   0     0     0
X6      0   0   0   0   0 9.1     0     0
level   0   0   0   0   0   0   4.1   2.2
slope   0   0   0   0   0   0   2.2   2.8

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     0     0
X2     0  0  0  0  0  0     0 0.018
X3     0  0  0  0  0  0     0 0.017
X4     0  0  0  0  0  0     0 0.017
X5     0  0  0  0  0  0     0 0.017
X6     0  0  0  0  0  0     0     0
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

        X1   X2   X3   X4   X5   X6 level slope
X1    0.29    0    0    0    0    0     0     0
X2       0 0.29    0    0    0    0     0     0
X3       0    0 0.29    0    0    0     0     0
X4       0    0    0 0.29    0    0     0     0
X5       0    0    0    0 0.29    0     0     0
X6       0    0    0    0    0 0.29     0     0
level    0    0    0    0    0    0  0.53  0.24
slope    0    0    0    0    0    0  0.24  0.21


lavaan 0.6-3 ended normally after 79 iterations

  Optimization method                           NLMINB
  Number of free parameters                         15
  Number of equality constraints                     5

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                       9.523
  Degrees of freedom                                17
  P-value (Chi-square)                           0.922

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    1.000
  Tucker-Lewis Index (TLI)                       1.003

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8440.598
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                         10
  Akaike (AIC)                               16901.195
  Bayesian (BIC)                             16943.342
  Sample-size adjusted Bayesian (BIC)        16911.601

Root Mean Square Error of Approximation:

  RMSEA                                          0.000
  90 Percent Confidence Interval          0.000  0.014
  P-value RMSEA <= 0.05                          1.000

Standardized Root Mean Square Residual:

  SRMR                                           0.019

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                0.000                           
    X2                0.701    0.018   38.503    0.000
    X3                1.552    0.017   90.122    0.000
    X4                2.508    0.017  149.083    0.000
    X5                3.635    0.017  209.020    0.000
    X6                5.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             2.188    0.241    9.086    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            20.196    0.161  125.123    0.000
    slope             9.683    0.084  115.784    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)    9.088    0.287   31.623    0.000
   .X2      (vare)    9.088    0.287   31.623    0.000
   .X3      (vare)    9.088    0.287   31.623    0.000
   .X4      (vare)    9.088    0.287   31.623    0.000
   .X5      (vare)    9.088    0.287   31.623    0.000
   .X6      (vare)    9.088    0.287   31.623    0.000
    level             4.071    0.535    7.610    0.000
    slope             2.776    0.209   13.257    0.000



=============================================
Results from the quadratic growth curve model
=============================================


--------------------
Parameter estimates:
--------------------

Matrix A

          X1 X2 X3 X4 X5 X6 level slope quadratic
X1         0  0  0  0  0  0     1     0         0
X2         0  0  0  0  0  0     1     1         1
X3         0  0  0  0  0  0     1     2         4
X4         0  0  0  0  0  0     1     3         9
X5         0  0  0  0  0  0     1     4        16
X6         0  0  0  0  0  0     1     5        25
level      0  0  0  0  0  0     0     0         0
slope      0  0  0  0  0  0     0     0         0
quadratic  0  0  0  0  0  0     0     0         0

Matrix S

           X1  X2  X3  X4  X5  X6 level slope quadratic
X1        9.3   0   0   0   0   0     0     0         0
X2          0 9.3   0   0   0   0     0     0         0
X3          0   0 9.3   0   0   0     0     0         0
X4          0   0   0 9.3   0   0     0     0         0
X5          0   0   0   0 9.3   0     0     0         0
X6          0   0   0   0   0 9.3     0     0         0
level       0   0   0   0   0   0  3.82  1.73   0.11986
slope       0   0   0   0   0   0  1.73  0.32   0.23929
quadratic   0   0   0   0   0   0  0.12  0.24  -0.00009

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

          X1 X2 X3 X4 X5 X6 level slope quadratic
X1         0  0  0  0  0  0     0     0         0
X2         0  0  0  0  0  0     0     0         0
X3         0  0  0  0  0  0     0     0         0
X4         0  0  0  0  0  0     0     0         0
X5         0  0  0  0  0  0     0     0         0
X6         0  0  0  0  0  0     0     0         0
level      0  0  0  0  0  0     0     0         0
slope      0  0  0  0  0  0     0     0         0
quadratic  0  0  0  0  0  0     0     0         0

Matrix S

            X1   X2   X3   X4   X5   X6 level slope quadratic
X1        0.34    0    0    0    0    0     0     0         0
X2           0 0.34    0    0    0    0     0     0         0
X3           0    0 0.34    0    0    0     0     0         0
X4           0    0    0 0.34    0    0     0     0         0
X5           0    0    0    0 0.34    0     0     0         0
X6           0    0    0    0    0 0.34     0     0         0
level        0    0    0    0    0    0 0.779 0.482     0.092
slope        0    0    0    0    0    0 0.482 0.514     0.088
quadratic    0    0    0    0    0    0 0.092 0.088     0.018


lavaan 0.6-3 ended normally after 77 iterations

  Optimization method                           NLMINB
  Number of free parameters                         15
  Number of equality constraints                     5

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                      22.360
  Degrees of freedom                                17
  P-value (Chi-square)                           0.171

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.998
  Tucker-Lewis Index (TLI)                       0.998

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8447.016
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                         10
  Akaike (AIC)                               16914.032
  Bayesian (BIC)                             16956.178
  Sample-size adjusted Bayesian (BIC)        16924.438

Root Mean Square Error of Approximation:

  RMSEA                                          0.025
  90 Percent Confidence Interval          0.000  0.051
  P-value RMSEA <= 0.05                          0.945

Standardized Root Mean Square Residual:

  SRMR                                           0.025

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                0.000                           
    X2                1.000                           
    X3                2.000                           
    X4                3.000                           
    X5                4.000                           
    X6                5.000                           
  quadratic =~                                        
    X1                0.000                           
    X2                1.000                           
    X3                4.000                           
    X4                9.000                           
    X5               16.000                           
    X6               25.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             1.728    0.482    3.581    0.000
    quadratic         0.120    0.092    1.300    0.194
  slope ~~                                            
    quadratic         0.239    0.088    2.726    0.006

