RICLPM results

Goal

Estimate the main RI-CLPM with lavaan.

Set up and data import

#library
library(tidyverse)
library(lavaan)
library(data.table)
library(doParallel)
library(parallel)

#data
load("results/predicted_means/240816_pred-means-cleaned-df.Rdata")

#extract datafile from pref_results
MyData <- pred_results$df_combined

#create between variables for 
MyData <- MyData %>% 
  rowwise() %>% 
  mutate(between_educ = mean(c_across(cols = matches("^educ_[[:digit:]]{1,2}")),na.rm = T),
         between_age = mean(c_across(cols = matches("^age_[[:digit:]]{1,2}")),na.rm = T),
         between_female = mean(c_across(cols = matches("^female_[[:digit:]]{1,2}")),na.rm = T),
         between_origin = mean(c_across(cols = matches("^origin_[[:digit:]]{1,2}")),na.rm = T)) %>%
  ungroup()

RI-CLPM with biased corrected means

Main effects

Create lavaan model objects

EU integration

EU_model1_unconstrained <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*eu_1 + 1*eu_2 + 1*eu_3 + 1*eu_4 + 1*eu_5 + 1*eu_6 + 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11
  
  # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  weu_1 =~ 1*eu_1
  weu_2 =~ 1*eu_2
  weu_3 =~ 1*eu_3
  weu_4 =~ 1*eu_4
  weu_5 =~ 1*eu_5
  weu_6 =~ 1*eu_6
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_2   ~ weu_1 + wFeduc_a_1
  weu_3   ~ weu_2 + wFeduc_a_2
  weu_4   ~ weu_3 + wFeduc_a_3
  weu_5   ~ weu_4 + wFeduc_a_4
  weu_6   ~ weu_5 + wFeduc_a_5
  weu_7   ~ weu_6 + wFeduc_a_6
  weu_8   ~ weu_7 + wFeduc_a_7
  weu_9   ~ weu_8 + wFeduc_a_8
  weu_10  ~ weu_9 + wFeduc_a_9
  weu_11  ~ weu_10 + wFeduc_a_10
  
  
  wFeduc_a_2  ~ weu_1 + wFeduc_a_1
  wFeduc_a_3  ~ weu_2 + wFeduc_a_2
  wFeduc_a_4  ~ weu_3 + wFeduc_a_3
  wFeduc_a_5  ~ weu_4 + wFeduc_a_4
  wFeduc_a_6  ~ weu_5 + wFeduc_a_5
  wFeduc_a_7  ~ weu_6 + wFeduc_a_6
  wFeduc_a_8  ~ weu_7 + wFeduc_a_7
  wFeduc_a_9  ~ weu_8 + wFeduc_a_8
  wFeduc_a_10  ~ weu_9 + wFeduc_a_9
  wFeduc_a_11  ~ weu_10 + wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  weu_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  weu_2 ~~ wFeduc_a_2
  weu_3 ~~ wFeduc_a_3
  weu_4 ~~ wFeduc_a_4
  weu_5 ~~ wFeduc_a_5
  weu_6 ~~ wFeduc_a_6
  weu_7 ~~ wFeduc_a_7
  weu_8 ~~ wFeduc_a_8
  weu_9 ~~ wFeduc_a_9
  weu_10 ~~ wFeduc_a_10
  weu_11 ~~ wFeduc_a_11
  
  # Estimate the variance 
  weu_1 ~~ weu_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  weu_2 ~~ weu_2 
  wFeduc_a_2 ~~ wFeduc_a_2
  weu_3 ~~ weu_3
  wFeduc_a_3 ~~ wFeduc_a_3
  weu_4 ~~ weu_4 
  wFeduc_a_4 ~~ wFeduc_a_4
  weu_5 ~~ vy*weu_5
  wFeduc_a_5 ~~ wFeduc_a_5
  weu_6 ~~ weu_6 
  wFeduc_a_6 ~~ wFeduc_a_6
  weu_7 ~~ weu_7 
  wFeduc_a_7 ~~ wFeduc_a_7
  weu_8 ~~ weu_8 
  wFeduc_a_8 ~~ wFeduc_a_8
  weu_9 ~~ weu_9 
  wFeduc_a_9 ~~ wFeduc_a_9
  weu_10 ~~ weu_10 
  wFeduc_a_10 ~~ wFeduc_a_10
  weu_11 ~~ weu_11 
  wFeduc_a_11 ~~ wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*weu_1
  
