Zukunft Paper: LGCM Nonlinear – Latent Growth Curve Models
Dieses Dokument zeigt den kompletten Workflow von der
Datenaufbereitung über die Modellschätzung bis zur Visualisierung der
latent growth curve Modelle.
1. Setup und Datenimport
# Setze das Working Directory auf den Ordner dieser Datei
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
# Lade benötigte Pakete (falls nicht installiert, installiere sie vorher)
library(lavaan)
library(readr)
library(dplyr)
library(semPlot)
library(semTools)
library(ggplot2)
library(haven)
library(skimr)
library(purrr)
library(stringr)
library(tidyr)
# Lade externe Funktionen (z.B. transform_data, model_fit_calc) aus einer separaten Datei
source("functions_for_models.R")
# Lese den Datensatz ein (Passe den Pfad ggf. an)
data <- read_dta("Quantitative Daten/Datensatz/allwaves_2850cases(1).dta")
# Optional: View(data)
# Transformiere die Daten (Funktion aus functions_for_models.R)
data <- transform_data(data)
# Wandele alle 'haven_labelled'-Spalten in numerische Spalten um
data[] <- lapply(data, function(x) {
if (inherits(x, "haven_labelled")) {
as.numeric(x)
} else {
x
}
})
2. Überblick über die Originalvariablen
# Übersicht für das "Gesund"-Modell:
skim(data %>% select(gesund2, gesund3, gesund4, gesund5))
Data summary
| Name |
data %>% select(gesund2, … |
| Number of rows |
772 |
| Number of columns |
4 |
| _______________________ |
|
| Column type frequency: |
|
| numeric |
4 |
| ________________________ |
|
| Group variables |
None |
Variable type: numeric
| gesund2 |
84 |
0.89 |
1.24 |
0.50 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| gesund3 |
335 |
0.57 |
1.28 |
0.55 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| gesund4 |
341 |
0.56 |
1.32 |
0.60 |
1 |
1 |
1 |
2 |
4 |
▇▂▁▁▁ |
| gesund5 |
462 |
0.40 |
1.39 |
0.62 |
1 |
1 |
1 |
2 |
4 |
▇▃▁▁▁ |
skim(data %>% select(v_201_22, v_201_32, v_201_41, v_201_51))
Data summary
| Name |
data %>% select(v_201_22,… |
| Number of rows |
772 |
| Number of columns |
4 |
| _______________________ |
|
| Column type frequency: |
|
| numeric |
4 |
| ________________________ |
|
| Group variables |
None |
Variable type: numeric
| v_201_22 |
84 |
0.89 |
1.24 |
0.50 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| v_201_32 |
335 |
0.57 |
1.28 |
0.55 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| v_201_41 |
336 |
0.56 |
1.36 |
0.73 |
1 |
1 |
1 |
2 |
6 |
▇▁▁▁▁ |
| v_201_51 |
462 |
0.40 |
1.39 |
0.62 |
1 |
1 |
1 |
2 |
4 |
▇▃▁▁▁ |
# Übersicht für das "Beruf"-Modell:
skim(data %>% select(beruf2, beruf3, beruf4, beruf5))
Data summary
| Name |
data %>% select(beruf2, b… |
| Number of rows |
772 |
| Number of columns |
4 |
| _______________________ |
|
| Column type frequency: |
|
| numeric |
4 |
| ________________________ |
|
| Group variables |
None |
Variable type: numeric
| beruf2 |
88 |
0.89 |
1.23 |
0.53 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| beruf3 |
337 |
0.56 |
1.17 |
0.43 |
1 |
1 |
1 |
1 |
3 |
▇▁▁▁▁ |
| beruf4 |
337 |
0.56 |
1.22 |
0.51 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| beruf5 |
462 |
0.40 |
1.27 |
0.58 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
# Übersicht für das "Familie"-Modell:
skim(data %>% select(familie2, familie3, familie4, familie5))
Data summary
| Name |
data %>% select(familie2,… |
| Number of rows |
772 |
| Number of columns |