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            20.319    0.152  133.998    0.000
    slope             5.802    0.119   48.632    0.000
    quadratic         0.763    0.022   34.096    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)    9.348    0.341   27.386    0.000
   .X2      (vare)    9.348    0.341   27.386    0.000
   .X3      (vare)    9.348    0.341   27.386    0.000
   .X4      (vare)    9.348    0.341   27.386    0.000
   .X5      (vare)    9.348    0.341   27.386    0.000
   .X6      (vare)    9.348    0.341   27.386    0.000
    level             3.818    0.779    4.899    0.000
    slope             0.324    0.514    0.630    0.529
    quadrtc          -0.000    0.018   -0.005    0.996



====================================================
Fit Statistics and Fit Indices for Model Comparisons
====================================================

                           No    Linear    Latent Quadratic
npar                 3.00e+00     6.000  1.00e+01  1.00e+01
fmin                 8.85e+00     0.978  9.52e-03  2.24e-02
chisq.per.df         3.39e-01     6.135  1.05e+03  4.47e+02
chisq                8.85e+03   978.024  9.52e+00  2.24e+01
df                   2.40e+01    21.000  1.70e+01  1.70e+01
pvalue               0.00e+00     0.000  9.22e-01  1.71e-01
baseline.chisq       2.28e+03  2281.743  2.28e+03  2.28e+03
baseline.df          1.50e+01    15.000  1.50e+01  1.50e+01
baseline.pvalue      0.00e+00     0.000  0.00e+00  0.00e+00
cfi                  0.00e+00     0.578  1.00e+00  9.98e-01
tli                 -1.43e+00     0.698  1.00e+00  9.98e-01
nnfi                -1.43e+00     0.698  1.00e+00  9.98e-01
rfi                        NA        NA        NA        NA
nfi                        NA        NA        NA        NA
pnfi                -4.60e+00     0.800  1.13e+00  1.12e+00
ifi                 -2.91e+00     0.577  1.00e+00  9.98e-01
rni                 -2.89e+00     0.578  1.00e+00  9.98e-01
logl                -1.29e+04 -8924.848 -8.44e+03 -8.45e+03
unrestricted.logl   -8.44e+03 -8435.836 -8.44e+03 -8.44e+03
aic                  2.57e+04 17861.696  1.69e+04  1.69e+04
bic                  2.57e+04 17886.984  1.69e+04  1.70e+04
ntotal               5.00e+02   500.000  5.00e+02  5.00e+02
bic2                 2.57e+04 17867.940  1.69e+04  1.69e+04
rmsea                8.57e-01     0.302  0.00e+00  2.51e-02
rmsea.ci.lower       8.43e-01     0.286  0.00e+00  0.00e+00
rmsea.ci.upper       8.73e-01     0.318  1.38e-02  5.06e-02
rmsea.pvalue         0.00e+00     0.000  1.00e+00  9.45e-01
rmr                  1.37e+02     3.807  8.34e-01  9.72e-01
rmr_nomean           1.55e+02     4.193  9.45e-01  1.10e+00
srmr                 6.42e+00     0.203  1.89e-02  2.51e-02
srmr_bentler         6.42e+00     0.203  1.89e-02  2.51e-02
srmr_bentler_nomean  7.08e+00     0.128  2.14e-02  2.23e-02
crmr                 2.34e+00     0.306  5.46e-02  5.28e-02
crmr_nomean          7.20e-01     0.117  1.24e-02  1.17e-02
srmr_mplus           6.48e+00     0.284  5.01e-02  4.86e-02
srmr_mplus_nomean    6.99e+00     0.143  1.88e-02  1.89e-02
cn_05                3.06e+00    17.702  1.45e+03  6.18e+02
cn_01                3.43e+00    20.903  1.76e+03  7.48e+02
gfi                  8.91e-01     0.974  1.00e+00  9.99e-01
agfi                 8.78e-01     0.966  1.00e+00  9.99e-01
pgfi                 7.92e-01     0.757  6.29e-01  6.29e-01
mfi                  1.47e-04     0.384  1.01e+00  9.95e-01
ecvi                 1.77e+01     1.980  5.90e-02  8.47e-02
Warning messages:
1: In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative
2: In lav_object_post_check(object) :
  lavaan WARNING: covariance matrix of latent variables
                is not positive definite;
                use lavInspect(fit, "cov.lv") to investigate.
3: In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative
Running  dot -Tpdf -o latent.pdf  latent.dot 


======================================
Results from the no growth curve model
======================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level
X1     0  0  0  0  0  0     1
X2     0  0  0  0  0  0     1
X3     0  0  0  0  0  0     1
X4     0  0  0  0  0  0     1
X5     0  0  0  0  0  0     1
X6     0  0  0  0  0  0     1
level  0  0  0  0  0  0     0

Matrix S

       X1 X2    X3  X4  X5   X6 level
X1    251  0     0   0   0    0     0
X2      0 89     0   0   0    0     0
X3      0  0 -0.86   0   0    0     0
X4      0  0     0 107   0    0     0
X5      0  0     0   0 436    0     0
X6      0  0     0   0   0 1164     0
level   0  0     0   0   0    0    27

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level
X1     0  0  0  0  0  0     0
X2     0  0  0  0  0  0     0
X3     0  0  0  0  0  0     0
X4     0  0  0  0  0  0     0
X5     0  0  0  0  0  0     0
X6     0  0  0  0  0  0     0
level  0  0  0  0  0  0     0

Matrix S

      X1  X2  X3  X4 X5 X6 level
X1    16   0   0   0  0  0     0
X2     0 5.7   0   0  0  0     0
X3     0   0 1.2   0  0  0     0
X4     0   0   0 6.8  0  0     0
X5     0   0   0   0 28  0     0
X6     0   0   0   0  0 74     0
level  0   0   0   0  0  0   2.1


lavaan 0.6-3 ended normally after 84 iterations

  Optimization method                           NLMINB
  Number of free parameters                          8

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                    7170.901
  Degrees of freedom                                19
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.000
  Tucker-Lewis Index (TLI)                      -1.491