'
EU_model1_constrained_lag <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*eu_1 + 1*eu_2 + 1*eu_3 + 1*eu_4 + 1*eu_5 + 1*eu_6 + 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11

  # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  weu_1 =~ 1*eu_1
  weu_2 =~ 1*eu_2
  weu_3 =~ 1*eu_3
  weu_4 =~ 1*eu_4
  weu_5 =~ 1*eu_5
  weu_6 =~ 1*eu_6
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_2   ~ a*weu_1 + b*wFeduc_a_1
  weu_3   ~ a*weu_2 + b*wFeduc_a_2
  weu_4   ~ a*weu_3 + b*wFeduc_a_3
  weu_5   ~ a*weu_4 + b*wFeduc_a_4
  weu_6   ~ a*weu_5 + b*wFeduc_a_5
  weu_7   ~ a*weu_6 + b*wFeduc_a_6
  weu_8   ~ a*weu_7 + b*wFeduc_a_7
  weu_9   ~ a*weu_8 + b*wFeduc_a_8
  weu_10  ~ a*weu_9 + b*wFeduc_a_9
  weu_11  ~ a*weu_10 + b*wFeduc_a_10
  
  
  wFeduc_a_2  ~ c*weu_1 + d*wFeduc_a_1
  wFeduc_a_3  ~ c*weu_2 + d*wFeduc_a_2
  wFeduc_a_4  ~ c*weu_3 + d*wFeduc_a_3
  wFeduc_a_5  ~ c*weu_4 + d*wFeduc_a_4
  wFeduc_a_6  ~ c*weu_5 + d*wFeduc_a_5
  wFeduc_a_7  ~ c*weu_6 + d*wFeduc_a_6
  wFeduc_a_8  ~ c*weu_7 + d*wFeduc_a_7
  wFeduc_a_9  ~ c*weu_8 + d*wFeduc_a_8
  wFeduc_a_10  ~ c*weu_9 + d*wFeduc_a_9
  wFeduc_a_11  ~ c*weu_10 + d*wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  weu_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  weu_2 ~~ cov*wFeduc_a_2
  weu_3 ~~ cov*wFeduc_a_3
  weu_4 ~~ cov*wFeduc_a_4
  weu_5 ~~ cov*wFeduc_a_5
  weu_6 ~~ cov*wFeduc_a_6
  weu_7 ~~ cov*wFeduc_a_7
  weu_8 ~~ cov*wFeduc_a_8
  weu_9 ~~ cov*wFeduc_a_9
  weu_10 ~~ cov*wFeduc_a_10
  weu_11 ~~ cov*wFeduc_a_11
  
  # Estimate the variance 
  weu_1 ~~ weu_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  weu_2 ~~ vy*weu_2 
  wFeduc_a_2 ~~ vx*wFeduc_a_2
  weu_3 ~~ vy*weu_3
  wFeduc_a_3 ~~ vx*wFeduc_a_3
  weu_4 ~~ vy*weu_4 
  wFeduc_a_4 ~~ vx*wFeduc_a_4
  weu_5 ~~ vy*weu_5
  wFeduc_a_5 ~~ vx*wFeduc_a_5
  weu_6 ~~ vy*weu_6 
  wFeduc_a_6 ~~ vx*wFeduc_a_6
  weu_7 ~~ vy*weu_7 
  wFeduc_a_7 ~~ vx*wFeduc_a_7
  weu_8 ~~ vy*weu_8 
  wFeduc_a_8 ~~ vx*wFeduc_a_8
  weu_9 ~~ vy*weu_9 
  wFeduc_a_9 ~~ vx*wFeduc_a_9
  weu_10 ~~ vy*weu_10 
  wFeduc_a_10 ~~ vx*wFeduc_a_10
  weu_11 ~~ vy*weu_11 
  wFeduc_a_11 ~~ vx*wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*weu_1