4 |
| _______________________ |
|
| Column type frequency: |
|
| numeric |
4 |
| ________________________ |
|
| Group variables |
None |
Variable type: numeric
| familie2 |
115 |
0.85 |
1.52 |
0.79 |
1 |
1 |
1 |
2 |
4 |
▇▃▁▁▁ |
| familie3 |
346 |
0.55 |
1.56 |
0.87 |
1 |
1 |
1 |
2 |
4 |
▇▂▁▂▁ |
| familie4 |
365 |
0.53 |
1.70 |
0.94 |
1 |
1 |
1 |
2 |
4 |
▇▃▁▂▁ |
| familie5 |
478 |
0.38 |
1.81 |
1.00 |
1 |
1 |
1 |
2 |
4 |
▇▃▁▂▂ |
# Übersicht für das "Freunde"-Modell:
skim(data %>% select(freunde2, freunde3, freunde4, freunde5))
Data summary
| Name |
data %>% select(freunde2,… |
| Number of rows |
772 |
| Number of columns |
4 |
| _______________________ |
|
| Column type frequency: |
|
| numeric |
4 |
| ________________________ |
|
| Group variables |
None |
Variable type: numeric
| freunde2 |
79 |
0.90 |
1.27 |
0.54 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| freunde3 |
331 |
0.57 |
1.25 |
0.53 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| freunde4 |
344 |
0.55 |
1.30 |
0.59 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
| freunde5 |
462 |
0.40 |
1.31 |
0.66 |
1 |
1 |
1 |
1 |
4 |
▇▂▁▁▁ |
3. Schätzung der Latent Growth Curve Modelle
3.1 Familie
model_familie <- '
i =~ 1*familie2 + 1*familie3 + 1*familie4 + 1*familie5
s =~ 0*familie2 + a*familie3 + b*familie4 + 3*familie5
i ~ 1
s ~ 1
familie2 ~ 0*1
familie3 ~ 0*1
familie4 ~ 0*1
familie5 ~ 0*1
i ~~ i
s ~~ s
i ~~ s
'
fit_familie <- sem(
model_familie,
data = data,
missing = "ML",
estimator = "MLR",
cluster = "schulid"
)
cat("Fit Familie:\n")
## Fit Familie:
summary(fit_familie, fit.measures = TRUE, standardized = TRUE)
## lavaan 0.6-18 ended normally after 36 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
##
## Used Total
## Number of observations 705 772
## Number of clusters [schulid] 97
## Number of missing patterns 15
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 10.780 11.897
## Degrees of freedom 3 3
## P-value (Chi-square) 0.013 0.008
## Scaling correction factor 0.906
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 637.575 386.607
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.649
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.988 0.977
## Tucker-Lewis Index (TLI) 0.975 0.953
##
## Robust Comparative Fit Index (CFI) 0.986
## Robust Tucker-Lewis Index (TLI) 0.972
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1971.426 -1971.426
## Scaling correction factor 1.504
## for the MLR correction
## Loglikelihood unrestricted model (H1) -1966.036 -1966.036
## Scaling correction factor 1.376
## for the MLR correction
##
## Akaike (AIC) 3964.852 3964.852
## Bayesian (BIC) 4014.992 4014.992
## Sample-size adjusted Bayesian (SABIC) 3980.065 3980.065
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.061 0.065
## 90 Percent confidence interval - lower 0.024 0.028
## 90 Percent confidence interval - upper 0.102 0.108
## P-value H_0: RMSEA <= 0.050 0.270 0.221
## P-value H_0: RMSEA >= 0.080 0.246 0.317
##
## Robust RMSEA 0.090
## 90 Percent confidence interval - lower 0.029
## 90 Percent confidence interval - upper 0.157
## P-value H_0: Robust RMSEA <= 0.050 0.118
## P-value H_0: Robust RMSEA >= 0.080 0.667
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.045 0.045
##
## Parameter Estimates:
##
## Standard errors Robust.cluster
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i =~