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)             -12021.286
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                          8
  Akaike (AIC)                               24058.573
  Bayesian (BIC)                             24092.290
  Sample-size adjusted Bayesian (BIC)        24066.897

Root Mean Square Error of Approximation:

  RMSEA                                          0.868
  90 Percent Confidence Interval          0.851  0.885
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           4.868

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            35.226    0.229  154.111    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1              251.377   15.897   15.813    0.000
   .X2               88.644    5.702   15.546    0.000
   .X3               -0.857    1.194   -0.718    0.473
   .X4              106.607    6.814   15.646    0.000
   .X5              436.335   27.571   15.826    0.000
   .X6             1164.465   73.602   15.821    0.000
    level            27.002    2.073   13.022    0.000



==========================================
Results from the linear growth curve model
==========================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     1     0
X2     0  0  0  0  0  0     1     1
X3     0  0  0  0  0  0     1     2
X4     0  0  0  0  0  0     1     3
X5     0  0  0  0  0  0     1     4
X6     0  0  0  0  0  0     1     5
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

      X1 X2 X3 X4  X5 X6 level slope
X1    16  0  0  0   0  0     0     0
X2     0 11  0  0   0  0     0     0
X3     0  0 11  0   0  0     0     0
X4     0  0  0 13   0  0     0     0
X5     0  0  0  0 7.2  0     0     0
X6     0  0  0  0   0 34     0     0
level  0  0  0  0   0  0   1.0   2.1
slope  0  0  0  0   0  0   2.1   2.3

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     0     0
X2     0  0  0  0  0  0     0     0
X3     0  0  0  0  0  0     0     0
X4     0  0  0  0  0  0     0     0
X5     0  0  0  0  0  0     0     0
X6     0  0  0  0  0  0     0     0
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

       X1   X2   X3   X4  X5  X6 level slope
X1    1.1    0    0    0   0   0     0     0
X2      0 0.76    0    0   0   0     0     0
X3      0    0 0.81    0   0   0     0     0
X4      0    0    0 0.98   0   0     0     0
X5      0    0    0    0 0.9   0     0     0
X6      0    0    0    0   0 2.5     0     0
level   0    0    0    0   0   0  0.63  0.25
slope   0    0    0    0   0   0  0.25  0.21


lavaan 0.6-3 ended normally after 73 iterations

  Optimization method                           NLMINB
  Number of free parameters                         11

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                     802.913
  Degrees of freedom                                16
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.653
  Tucker-Lewis Index (TLI)                       0.675

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8837.293
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                         11
  Akaike (AIC)                               17696.585
  Bayesian (BIC)                             17742.946
  Sample-size adjusted Bayesian (BIC)        17708.031

Root Mean Square Error of Approximation:

  RMSEA                                          0.314
  90 Percent Confidence Interval          0.295  0.332
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           0.183

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                0.000                           
    X2                1.000                           
    X3                2.000                           
    X4                3.000                           
    X5                4.000                           
    X6                5.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             2.147    0.252    8.515    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            17.933    0.130  138.207    0.000
    slope             9.351    0.080  117.166    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1               16.004    1.145   13.977    0.000
   .X2               10.795    0.760   14.208    0.000
   .X3               11.400    0.807   14.123    0.000
   .X4               12.724    0.983   12.942    0.000
   .X5                7.216    0.895    8.060    0.000
   .X6               33.514    2.505   13.381    0.000
    level             1.039    0.633    1.642    0.101
    slope             2.307    0.206   11.210    0.000



==========================================
Results from the latent growth curve model
==========================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     1     0
X2     0  0  0  0  0  0     1   0.7
X3     0  0  0  0  0  0     1   1.6
X4     0  0  0  0  0  0     1   2.5
X5     0  0  0  0  0  0     1   3.6
X6     0  0  0  0  0  0     1   5.0
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

       X1  X2  X3  X4  X5  X6 level slope
X1    8.8   0   0   0   0   0     0     0
X2      0 9.5   0   0   0   0     0     0
X3      0   0 8.7   0   0   0     0     0
X4      0   0   0 9.5   0   0     0     0
X5      0   0   0   0 8.8   0     0     0
X6      0   0   0   0   0 9.3     0     0
level   0   0   0   0   0   0   4.1   2.2
slope   0   0   0   0   0   0   2.2   2.8

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     0     0
X2     0  0  0  0  0  0     0 0.018
X3     0  0  0  0  0  0     0 0.017
X4     0  0  0  0  0  0     0 0.017
X5     0  0  0  0  0  0     0 0.017
X6     0  0  0  0  0  0     0     0
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

       X1   X2   X3   X4  X5  X6 level slope
X1    0.7    0    0    0   0   0     0     0
X2      0 0.68    0    0   0   0     0     0
X3      0    0 0.62    0   0   0     0     0
X4      0    0    0 0.71   0   0     0     0
X5      0    0    0    0 0.8   0     0     0
X6      0    0    0    0   0 1.2     0     0
level   0    0    0    0   0   0  0.55  0.25
slope   0    0    0    0   0   0  0.25  0.21


lavaan 0.6-3 ended normally after 84 iterations

  Optimization method                           NLMINB
  Number of free parameters                         15

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                       7.995
  Degrees of freedom                                12
  P-value (Chi-square)                           0.786

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    1.000
  Tucker-Lewis Index (TLI)                       1.002

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8439.834
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                         15
  Akaike (AIC)                               16909.668
  Bayesian (BIC)                             16972.887
  Sample-size adjusted Bayesian (BIC)        16925.276

Root Mean Square Error of Approximation:

  RMSEA                                          0.000
  90 Percent Confidence Interval          0.000  0.031
  P-value RMSEA <= 0.05                          0.997

Standardized Root Mean Square Residual:

  SRMR                                           0.016

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                0.000                           
    X2                0.702    0.018   38.288    0.000
    X3                1.552    0.017   91.817    0.000
    X4                2.508    0.017  146.715    0.000
    X5                3.636    0.017  210.252    0.000
    X6                5.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             2.182    0.246    8.883    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            20.196    0.160  126.416    0.000
    slope             9.683    0.084  115.885    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                8.801    0.699   12.591    0.000
   .X2                9.481    0.684   13.871    0.000
   .X3                8.680    0.623   13.943    0.000
   .X4                9.536    0.711   13.411    0.000
   .X5                8.783    0.803   10.937    0.000
   .X6                9.273    1.203    7.706    0.000
    level             4.083    0.552    7.398    0.000
    slope             2.773    0.211   13.140    0.000