'

EU_model1_constrained_lag_means <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*eu_1 + 1*eu_2 + 1*eu_3 + 1*eu_4 + 1*eu_5 + 1*eu_6 + 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11

  # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  weu_1 =~ 1*eu_1
  weu_2 =~ 1*eu_2
  weu_3 =~ 1*eu_3
  weu_4 =~ 1*eu_4
  weu_5 =~ 1*eu_5
  weu_6 =~ 1*eu_6
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_2   ~ a*weu_1 + b*wFeduc_a_1
  weu_3   ~ a*weu_2 + b*wFeduc_a_2
  weu_4   ~ a*weu_3 + b*wFeduc_a_3
  weu_5   ~ a*weu_4 + b*wFeduc_a_4
  weu_6   ~ a*weu_5 + b*wFeduc_a_5
  weu_7   ~ a*weu_6 + b*wFeduc_a_6
  weu_8   ~ a*weu_7 + b*wFeduc_a_7
  weu_9   ~ a*weu_8 + b*wFeduc_a_8
  weu_10  ~ a*weu_9 + b*wFeduc_a_9
  weu_11  ~ a*weu_10 + b*wFeduc_a_10
  
  
  wFeduc_a_2  ~ c*weu_1 + d*wFeduc_a_1
  wFeduc_a_3  ~ c*weu_2 + d*wFeduc_a_2
  wFeduc_a_4  ~ c*weu_3 + d*wFeduc_a_3
  wFeduc_a_5  ~ c*weu_4 + d*wFeduc_a_4
  wFeduc_a_6  ~ c*weu_5 + d*wFeduc_a_5
  wFeduc_a_7  ~ c*weu_6 + d*wFeduc_a_6
  wFeduc_a_8  ~ c*weu_7 + d*wFeduc_a_7
  wFeduc_a_9  ~ c*weu_8 + d*wFeduc_a_8
  wFeduc_a_10  ~ c*weu_9 + d*wFeduc_a_9
  wFeduc_a_11  ~ c*weu_10 + d*wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  weu_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  weu_2 ~~ cov*wFeduc_a_2
  weu_3 ~~ cov*wFeduc_a_3
  weu_4 ~~ cov*wFeduc_a_4
  weu_5 ~~ cov*wFeduc_a_5
  weu_6 ~~ cov*wFeduc_a_6
  weu_7 ~~ cov*wFeduc_a_7
  weu_8 ~~ cov*wFeduc_a_8
  weu_9 ~~ cov*wFeduc_a_9
  weu_10 ~~ cov*wFeduc_a_10
  weu_11 ~~ cov*wFeduc_a_11
  
  # Estimate the variance 
  weu_1 ~~ weu_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  weu_2 ~~ vy*weu_2 
  wFeduc_a_2 ~~ vx*wFeduc_a_2
  weu_3 ~~ vy*weu_3
  wFeduc_a_3 ~~ vx*wFeduc_a_3
  weu_4 ~~ vy*weu_4 
  wFeduc_a_4 ~~ vx*wFeduc_a_4
  weu_5 ~~ vy*weu_5
  wFeduc_a_5 ~~ vx*wFeduc_a_5
  weu_6 ~~ vy*weu_6 
  wFeduc_a_6 ~~ vx*wFeduc_a_6
  weu_7 ~~ vy*weu_7 
  wFeduc_a_7 ~~ vx*wFeduc_a_7
  weu_8 ~~ vy*weu_8 
  wFeduc_a_8 ~~ vx*wFeduc_a_8
  weu_9 ~~ vy*weu_9 
  wFeduc_a_9 ~~ vx*wFeduc_a_9
  weu_10 ~~ vy*weu_10 
  wFeduc_a_10 ~~ vx*wFeduc_a_10
  weu_11 ~~ vy*weu_11 
  wFeduc_a_11 ~~ vx*wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*weu_1
  