## familie2 1.000 0.725 0.918
## familie3 1.000 0.725 0.858
## familie4 1.000 0.725 0.802
## familie5 1.000 0.725 0.715
## s =~
## familie2 0.000 0.000 0.000
## familie3 (a) 1.265 0.319 3.960 0.000 0.291 0.344
## familie4 (b) 2.831 0.529 5.357 0.000 0.651 0.720
## familie5 3.000 0.690 0.680
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~~
## s -0.060 0.036 -1.655 0.098 -0.361 -0.361
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 1.519 0.033 45.739 0.000 2.094 2.094
## s 0.060 0.014 4.404 0.000 0.259 0.259
## .familie2 0.000 0.000 0.000
## .familie3 0.000 0.000 0.000
## .familie4 0.000 0.000 0.000
## .familie5 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 0.526 0.085 6.226 0.000 1.000 1.000
## s 0.053 0.020 2.617 0.009 1.000 1.000
## .familie2 0.099 0.075 1.308 0.191 0.099 0.158
## .familie3 0.256 0.037 6.845 0.000 0.256 0.358
## .familie4 0.208 0.067 3.099 0.002 0.208 0.255
## .familie5 0.388 0.086 4.532 0.000 0.388 0.377
3.2 Freunde
model_freunde <- '
i =~ 1*freunde2 + 1*freunde3 + 1*freunde4 + 1*freunde5
s =~ 0*freunde2 + a*freunde3 + b*freunde4 + 3*freunde5
i ~ 1
s ~ 1
freunde2 ~ 0*1
freunde3 ~ 0*1
freunde4 ~ 0*1
freunde5 ~ 0*1
i ~~ i
s ~~ s
i ~~ s
'
fit_freunde <- sem(
model_freunde,
data = data,
missing = "ML",
estimator = "MLR",
cluster = "schulid"
)
cat("Fit Freunde:\n")
## Fit Freunde:
summary(fit_freunde, fit.measures = TRUE, standardized = TRUE)
## lavaan 0.6-18 ended normally after 56 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
##
## Used Total
## Number of observations 722 772
## Number of clusters [schulid] 97
## Number of missing patterns 15
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 4.513 NA
## Degrees of freedom 3 3
## P-value (Chi-square) 0.211 NA
## Scaling correction factor NA
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 163.959 97.810
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.676
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.990 NA
## Tucker-Lewis Index (TLI) 0.981 NA
##
## Robust Comparative Fit Index (CFI) 0.991
## Robust Tucker-Lewis Index (TLI) 0.981
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1511.966 -1511.966
## Scaling correction factor 2.350
## for the MLR correction
## Loglikelihood unrestricted model (H1) -1509.709 -1509.709
## Scaling correction factor 1.779
## for the MLR correction
##
## Akaike (AIC) 3045.931 3045.931
## Bayesian (BIC) 3096.333 3096.333
## Sample-size adjusted Bayesian (SABIC) 3061.405 3061.405
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.026 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.073 0.000
## P-value H_0: RMSEA <= 0.050 0.748 NA
## P-value H_0: RMSEA >= 0.080 0.025 NA
##
## Robust RMSEA 0.038
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.135
## P-value H_0: Robust RMSEA <= 0.050 0.469
## P-value H_0: Robust RMSEA >= 0.080 0.316
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.026 0.026
##
## Parameter Estimates:
##
## Standard errors Robust.cluster
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i =~
## freunde2 1.000 0.325 0.602
## freunde3 1.000 0.325 0.610
## freunde4 1.000 0.325 0.544
## freunde5 1.000 0.325 0.495
## s =~
## freunde2 0.000 0.000 0.000
## freunde3 (a) -0.473 5.836 -0.081 0.935 -0.026 -0.048
## freunde4 (b) 2.864 8.116 0.353 0.724 0.155 0.259
## freunde5 3.000 0.162 0.247
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~~