=============================================
Results from the quadratic growth curve model
=============================================


--------------------
Parameter estimates:
--------------------

Matrix A

          X1 X2 X3 X4 X5 X6 level slope quadratic
X1         0  0  0  0  0  0     1     0         0
X2         0  0  0  0  0  0     1     1         1
X3         0  0  0  0  0  0     1     2         4
X4         0  0  0  0  0  0     1     3         9
X5         0  0  0  0  0  0     1     4        16
X6         0  0  0  0  0  0     1     5        25
level      0  0  0  0  0  0     0     0         0
slope      0  0  0  0  0  0     0     0         0
quadratic  0  0  0  0  0  0     0     0         0

Matrix S

           X1  X2  X3  X4  X5 X6 level slope quadratic
X1        9.3   0   0   0   0  0     0     0         0
X2          0 9.6   0   0   0  0     0     0         0
X3          0   0 9.1   0   0  0     0     0         0
X4          0   0   0 9.7   0  0     0     0         0
X5          0   0   0   0 8.6  0     0     0         0
X6          0   0   0   0   0 11     0     0         0
level       0   0   0   0   0  0  3.79  1.76     0.108
slope       0   0   0   0   0  0  1.76  0.21     0.275
quadratic   0   0   0   0   0  0  0.11  0.27    -0.011

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

          X1 X2 X3 X4 X5 X6 level slope quadratic
X1         0  0  0  0  0  0     0     0         0
X2         0  0  0  0  0  0     0     0         0
X3         0  0  0  0  0  0     0     0         0
X4         0  0  0  0  0  0     0     0         0
X5         0  0  0  0  0  0     0     0         0
X6         0  0  0  0  0  0     0     0         0
level      0  0  0  0  0  0     0     0         0
slope      0  0  0  0  0  0     0     0         0
quadratic  0  0  0  0  0  0     0     0         0

Matrix S

           X1   X2   X3   X4   X5  X6 level slope quadratic
X1        1.1    0    0    0    0   0     0     0         0
X2          0 0.69    0    0    0   0     0     0         0
X3          0    0 0.68    0    0   0     0     0         0
X4          0    0    0 0.74    0   0     0     0         0
X5          0    0    0    0 0.85   0     0     0         0
X6          0    0    0    0    0 1.6     0     0         0
level       0    0    0    0    0   0  1.06  0.71     0.122
slope       0    0    0    0    0   0  0.71  0.65     0.113
quadratic   0    0    0    0    0   0  0.12  0.11     0.024


lavaan 0.6-3 ended normally after 81 iterations

  Optimization method                           NLMINB
  Number of free parameters                         15

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                      20.678
  Degrees of freedom                                12
  P-value (Chi-square)                           0.055

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.996
  Tucker-Lewis Index (TLI)                       0.995

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8446.175
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                         15
  Akaike (AIC)                               16922.350
  Bayesian (BIC)                             16985.569
  Sample-size adjusted Bayesian (BIC)        16937.958

Root Mean Square Error of Approximation:

  RMSEA                                          0.038
  90 Percent Confidence Interval          0.000  0.065
  P-value RMSEA <= 0.05                          0.739

Standardized Root Mean Square Residual:

  SRMR                                           0.023

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                0.000                           
    X2                1.000                           
    X3                2.000                           
    X4                3.000                           
    X5                4.000                           
    X6                5.000                           
  quadratic =~                                        
    X1                0.000                           
    X2                1.000                           
    X3                4.000                           
    X4                9.000                           
    X5               16.000                           
    X6               25.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             1.760    0.707    2.488    0.013
    quadratic         0.108    0.122    0.880    0.379
  slope ~~                                            
    quadratic         0.275    0.113    2.434    0.015

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            20.317    0.152  133.944    0.000
    slope             5.811    0.119   48.663    0.000
    quadratic         0.760    0.022   33.958    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                9.337    1.107    8.432    0.000
   .X2                9.584    0.691   13.865    0.000
   .X3                9.093    0.684   13.298    0.000
   .X4                9.745    0.738   13.213    0.000
   .X5                8.622    0.851   10.133    0.000
   .X6               10.714    1.648    6.502    0.000
    level             3.794    1.057    3.590    0.000
    slope             0.210    0.646    0.325    0.745
    quadratic        -0.011    0.024   -0.461    0.645



====================================================
Fit Statistics and Fit Indices for Model Comparisons
====================================================