  
  #constrain grand means over time
  eu_1 + eu_2 + eu_3 + eu_4 + eu_5 + eu_6 + eu_7 + eu_8 + eu_9 + eu_10 + eu_11 ~ my*1
  
  Feduc_a_1 + Feduc_a_2 + Feduc_a_3 + Feduc_a_4 + Feduc_a_5 + Feduc_a_6 + Feduc_a_7 + Feduc_a_8 + Feduc_a_9 + Feduc_a_10 + Feduc_a_11 ~ mx*1

'

#save model specifications in list
eu_lavaan_models <- list(EU_model1_unconstrained,
     EU_model1_constrained_lag,
     EU_model1_constrained_lag_means
     )

Cultural Inclusion

cult_model1_unconstrained <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*cult_1 + 1*cult_2 + 1*cult_3 + 1*cult_4 + 1*cult_5 + 1*cult_6 + 1*cult_7 + 1*cult_8 + 1*cult_9 + 1*cult_10 + 1*cult_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11

  # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  wcult_1 =~ 1*cult_1
  wcult_2 =~ 1*cult_2
  wcult_3 =~ 1*cult_3
  wcult_4 =~ 1*cult_4
  wcult_5 =~ 1*cult_5
  wcult_6 =~ 1*cult_6
  wcult_7 =~ 1*cult_7
  wcult_8 =~ 1*cult_8
  wcult_9 =~ 1*cult_9
  wcult_10 =~ 1*cult_10
  wcult_11 =~ 1*cult_11 
  
  # Estimate the lagged effects
  wcult_2   ~ wcult_1 + wFeduc_a_1
  wcult_3   ~ wcult_2 + wFeduc_a_2
  wcult_4   ~ wcult_3 + wFeduc_a_3
  wcult_5   ~ wcult_4 + wFeduc_a_4
  wcult_6   ~ wcult_5 + wFeduc_a_5
  wcult_7   ~ wcult_6 + wFeduc_a_6
  wcult_8   ~ wcult_7 + wFeduc_a_7
  wcult_9   ~ wcult_8 + wFeduc_a_8
  wcult_10  ~ wcult_9 + wFeduc_a_9
  wcult_11  ~ wcult_10 + wFeduc_a_10
  
  
  wFeduc_a_2  ~ wcult_1 + wFeduc_a_1
  wFeduc_a_3  ~ wcult_2 + wFeduc_a_2
  wFeduc_a_4  ~ wcult_3 + wFeduc_a_3
  wFeduc_a_5  ~ wcult_4 + wFeduc_a_4
  wFeduc_a_6  ~ wcult_5 + wFeduc_a_5
  wFeduc_a_7  ~ wcult_6 + wFeduc_a_6
  wFeduc_a_8  ~ wcult_7 + wFeduc_a_7
  wFeduc_a_9  ~ wcult_8 + wFeduc_a_8
  wFeduc_a_10  ~ wcult_9 + wFeduc_a_9
  wFeduc_a_11  ~ wcult_10 + wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  wcult_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  wcult_2 ~~ wFeduc_a_2
  wcult_3 ~~ wFeduc_a_3
  wcult_4 ~~ wFeduc_a_4
  wcult_5 ~~ wFeduc_a_5
  wcult_6 ~~ wFeduc_a_6
  wcult_7 ~~ wFeduc_a_7
  wcult_8 ~~ wFeduc_a_8
  wcult_9 ~~ wFeduc_a_9
  wcult_10 ~~ wFeduc_a_10
  wcult_11 ~~ wFeduc_a_11
  
