# ramLCM: Conduct growth curve analysis In RAMpath: Structural Equation Modeling Using the Reticular Action Model (RAM) Notation

## Description

Conduct growth curve analysis

## Usage

 1 2 3 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

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 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

This is lavaan 0.6-3
lavaan is BETA software! Please report any bugs.

Attaching package: 'ellipse'

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

pairs

======================================
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

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

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

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

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
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
slope ~~

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

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

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

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

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

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

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

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
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
slope ~~

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

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

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

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

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

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

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

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
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
slope ~~

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

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

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

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

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

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.