## s -0.000 0.006 -0.053 0.958 -0.018 -0.018
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 1.269 0.039 32.756 0.000 3.903 3.903
## s 0.018 0.054 0.325 0.745 0.324 0.324
## .freunde2 0.000 0.000 0.000
## .freunde3 0.000 0.000 0.000
## .freunde4 0.000 0.000 0.000
## .freunde5 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 0.106 0.024 4.403 0.000 1.000 1.000
## s 0.003 0.009 0.320 0.749 1.000 1.000
## .freunde2 0.186 0.029 6.483 0.000 0.186 0.638
## .freunde3 0.177 0.048 3.723 0.000 0.177 0.625
## .freunde4 0.229 0.082 2.783 0.005 0.229 0.642
## .freunde5 0.302 0.070 4.331 0.000 0.302 0.699
3.3 Beruf
model_beruf <- '
i =~ 1*beruf2 + 1*beruf3 + 1*beruf4 + 1*beruf5
s =~ 0*beruf2 + a*beruf3 + b*beruf4 + 3*beruf5
i ~ 1
s ~ 1
beruf2 ~ 0*1
beruf3 ~ 0*1
beruf4 ~ 0*1
beruf5 ~ 0*1
i ~~ i
s ~~ 0*s
i ~~ 0*s
'
fit_beruf <- sem(
model_beruf,
data = data,
missing = "ML",
estimator = "MLR",
cluster = "schulid"
)
cat("Fit Beruf:\n")
## Fit Beruf:
summary(fit_beruf, fit.measures = TRUE, standardized = TRUE)
## lavaan 0.6-18 ended normally after 113 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 9
##
## Used Total
## Number of observations 719 772
## Number of clusters [schulid] 97
## Number of missing patterns 15
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 7.297 4.741
## Degrees of freedom 5 5
## P-value (Chi-square) 0.199 0.448
## Scaling correction factor 1.539
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 116.020 65.092
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.782
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.979 1.000
## Tucker-Lewis Index (TLI) 0.975 1.005
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.003
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1323.825 -1323.825
## Scaling correction factor 2.708
## for the MLR correction
## Loglikelihood unrestricted model (H1) -1320.177 -1320.177
## Scaling correction factor 2.291
## for the MLR correction
##
## Akaike (AIC) 2665.650 2665.650
## Bayesian (BIC) 2706.851 2706.851
## Sample-size adjusted Bayesian (SABIC) 2678.274 2678.274
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.025 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.062 0.043
## P-value H_0: RMSEA <= 0.050 0.845 0.982
## P-value H_0: RMSEA >= 0.080 0.004 0.000
##
## Robust RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.101
## P-value H_0: Robust RMSEA <= 0.050 0.665
## P-value H_0: Robust RMSEA >= 0.080 0.134
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.045 0.045
##
## Parameter Estimates:
##
## Standard errors Robust.cluster
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i =~
## beruf2 1.000 0.260 0.484
## beruf3 1.000 0.260 0.599
## beruf4 1.000 0.260 0.520
## beruf5 1.000 0.260 0.453
## s =~
## beruf2 0.000 0.000 0.000
## beruf3 (a) -4.383 4.513 -0.971 0.331 -0.000 -0.000
## beruf4 (b) -0.345 2.232 -0.155 0.877 -0.000 -0.000
## beruf5 3.000 0.000 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~~
## s 0.000 NaN NaN
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 1.233 0.021 60.113 0.000 4.739 4.739
## s 0.014 0.011 1.295 0.195 Inf Inf
## .beruf2 0.000 0.000 0.000
## .beruf3 0.000 0.000 0.000
## .beruf4 0.000 0.000 0.000
## .beruf5 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 0.068 0.014 4.708 0.000 1.000 1.000
## s 0.000 NaN NaN
## .beruf2 0.221 0.032 6.959 0.000 0.221 0.766
## .beruf3 0.121 0.022 5.391 0.000 0.121 0.641
## .beruf4 0.182 0.030 6.154 0.000 0.182 0.729
## .beruf5 0.262 0.047 5.568 0.000 0.262 0.794
3.4 Gesundheit