  # Estimate the variance 
  wcult_1 ~~ wcult_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  wcult_2 ~~ wcult_2 
  wFeduc_a_2 ~~ wFeduc_a_2
  wcult_3 ~~ wcult_3
  wFeduc_a_3 ~~ wFeduc_a_3
  wcult_4 ~~ wcult_4 
  wFeduc_a_4 ~~ wFeduc_a_4
  wcult_5 ~~ vy*wcult_5
  wFeduc_a_5 ~~ wFeduc_a_5
  wcult_6 ~~ wcult_6 
  wFeduc_a_6 ~~ wFeduc_a_6
  wcult_7 ~~ wcult_7 
  wFeduc_a_7 ~~ wFeduc_a_7
  wcult_8 ~~ wcult_8 
  wFeduc_a_8 ~~ wFeduc_a_8
  wcult_9 ~~ wcult_9 
  wFeduc_a_9 ~~ wFeduc_a_9
  wcult_10 ~~ wcult_10 
  wFeduc_a_10 ~~ wFeduc_a_10
  wcult_11 ~~ wcult_11 
  wFeduc_a_11 ~~ wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*wcult_1
  
'

cult_model1_constrained_lag <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*cult_1 + 1*cult_2 + 1*cult_3 + 1*cult_4 + 1*cult_5 + 1*cult_6 + 1*cult_7 + 1*cult_8 + 1*cult_9 + 1*cult_10 + 1*cult_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11

  # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  wcult_1 =~ 1*cult_1
  wcult_2 =~ 1*cult_2
  wcult_3 =~ 1*cult_3
  wcult_4 =~ 1*cult_4
  wcult_5 =~ 1*cult_5
  wcult_6 =~ 1*cult_6
  wcult_7 =~ 1*cult_7
  wcult_8 =~ 1*cult_8
  wcult_9 =~ 1*cult_9
  wcult_10 =~ 1*cult_10
  wcult_11 =~ 1*cult_11 
  
  # Estimate the lagged effects (constrained)
  wcult_2   ~ a*wcult_1 + b*wFeduc_a_1
  wcult_3   ~ a*wcult_2 + b*wFeduc_a_2
  wcult_4   ~ a*wcult_3 + b*wFeduc_a_3
  wcult_5   ~ a*wcult_4 + b*wFeduc_a_4
  wcult_6   ~ a*wcult_5 + b*wFeduc_a_5
  wcult_7   ~ a*wcult_6 + b*wFeduc_a_6
  wcult_8   ~ a*wcult_7 + b*wFeduc_a_7
  wcult_9   ~ a*wcult_8 + b*wFeduc_a_8
  wcult_10  ~ a*wcult_9 + b*wFeduc_a_9
  wcult_11  ~ a*wcult_10 + b*wFeduc_a_10
  
  
  wFeduc_a_2  ~ c*wcult_1 + d*wFeduc_a_1
  wFeduc_a_3  ~ c*wcult_2 + d*wFeduc_a_2
  wFeduc_a_4  ~ c*wcult_3 + d*wFeduc_a_3
  wFeduc_a_5  ~ c*wcult_4 + d*wFeduc_a_4
  wFeduc_a_6  ~ c*wcult_5 + d*wFeduc_a_5
  wFeduc_a_7  ~ c*wcult_6 + d*wFeduc_a_6
  wFeduc_a_8  ~ c*wcult_7 + d*wFeduc_a_7
  wFeduc_a_9  ~ c*wcult_8 + d*wFeduc_a_8
  wFeduc_a_10  ~ c*wcult_9 + d*wFeduc_a_9
  wFeduc_a_11  ~ c*wcult_10 + d*wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  wcult_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  wcult_2 ~~ cov*wFeduc_a_2
  wcult_3 ~~ cov*wFeduc_a_3
  wcult_4 ~~ cov*wFeduc_a_4
  wcult_5 ~~ cov*wFeduc_a_5
  wcult_6 ~~ cov*wFeduc_a_6
  wcult_7 ~~ cov*wFeduc_a_7
  wcult_8 ~~ cov*wFeduc_a_8
  wcult_9 ~~ cov*wFeduc_a_9
  wcult_10 ~~ cov*wFeduc_a_10
  wcult_11 ~~ cov*wFeduc_a_11
  