                           No    Linear    Latent Quadratic
npar                 8.00e+00    11.000  1.50e+01  1.50e+01
fmin                 7.17e+00     0.803  8.00e-03  2.07e-02
chisq.per.df         1.12e+00    13.700  1.88e+03  7.25e+02
chisq                7.17e+03   802.913  8.00e+00  2.07e+01
df                   1.90e+01    16.000  1.20e+01  1.20e+01
pvalue               0.00e+00     0.000  7.86e-01  5.53e-02
baseline.chisq       2.28e+03  2281.743  2.28e+03  2.28e+03
baseline.df          1.50e+01    15.000  1.50e+01  1.50e+01
baseline.pvalue      0.00e+00     0.000  0.00e+00  0.00e+00
cfi                  0.00e+00     0.653  1.00e+00  9.96e-01
tli                 -1.49e+00     0.675  1.00e+00  9.95e-01
nnfi                -1.49e+00     0.675  1.00e+00  9.95e-01
rfi                        NA        NA  9.96e-01  9.89e-01
nfi                        NA        NA  9.96e-01  9.91e-01
pnfi                -2.71e+00     0.691  7.97e-01  7.93e-01
ifi                 -2.16e+00     0.653  1.00e+00  9.96e-01
rni                 -2.16e+00     0.653  1.00e+00  9.96e-01
logl                -1.20e+04 -8837.293 -8.44e+03 -8.45e+03
unrestricted.logl   -8.44e+03 -8435.836 -8.44e+03 -8.44e+03
aic                  2.41e+04 17696.585  1.69e+04  1.69e+04
bic                  2.41e+04 17742.946  1.70e+04  1.70e+04
ntotal               5.00e+02   500.000  5.00e+02  5.00e+02
bic2                 2.41e+04 17708.031  1.69e+04  1.69e+04
rmsea                8.68e-01     0.314  0.00e+00  3.80e-02
rmsea.ci.lower       8.51e-01     0.295  0.00e+00  0.00e+00
rmsea.ci.upper       8.85e-01     0.332  3.06e-02  6.50e-02
rmsea.pvalue         0.00e+00     0.000  9.97e-01  7.39e-01
rmr                  2.30e+02     2.976  7.44e-01  7.84e-01
rmr_nomean           2.61e+02     3.195  8.43e-01  8.82e-01
srmr                 4.87e+00     0.183  1.61e-02  2.27e-02
srmr_bentler         4.87e+00     0.183  1.61e-02  2.27e-02
srmr_bentler_nomean  5.34e+00     0.105  1.83e-02  1.88e-02
crmr                 2.18e+00     0.323  3.94e-02  3.74e-02
crmr_nomean          4.87e-01     0.107  1.21e-02  1.22e-02
srmr_mplus           5.07e+00     0.294  3.60e-02  3.45e-02
srmr_mplus_nomean    5.34e+00     0.122  1.50e-02  1.54e-02
cn_05                3.10e+00    17.376  1.32e+03  5.09e+02
cn_01                3.52e+00    20.927  1.64e+03  6.35e+02
gfi                  8.77e-01     0.979  1.00e+00  9.99e-01
agfi                 8.26e-01     0.965  9.99e-01  9.99e-01
pgfi                 6.17e-01     0.580  4.44e-01  4.44e-01
mfi                  7.83e-04     0.455  1.00e+00  9.91e-01
ecvi                 1.44e+01     1.650  7.60e-02  1.01e-01
Warning messages:
1: In lav_object_post_check(object) :
  lavaan WARNING: some estimated ov variances are negative
2: In lav_object_post_check(object) :
  lavaan WARNING: covariance matrix of latent variables
                is not positive definite;
                use lavInspect(fit, "cov.lv") to investigate.
3: In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative


======================================
Results from the no growth curve model
======================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X4 X6 level
X1     0  0  0  0     1
X2     0  0  0  0     1
X4     0  0  0  0     1
X6     0  0  0  0     1
level  0  0  0  0     0

Matrix S

       X1  X2  X4  X6 level
X1    490   0   0   0     0
X2      0 490   0   0     0
X4      0   0 490   0     0
X6      0   0   0 490     0
level   0   0   0   0   -95

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X4 X6 level
X1     0  0  0  0     0
X2     0  0  0  0     0
X4     0  0  0  0     0
X6     0  0  0  0     0
level  0  0  0  0     0

Matrix S

      X1 X2 X4 X6 level
X1    18  0  0  0     0
X2     0 18  0  0     0
X4     0  0 18  0     0
X6     0  0  0 18     0
level  0  0  0  0   4.8


lavaan 0.6-3 ended normally after 43 iterations

  Optimization method                           NLMINB
  Number of free parameters                          6
  Number of equality constraints                     3

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                    5679.277
  Degrees of freedom                                11
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic              978.529
  Degrees of freedom                                 6
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.000
  Tucker-Lewis Index (TLI)                      -2.179

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8659.914
  Loglikelihood unrestricted model (H1)      -5820.276

  Number of free parameters                          3
  Akaike (AIC)                               17325.829
  Bayesian (BIC)                             17338.473
  Sample-size adjusted Bayesian (BIC)        17328.950

Root Mean Square Error of Approximation:

  RMSEA                                          1.015
  90 Percent Confidence Interval          0.993  1.037
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                          10.418

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X4                1.000                           
    X6                1.000                           

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X4                0.000                           
   .X6                0.000                           
    level            40.062    0.235  170.288    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)  489.701   17.881   27.386    0.000
   .X2      (vare)  489.701   17.881   27.386    0.000
   .X4      (vare)  489.701   17.881   27.386    0.000
   .X6      (vare)  489.701   17.881   27.386    0.000
    level           -94.752    4.801  -19.737    0.000



==========================================
Results from the linear growth curve model
==========================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X4 X6 level slope
X1     0  0  0  0     1     1
X2     0  0  0  0     1     2
X4     0  0  0  0     1     4
X6     0  0  0  0     1     6
level  0  0  0  0     0     0
slope  0  0  0  0     0     0

Matrix S

      X1 X2 X4 X6 level slope
X1    18  0  0  0     0     0
X2     0 18  0  0     0     0
X4     0  0 18  0     0     0
X6     0  0  0 18     0     0
level  0  0  0  0 -5.25  0.74
slope  0  0  0  0  0.74  2.25

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X4 X6 level slope
X1     0  0  0  0     0     0
X2     0  0  0  0     0     0
X4     0  0  0  0     0     0
X6     0  0  0  0     0     0
level  0  0  0  0     0     0
slope  0  0  0  0     0     0

Matrix S

        X1   X2   X4   X6 level slope
X1    0.79    0    0    0     0     0
X2       0 0.79    0    0     0     0
X4       0    0 0.79    0     0     0
X6       0    0    0 0.79     0     0
level    0    0    0    0  1.07  0.36
slope    0    0    0    0  0.36  0.22


lavaan 0.6-3 ended normally after 48 iterations

  Optimization method                           NLMINB
  Number of free parameters                          9
  Number of equality constraints                     3

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                     654.237
  Degrees of freedom                                 8
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic              978.529
  Degrees of freedom                                 6
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.336
  Tucker-Lewis Index (TLI)                       0.502

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -6147.394
  Loglikelihood unrestricted model (H1)      -5820.276

  Number of free parameters                          6
  Akaike (AIC)                               12306.789
  Bayesian (BIC)                             12332.077
  Sample-size adjusted Bayesian (BIC)        12313.032

Root Mean Square Error of Approximation:

  RMSEA                                          0.402
  90 Percent Confidence Interval          0.376  0.428
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           0.254