model_gesund <- '
i =~ 1*gesund2 + 1*gesund3 + 1*gesund4 + 1*gesund5
s =~ 0*gesund2 + a*gesund3 + b*gesund4 + 3*gesund5
i ~ 1
s ~ 1
gesund2 ~ 0*1
gesund3 ~ 0*1
gesund4 ~ 0*1
gesund5 ~ 0*1
i ~~ i
s ~~ s
i ~~ s
'
fit_gesund <- sem(
model_gesund,
data = data,
missing = "ML",
estimator = "MLR",
cluster = "schulid"
)
cat("Fit Gesundheit:\n")
## Fit Gesundheit:
summary(fit_gesund, fit.measures = TRUE, standardized = TRUE)
## lavaan 0.6-18 ended normally after 49 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 11
##
## Used Total
## Number of observations 719 772
## Number of clusters [schulid] 97
## Number of missing patterns 15
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 6.603 7.090
## Degrees of freedom 3 3
## P-value (Chi-square) 0.086 0.069
## Scaling correction factor 0.931
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 163.925 89.263
## Degrees of freedom 6 6
## P-value 0.000 0.000
## Scaling correction factor 1.836
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.977 0.951
## Tucker-Lewis Index (TLI) 0.954 0.902
##
## Robust Comparative Fit Index (CFI) 0.982
## Robust Tucker-Lewis Index (TLI) 0.963
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1449.145 -1449.145
## Scaling correction factor 2.150
## for the MLR correction
## Loglikelihood unrestricted model (H1) -1445.844 -1445.844
## Scaling correction factor 1.889
## for the MLR correction
##
## Akaike (AIC) 2920.291 2920.291
## Bayesian (BIC) 2970.647 2970.647
## Sample-size adjusted Bayesian (SABIC) 2935.719 2935.719
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.041 0.044
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.084 0.088
## P-value H_0: RMSEA <= 0.050 0.569 0.522
## P-value H_0: RMSEA >= 0.080 0.070 0.094
##
## Robust RMSEA 0.054
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.130
## P-value H_0: Robust RMSEA <= 0.050 0.372
## P-value H_0: Robust RMSEA >= 0.080 0.353
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.030 0.030
##
## Parameter Estimates:
##
## Standard errors Robust.cluster
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i =~
## gesund2 1.000 0.367 0.740
## gesund3 1.000 0.367 0.671
## gesund4 1.000 0.367 0.617
## gesund5 1.000 0.367 0.589
## s =~
## gesund2 0.000 0.000 0.000
## gesund3 (a) 2.044 0.990 2.066 0.039 0.281 0.513
## gesund4 (b) 3.360 0.826 4.069 0.000 0.461 0.774
## gesund5 3.000 0.412 0.660
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i ~~
## s -0.026 0.024 -1.089 0.276 -0.515 -0.515
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 1.239 0.021 59.930 0.000 3.374 3.374
## s 0.028 0.013 2.191 0.028 0.206 0.206
## .gesund2 0.000 0.000 0.000
## .gesund3 0.000 0.000 0.000
## .gesund4 0.000 0.000 0.000
## .gesund5 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## i 0.135 0.078 1.727 0.084 1.000 1.000
## s 0.019 0.007 2.613 0.009 1.000 1.000
## .gesund2 0.112 0.082 1.365 0.172 0.112 0.453
## .gesund3 0.192 0.024 7.961 0.000 0.192 0.641
## .gesund4 0.182 0.041 4.445 0.000 0.182 0.513
## .gesund5 0.240 0.042 5.740 0.000 0.240 0.618
3.2 Ausgabe der Modellfit Werte fuer die Modelle