  # Estimate the variance 
  wcult_1 ~~ wcult_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  wcult_2 ~~ vy*wcult_2 
  wFeduc_a_2 ~~ vx*wFeduc_a_2
  wcult_3 ~~ vy*wcult_3
  wFeduc_a_3 ~~ vx*wFeduc_a_3
  wcult_4 ~~ vy*wcult_4 
  wFeduc_a_4 ~~ vx*wFeduc_a_4
  wcult_5 ~~ vy*wcult_5
  wFeduc_a_5 ~~ vx*wFeduc_a_5
  wcult_6 ~~ vy*wcult_6 
  wFeduc_a_6 ~~ vx*wFeduc_a_6
  wcult_7 ~~ vy*wcult_7 
  wFeduc_a_7 ~~ vx*wFeduc_a_7
  wcult_8 ~~ vy*wcult_8 
  wFeduc_a_8 ~~ vx*wFeduc_a_8
  wcult_9 ~~ vy*wcult_9 
  wFeduc_a_9 ~~ vx*wFeduc_a_9
  wcult_10 ~~ vy*wcult_10 
  wFeduc_a_10 ~~ vx*wFeduc_a_10
  wcult_11 ~~ vy*wcult_11 
  wFeduc_a_11 ~~ vx*wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*wcult_1

'

cult_model1_constrained_lag_means <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*cult_1 + 1*cult_2 + 1*cult_3 + 1*cult_4 + 1*cult_5 + 1*cult_6 + 1*cult_7 + 1*cult_8 + 1*cult_9 + 1*cult_10 + 1*cult_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11
  
    # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  wcult_1 =~ 1*cult_1
  wcult_2 =~ 1*cult_2
  wcult_3 =~ 1*cult_3
  wcult_4 =~ 1*cult_4
  wcult_5 =~ 1*cult_5
  wcult_6 =~ 1*cult_6
  wcult_7 =~ 1*cult_7
  wcult_8 =~ 1*cult_8
  wcult_9 =~ 1*cult_9
  wcult_10 =~ 1*cult_10
  wcult_11 =~ 1*cult_11 
  
  # Estimate the lagged effects (constrained)
  wcult_2   ~ a*wcult_1 + b*wFeduc_a_1
  wcult_3   ~ a*wcult_2 + b*wFeduc_a_2
  wcult_4   ~ a*wcult_3 + b*wFeduc_a_3
  wcult_5   ~ a*wcult_4 + b*wFeduc_a_4
  wcult_6   ~ a*wcult_5 + b*wFeduc_a_5
  wcult_7   ~ a*wcult_6 + b*wFeduc_a_6
  wcult_8   ~ a*wcult_7 + b*wFeduc_a_7
  wcult_9   ~ a*wcult_8 + b*wFeduc_a_8
  wcult_10  ~ a*wcult_9 + b*wFeduc_a_9
  wcult_11  ~ a*wcult_10 + b*wFeduc_a_10
  