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X4                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                1.000                           
    X2                2.000                           
    X4                4.000                           
    X6                6.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             0.739    0.362    2.043    0.041

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X4                0.000                           
   .X6                0.000                           
    level             8.590    0.153   55.975    0.000
    slope             9.684    0.083  116.744    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)   17.626    0.788   22.361    0.000
   .X2      (vare)   17.626    0.788   22.361    0.000
   .X4      (vare)   17.626    0.788   22.361    0.000
   .X6      (vare)   17.626    0.788   22.361    0.000
    level            -5.252    1.065   -4.931    0.000
    slope             2.245    0.224   10.021    0.000



==========================================
Results from the latent growth curve model
==========================================


--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X4 X6 level slope
X1     0  0  0  0     1   1.0
X2     0  0  0  0     1   6.9
X4     0  0  0  0     1   4.0
X6     0  0  0  0     1     0
level  0  0  0  0     0     0
slope  0  0  0  0     0     0

Matrix S

       X1  X2  X4  X6 level slope
X1    579   0   0   0     0     0
X2      0 579   0   0     0     0
X4      0   0 579   0     0     0
X6      0   0   0 579     0     0
level   0   0   0   0  -272    55
slope   0   0   0   0    55   -19

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X4 X6 level slope
X1     0  0  0  0     0     0
X2     0  0  0  0     0  0.07
X4     0  0  0  0     0     0
X6     0  0  0  0     0     0
level  0  0  0  0     0     0
slope  0  0  0  0     0     0

Matrix S

      X1 X2 X4 X6 level slope
X1    26  0  0  0     0     0
X2     0 26  0  0     0     0
X4     0  0 26  0     0     0
X6     0  0  0 26     0     0
level  0  0  0  0  14.7  2.76
slope  0  0  0  0   2.8  0.96


lavaan 0.6-3 ended normally after 322 iterations

  Optimization method                           NLMINB
  Number of free parameters                         10
  Number of equality constraints                     3

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                    3927.304
  Degrees of freedom                                 7
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic              978.529
  Degrees of freedom                                 6
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.000
  Tucker-Lewis Index (TLI)                      -2.455

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -7783.928
  Loglikelihood unrestricted model (H1)      -5820.276

  Number of free parameters                          7
  Akaike (AIC)                               15581.856
  Bayesian (BIC)                             15611.358
  Sample-size adjusted Bayesian (BIC)        15589.140

Root Mean Square Error of Approximation:

  RMSEA                                          1.058
  90 Percent Confidence Interval          1.031  1.086
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           9.233

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X4                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                1.000                           
    X2                6.880    0.070   98.845    0.000
    X4                4.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope            54.794    2.762   19.840    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X4                0.000                           
   .X6                0.000                           
    level            49.487    0.314  157.739    0.000
    slope            -3.174    0.046  -69.143    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)  579.379   25.911   22.361    0.000
   .X2      (vare)  579.379   25.911   22.361    0.000
   .X4      (vare)  579.379   25.911   22.361    0.000
   .X6      (vare)  579.379   25.911   22.361    0.000
    level          -272.106   14.716  -18.490    0.000
    slope           -19.334    0.964  -20.066    0.000



=============================================
Results from the quadratic growth curve model
=============================================


--------------------
Parameter estimates:
--------------------

Matrix A

          X1 X2 X4 X6 level slope quadratic
X1         0  0  0  0     1     1         1
X2         0  0  0  0     1     2         4
X4         0  0  0  0     1     4        16
X6         0  0  0  0     1     6        36
level      0  0  0  0     0     0         0
slope      0  0  0  0     0     0         0
quadratic  0  0  0  0     0     0         0

Matrix S

           X1  X2  X4  X6 level slope quadratic
X1        9.9   0   0   0     0     0         0
X2          0 9.9   0   0     0     0         0
X4          0   0 9.9   0     0     0         0
X6          0   0   0 9.9     0     0         0
level       0   0   0   0 -3.51  4.50    -0.479
slope       0   0   0   0  4.50 -2.34     0.483
quadratic   0   0   0   0 -0.48  0.48    -0.034

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

          X1 X2 X4 X6 level slope quadratic
X1         0  0  0  0     0     0         0
X2         0  0  0  0     0     0         0
X4         0  0  0  0     0     0         0
X6         0  0  0  0     0     0         0
level      0  0  0  0     0     0         0
slope      0  0  0  0     0     0         0
quadratic  0  0  0  0     0     0         0

Matrix S

            X1   X2   X4   X6 level slope quadratic
X1        0.63    0    0    0     0     0         0
X2           0 0.63    0    0     0     0         0
X4           0    0 0.63    0     0     0         0
X6           0    0    0 0.63     0     0         0
level        0    0    0    0  3.14  2.07     0.277
slope        0    0    0    0  2.07  1.58     0.216
quadratic    0    0    0    0  0.28  0.22     0.031


lavaan 0.6-3 ended normally after 82 iterations

  Optimization method                           NLMINB
  Number of free parameters                         13
  Number of equality constraints                     3

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                       3.043
  Degrees of freedom                                 4
  P-value (Chi-square)                           0.551

Model test baseline model:

  Minimum Function Test Statistic              978.529
  Degrees of freedom                                 6
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    1.000
  Tucker-Lewis Index (TLI)                       1.001

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -5821.797
  Loglikelihood unrestricted model (H1)      -5820.276

  Number of free parameters                         10
  Akaike (AIC)                               11663.594
  Bayesian (BIC)                             11705.740
  Sample-size adjusted Bayesian (BIC)        11674.000

Root Mean Square Error of Approximation:

  RMSEA                                          0.000
  90 Percent Confidence Interval          0.000  0.060
  P-value RMSEA <= 0.05                          0.900

Standardized Root Mean Square Residual:

  SRMR                                           0.014

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X4                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                1.000                           
    X2                2.000                           
    X4                4.000                           
    X6                6.000                           
  quadratic =~                                        
    X1                1.000                           
    X2                4.000                           
    X4               16.000                           
    X6               36.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             4.497    2.069    2.174    0.030
    quadratic        -0.479    0.277   -1.730    0.084
  slope ~~                                            
    quadratic         0.483    0.216    2.239    0.025