# Speichere die Modelle
save(fit_gesund, fit_beruf, fit_familie, fit_freunde, file = "rev1_lgcm_models.RData")
models <- list(fit_gesund, fit_beruf, fit_familie, fit_freunde)
model_fit_calc(models, "rev1_lgcm_models.RData") # Funktion aus functions_for_models.R
## Model chisq df AIC BIC CFI CFI_scaled TLI
## 1 model_gesund 6.603210 3 2920.291 2970.647 0.9771840 0.9508832 0.9543680
## 2 model_beruf 7.296758 5 2665.650 2706.851 0.9791242 1.0000000 0.9749491
## 3 model_familie 10.780169 3 3964.852 4014.992 0.9876813 0.9766231 0.9753626
## 4 model_freunde 4.512578 3 3045.931 3096.333 0.9904242 NA 0.9808485
## TLI_scaled RMSEA RMSEA_scaled SRMR
## 1 0.9017663 0.04087142 0.04354279 0.03037172
## 2 1.0052655 0.02527599 0.00000000 0.04458265
## 3 0.9532461 0.06065119 0.06486005 0.04459053
## 4 NA 0.02642589 0.00000000 0.02604549
## Model chisq df AIC BIC CFI CFI_scaled TLI
## 1 model_gesund 6.603210 3 2920.291 2970.647 0.9771840 0.9508832 0.9543680
## 2 model_beruf 7.296758 5 2665.650 2706.851 0.9791242 1.0000000 0.9749491
## 3 model_familie 10.780169 3 3964.852 4014.992 0.9876813 0.9766231 0.9753626
## 4 model_freunde 4.512578 3 3045.931 3096.333 0.9904242 NA 0.9808485
## TLI_scaled RMSEA RMSEA_scaled SRMR
## 1 0.9017663 0.04087142 0.04354279 0.03037172
## 2 1.0052655 0.02527599 0.00000000 0.04458265
## 3 0.9532461 0.06065119 0.06486005 0.04459053
## 4 NA 0.02642589 0.00000000 0.02604549
4. Visualisierung der Growth-Kurven
Für alle vier Modelle werden die Slope‑Loadings extrahiert, die
latenten Faktorwerte via predict() genutzt und die
individuellen Trajektorien (sehr transparent) sowie die
durchschnittliche Kurve (grün) werden geplottet.
# Erstelle eine Liste der Modelle mit Namen
models <- list(
gesund = fit_gesund,
beruf = fit_beruf,
familie = fit_familie,
freunde = fit_freunde
)
# Für jedes Modell: Extrahiere Slope-Loadings, berechne Vorhersagen und bringe in langes Format
pred_all_long <- map2_df(models, names(models), function(fit_obj, model_name) {
# Extrahiere die Slope-Loadings (hier: frei geschätzte Werte für Wave3 und Wave4)
loadings <- parameterEstimates(fit_obj) %>%
filter(lhs == "s", op == "=~") %>%
pull(est)
if(length(loadings) == 0) {
stop("Für das Modell '", model_name, "' wurden keine Slope-Loadings gefunden. Überprüfe den Namen des latenten Faktors.")
}
# Vorhersage der latenten Faktorwerte (angenommen: 1. Spalte = Intercept, 2. = Slope)
pred_scores <- predict(fit_obj)
# Berechne für jede Loading: predicted_value = i + loading * s
pred_long <- map(loadings, function(x) {
pred_scores[,1] + x * pred_scores[,2]
}) %>%
reduce(cbind) %>%
as.data.frame() %>%
setNames(str_c("Wave ", 1:length(loadings))) %>%
mutate(id = row_number()) %>%
pivot_longer(-id, names_to = "wave", values_to = "pred") %>%
mutate(model = model_name)
pred_long
})
# Plot: Einzeltrajektorien (sehr transparent) plus durchschnittliche Kurve (grün), je Modell in Facetten
plot_obj <- pred_all_long %>%
ggplot(aes(x = wave, y = pred, group = id)) +
geom_line(alpha = 0.01) +
stat_summary(
aes(group = 1),
fun = mean,
geom = "line",
size = 1.0,
color = "green"
) +
facet_wrap(~ model) +
theme_bw() +
labs(y = "Outcome", x = "Survey Wave",
title = "Non-linear Growth Trajectories",
subtitle = "Einzelpfade und durchschnittlicher Verlauf pro Modell")
print(plot_obj)
library(svglite)
ggsave(filename = "rev1_plot_nonlinear_growth.svg",
plot = plot_obj, width = 12, height = 12, dpi = 300)