  
  wFeduc_a_2  ~ c*wcult_1 + d*wFeduc_a_1
  wFeduc_a_3  ~ c*wcult_2 + d*wFeduc_a_2
  wFeduc_a_4  ~ c*wcult_3 + d*wFeduc_a_3
  wFeduc_a_5  ~ c*wcult_4 + d*wFeduc_a_4
  wFeduc_a_6  ~ c*wcult_5 + d*wFeduc_a_5
  wFeduc_a_7  ~ c*wcult_6 + d*wFeduc_a_6
  wFeduc_a_8  ~ c*wcult_7 + d*wFeduc_a_7
  wFeduc_a_9  ~ c*wcult_8 + d*wFeduc_a_8
  wFeduc_a_10  ~ c*wcult_9 + d*wFeduc_a_9
  wFeduc_a_11  ~ c*wcult_10 + d*wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  wcult_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  wcult_2 ~~ cov*wFeduc_a_2
  wcult_3 ~~ cov*wFeduc_a_3
  wcult_4 ~~ cov*wFeduc_a_4
  wcult_5 ~~ cov*wFeduc_a_5
  wcult_6 ~~ cov*wFeduc_a_6
  wcult_7 ~~ cov*wFeduc_a_7
  wcult_8 ~~ cov*wFeduc_a_8
  wcult_9 ~~ cov*wFeduc_a_9
  wcult_10 ~~ cov*wFeduc_a_10
  wcult_11 ~~ cov*wFeduc_a_11
  
  # Estimate the variance 
  wcult_1 ~~ wcult_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  wcult_2 ~~ vy*wcult_2 
  wFeduc_a_2 ~~ vx*wFeduc_a_2
  wcult_3 ~~ vy*wcult_3
  wFeduc_a_3 ~~ vx*wFeduc_a_3
  wcult_4 ~~ vy*wcult_4 
  wFeduc_a_4 ~~ vx*wFeduc_a_4
  wcult_5 ~~ vy*wcult_5
  wFeduc_a_5 ~~ vx*wFeduc_a_5
  wcult_6 ~~ vy*wcult_6 
  wFeduc_a_6 ~~ vx*wFeduc_a_6
  wcult_7 ~~ vy*wcult_7 
  wFeduc_a_7 ~~ vx*wFeduc_a_7
  wcult_8 ~~ vy*wcult_8 
  wFeduc_a_8 ~~ vx*wFeduc_a_8
  wcult_9 ~~ vy*wcult_9 
  wFeduc_a_9 ~~ vx*wFeduc_a_9
  wcult_10 ~~ vy*wcult_10 
  wFeduc_a_10 ~~ vx*wFeduc_a_10
  wcult_11 ~~ vy*wcult_11 
  wFeduc_a_11 ~~ vx*wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*wcult_1
  
  
  #constrain grand means over time
  cult_1 + cult_2 + cult_3 + cult_4 + cult_5 + cult_6 + cult_7 + cult_8 + cult_9 + cult_10 + cult_11 ~ my*1
  
  Feduc_a_1 + Feduc_a_2 + Feduc_a_3 + Feduc_a_4 + Feduc_a_5 + Feduc_a_6 + Feduc_a_7 + Feduc_a_8 + Feduc_a_9 + Feduc_a_10 + Feduc_a_11 ~ mx*1

'



#save model specifications in list
cult_lavaan_models <- list(cult_model1_unconstrained,
     cult_model1_constrained_lag,
     cult_model1_constrained_lag_means
     )

Income Differences

inc_diff_model1_unconstrained <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*inc_diff_1 + 1*inc_diff_2 + 1*inc_diff_3 + 1*inc_diff_4 + 1*inc_diff_5 + 1*inc_diff_6 + 1*inc_diff_7 + 1*inc_diff_8 + 1*inc_diff_9 + 1*inc_diff_10 + 1*inc_diff_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11
  
    # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  winc_diff_1 =~ 1*inc_diff_1
  winc_diff_2 =~ 1*inc_diff_2
  winc_diff_3 =~ 1*inc_diff_3
  winc_diff_4 =~ 1*inc_diff_4
  winc_diff_5 =~ 1*inc_diff_5
  winc_diff_6 =~ 1*inc_diff_6
  winc_diff_7 =~ 1*inc_diff_7
  winc_diff_8 =~ 1*inc_diff_8
  winc_diff_9 =~ 1*inc_diff_9
  winc_diff_10 =~ 1*inc_diff_10
  winc_diff_11 =~ 1*inc_diff_11 
  