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X4                0.000                           
   .X6                0.000                           
    level            15.293    0.258   59.267    0.000
    slope             4.208    0.182   23.157    0.000
    quadratic         0.778    0.026   30.160    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)    9.911    0.627   15.811    0.000
   .X2      (vare)    9.911    0.627   15.811    0.000
   .X4      (vare)    9.911    0.627   15.811    0.000
   .X6      (vare)    9.911    0.627   15.811    0.000
    level            -3.512    3.139   -1.119    0.263
    slope            -2.336    1.584   -1.474    0.140
    quadrtc          -0.034    0.031   -1.090    0.276



====================================================
Fit Statistics and Fit Indices for Model Comparisons
====================================================

                           No    Linear    Latent Quadratic
npar                 3.00e+00     6.000  7.00e+00  1.00e+01
fmin                 5.68e+00     0.654  3.93e+00  3.04e-03
chisq.per.df         5.28e-01     9.171  1.78e+00  3.29e+03
chisq                5.68e+03   654.237  3.93e+03  3.04e+00
df                   1.10e+01     8.000  7.00e+00  4.00e+00
pvalue               0.00e+00     0.000  0.00e+00  5.51e-01
baseline.chisq       9.79e+02   978.529  9.79e+02  9.79e+02
baseline.df          6.00e+00     6.000  6.00e+00  6.00e+00
baseline.pvalue      0.00e+00     0.000  0.00e+00  0.00e+00
cfi                  0.00e+00     0.336  0.00e+00  1.00e+00
tli                 -2.18e+00     0.502 -2.46e+00  1.00e+00
nnfi                -2.18e+00     0.502 -2.46e+00  1.00e+00
rfi                        NA        NA        NA  9.95e-01
nfi                        NA        NA        NA  9.97e-01
pnfi                -8.81e+00     0.442 -3.52e+00  6.65e-01
ifi                 -4.86e+00     0.334 -3.04e+00  1.00e+00
rni                 -4.83e+00     0.336 -3.03e+00  1.00e+00
logl                -8.66e+03 -6147.394 -7.78e+03 -5.82e+03
unrestricted.logl   -5.82e+03 -5820.276 -5.82e+03 -5.82e+03
aic                  1.73e+04 12306.789  1.56e+04  1.17e+04
bic                  1.73e+04 12332.077  1.56e+04  1.17e+04
ntotal               5.00e+02   500.000  5.00e+02  5.00e+02
bic2                 1.73e+04 12313.032  1.56e+04  1.17e+04
rmsea                1.02e+00     0.402  1.06e+00  0.00e+00
rmsea.ci.lower       9.93e-01     0.376  1.03e+00  0.00e+00
rmsea.ci.upper       1.04e+00     0.428  1.09e+00  5.97e-02
rmsea.pvalue         0.00e+00     0.000  0.00e+00  9.00e-01
rmr                  2.04e+02     4.160  1.87e+02  1.36e-01
rmr_nomean           2.41e+02     4.753  2.21e+02  1.45e-01
srmr                 1.04e+01     0.254  9.23e+00  1.40e-02
srmr_bentler         1.04e+01     0.254  9.23e+00  1.40e-02
srmr_bentler_nomean  1.21e+01     0.186  1.07e+01  6.48e-03
crmr                 2.82e+00     0.429  2.68e+00  3.23e-02
crmr_nomean          8.00e-01     0.163  8.64e-01  5.57e-03
srmr_mplus           1.02e+01     0.386  8.80e+00  2.78e-02
srmr_mplus_nomean    1.17e+01     0.201  1.01e+01  7.27e-03
cn_05                2.73e+00    12.851  2.79e+00  1.56e+03
cn_01                3.18e+00    16.354  3.35e+00  2.18e+03
gfi                  9.30e-01     0.982  9.54e-01  1.00e+00
agfi                 9.11e-01     0.968  9.07e-01  1.00e+00
pgfi                 7.31e-01     0.561  4.77e-01  2.86e-01
mfi                  3.45e-03     0.524  1.98e-02  1.00e+00
ecvi                 1.14e+01     1.332  7.88e+00  4.61e-02
Warning messages:
1: In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative
2: In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative
3: In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative
4: In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative

--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     1     0
X2     0  0  0  0  0  0     1     1
X3     0  0  0  0  0  0     1     2
X4     0  0  0  0  0  0     1     3
X5     0  0  0  0  0  0     1     4
X6     0  0  0  0  0  0     1     5
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

      X1 X2 X3 X4 X5 X6 level slope
X1    15  0  0  0  0  0     0     0
X2     0 15  0  0  0  0     0     0
X3     0  0 15  0  0  0     0     0
X4     0  0  0 15  0  0     0     0
X5     0  0  0  0 15  0     0     0
X6     0  0  0  0  0 15     0     0
level  0  0  0  0  0  0  0.17   2.3
slope  0  0  0  0  0  0  2.31   2.4

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X3 X4 X5 X6 level slope
X1     0  0  0  0  0  0     0     0
X2     0  0  0  0  0  0     0     0
X3     0  0  0  0  0  0     0     0
X4     0  0  0  0  0  0     0     0
X5     0  0  0  0  0  0     0     0
X6     0  0  0  0  0  0     0     0
level  0  0  0  0  0  0     0     0
slope  0  0  0  0  0  0     0     0

Matrix S

        X1   X2   X3   X4   X5   X6 level slope
X1    0.47    0    0    0    0    0     0     0
X2       0 0.47    0    0    0    0     0     0
X3       0    0 0.47    0    0    0     0     0
X4       0    0    0 0.47    0    0     0     0
X5       0    0    0    0 0.47    0     0     0
X6       0    0    0    0    0 0.47     0     0
level    0    0    0    0    0    0  0.56  0.24
slope    0    0    0    0    0    0  0.24  0.21


lavaan 0.6-3 ended normally after 53 iterations

  Optimization method                           NLMINB
  Number of free parameters                         11
  Number of equality constraints                     5

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                     978.024
  Degrees of freedom                                21
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic             2281.743
  Degrees of freedom                                15
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.578
  Tucker-Lewis Index (TLI)                       0.698

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -8924.848
  Loglikelihood unrestricted model (H1)      -8435.836

  Number of free parameters                          6
  Akaike (AIC)                               17861.696
  Bayesian (BIC)                             17886.984
  Sample-size adjusted Bayesian (BIC)        17867.940

Root Mean Square Error of Approximation:

  RMSEA                                          0.302
  90 Percent Confidence Interval          0.286  0.318
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           0.203

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X3                1.000                           
    X4                1.000                           
    X5                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                0.000                           
    X2                1.000                           
    X3                2.000                           
    X4                3.000                           
    X5                4.000                           
    X6                5.000                           

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~~                                            
    slope             2.307    0.237    9.751    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X3                0.000                           
   .X4                0.000                           
   .X5                0.000                           
   .X6                0.000                           
    level            17.776    0.126  141.288    0.000
    slope             9.617    0.081  119.306    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)   14.779    0.467   31.623    0.000
   .X2      (vare)   14.779    0.467   31.623    0.000
   .X3      (vare)   14.779    0.467   31.623    0.000
   .X4      (vare)   14.779    0.467   31.623    0.000
   .X5      (vare)   14.779    0.467   31.623    0.000
   .X6      (vare)   14.779    0.467   31.623    0.000
    level             0.173    0.557    0.311    0.756
    slope             2.404    0.207   11.603    0.000

Warning message:
In lav_object_post_check(object) :
  lavaan WARNING: covariance matrix of latent variables
                is not positive definite;
                use lavInspect(fit, "cov.lv") to investigate.

--------------------
Parameter estimates:
--------------------

Matrix A

      X1 X2 X4 X6    X3     X5 level slope
X1     0  0  0  0     0      0     1     1
X2     0  0  0  0     0      0     1     2
X4     0  0  0  0     0      0     1     4
X6     0  0  0  0     0      0     1     6
X3     0  0  0  0     0      0     0     0
X5     0  0  0  0     0      0     0     0
level  0  0  0  0 0.060 -0.072     0     0
slope  0  0  0  0 0.068  0.161     0     0

Matrix S

      X1 X2 X4 X6 X3 X5 level slope
X1    18  0  0  0  0  0     0     0
X2     0 18  0  0  0  0     0     0
X4     0  0 18  0  0  0     0     0
X6     0  0  0 18  0  0     0     0
X3     0  0  0  0 26 30     0     0
X5     0  0  0  0 30 63     0     0
level  0  0  0  0  0  0  -5.4  1.23
slope  0  0  0  0  0  0   1.2 -0.15

----------------------------------------
Standard errors for parameter estimates:
----------------------------------------

Matrix A

      X1 X2 X4 X6    X3     X5 level slope
X1     0  0  0  0     0      0     0     0
X2     0  0  0  0     0      0     0     0
X4     0  0  0  0     0      0     0     0
X6     0  0  0  0     0      0     0     0
X3     0  0  0  0     0      0     0     0
X5     0  0  0  0     0      0     0     0
level  0  0  0  0 0.045 0.0287     0     0
slope  0  0  0  0 0.013 0.0086     0     0

Matrix S

        X1   X2   X4   X6 X3 X5 level slope
X1    0.79    0    0    0  0  0     0     0
X2       0 0.79    0    0  0  0     0     0
X4       0    0 0.79    0  0  0     0     0
X6       0    0    0 0.79  0  0     0     0
X3       0    0    0    0  0  0     0     0
X5       0    0    0    0  0  0     0     0
level    0    0    0    0  0  0  1.06 0.262
slope    0    0    0    0  0  0  0.26 0.085


lavaan 0.6-3 ended normally after 52 iterations

  Optimization method                           NLMINB
  Number of free parameters                         13
  Number of equality constraints                     3

  Number of observations                           500

  Estimator                                         ML
  Model Fit Test Statistic                     654.901
  Degrees of freedom                                12
  P-value (Chi-square)                           0.000

Model test baseline model:

  Minimum Function Test Statistic             1879.543
  Degrees of freedom                                14
  P-value                                        0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.655
  Tucker-Lewis Index (TLI)                       0.598

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -5697.219
  Loglikelihood unrestricted model (H1)      -5369.769

  Number of free parameters                         10
  Akaike (AIC)                               11414.438
  Bayesian (BIC)                             11456.584
  Sample-size adjusted Bayesian (BIC)        11424.844

Root Mean Square Error of Approximation:

  RMSEA                                          0.327
  90 Percent Confidence Interval          0.306  0.349
  P-value RMSEA <= 0.05                          0.000

Standardized Root Mean Square Residual:

  SRMR                                           0.185

Parameter Estimates:

  Information                                 Expected
  Information saturated (h1) model          Structured
  Standard Errors                             Standard

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  level =~                                            
    X1                1.000                           
    X2                1.000                           
    X4                1.000                           
    X6                1.000                           
  slope =~                                            
    X1                1.000                           
    X2                2.000                           
    X4                4.000                           
    X6                6.000                           

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  level ~                                             
    X3                0.060    0.045    1.333    0.183
    X5               -0.072    0.029   -2.528    0.011
  slope ~                                             
    X3                0.068    0.013    5.030    0.000
    X5                0.161    0.009   18.691    0.000

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
 .level ~~                                            
   .slope             1.229    0.262    4.697    0.000

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1                0.000                           
   .X2                0.000                           
   .X4                0.000                           
   .X6                0.000                           
   .level            10.498    1.146    9.157    0.000
   .slope            -1.601    0.343   -4.661    0.000

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .X1      (vare)   17.626    0.788   22.361    0.000
   .X2      (vare)   17.626    0.788   22.361    0.000
   .X4      (vare)   17.626    0.788   22.361    0.000
   .X6      (vare)   17.626    0.788   22.361    0.000
   .level            -5.416    1.058   -5.119    0.000
   .slope            -0.153    0.085   -1.797    0.072

Warning message:
In lav_object_post_check(object) :
  lavaan WARNING: some estimated lv variances are negative
Running  dot -Tpdf -o gcmlinear.pdf  gcmlinear.dot 

RAMpath documentation built on May 2, 2019, 9:12 a.m.