  # Estimate the lagged effects (constrained)
  winc_diff_2   ~ winc_diff_1 + wFeduc_a_1
  winc_diff_3   ~ winc_diff_2 + wFeduc_a_2
  winc_diff_4   ~ winc_diff_3 + wFeduc_a_3
  winc_diff_5   ~ winc_diff_4 + wFeduc_a_4
  winc_diff_6   ~ winc_diff_5 + wFeduc_a_5
  winc_diff_7   ~ winc_diff_6 + wFeduc_a_6
  winc_diff_8   ~ winc_diff_7 + wFeduc_a_7
  winc_diff_9   ~ winc_diff_8 + wFeduc_a_8
  winc_diff_10  ~ winc_diff_9 + wFeduc_a_9
  winc_diff_11  ~ winc_diff_10 + wFeduc_a_10
  
  
  wFeduc_a_2  ~ winc_diff_1 + wFeduc_a_1
  wFeduc_a_3  ~ winc_diff_2 + wFeduc_a_2
  wFeduc_a_4  ~ winc_diff_3 + wFeduc_a_3
  wFeduc_a_5  ~ winc_diff_4 + wFeduc_a_4
  wFeduc_a_6  ~ winc_diff_5 + wFeduc_a_5
  wFeduc_a_7  ~ winc_diff_6 + wFeduc_a_6
  wFeduc_a_8  ~ winc_diff_7 + wFeduc_a_7
  wFeduc_a_9  ~ winc_diff_8 + wFeduc_a_8
  wFeduc_a_10  ~ winc_diff_9 + wFeduc_a_9
  wFeduc_a_11  ~ winc_diff_10 + wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  winc_diff_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  winc_diff_2 ~~ wFeduc_a_2
  winc_diff_3 ~~ wFeduc_a_3
  winc_diff_4 ~~ wFeduc_a_4
  winc_diff_5 ~~ wFeduc_a_5
  winc_diff_6 ~~ wFeduc_a_6
  winc_diff_7 ~~ wFeduc_a_7
  winc_diff_8 ~~ wFeduc_a_8
  winc_diff_9 ~~ wFeduc_a_9
  winc_diff_10 ~~ wFeduc_a_10
  winc_diff_11 ~~ wFeduc_a_11
  
  # Estimate the variance 
  winc_diff_1 ~~ winc_diff_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  winc_diff_2 ~~ winc_diff_2 
  wFeduc_a_2 ~~ wFeduc_a_2
  winc_diff_3 ~~ winc_diff_3
  wFeduc_a_3 ~~ wFeduc_a_3
  winc_diff_4 ~~ winc_diff_4 
  wFeduc_a_4 ~~ wFeduc_a_4
  winc_diff_5 ~~ vy*winc_diff_5
  wFeduc_a_5 ~~ wFeduc_a_5
  winc_diff_6 ~~ winc_diff_6 
  wFeduc_a_6 ~~ wFeduc_a_6
  winc_diff_7 ~~ winc_diff_7 
  wFeduc_a_7 ~~ wFeduc_a_7
  winc_diff_8 ~~ winc_diff_8 
  wFeduc_a_8 ~~ wFeduc_a_8
  winc_diff_9 ~~ winc_diff_9 
  wFeduc_a_9 ~~ wFeduc_a_9
  winc_diff_10 ~~ winc_diff_10 
  wFeduc_a_10 ~~ wFeduc_a_10
  winc_diff_11 ~~ winc_diff_11 
  wFeduc_a_11 ~~ wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*winc_diff_1
  
'

inc_diff_model1_constrained_lag <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*inc_diff_1 + 1*inc_diff_2 + 1*inc_diff_3 + 1*inc_diff_4 + 1*inc_diff_5 + 1*inc_diff_6 + 1*inc_diff_7 + 1*inc_diff_8 + 1*inc_diff_9 + 1*inc_diff_10 + 1*inc_diff_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11
  
    # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  winc_diff_1 =~ 1*inc_diff_1
  winc_diff_2 =~ 1*inc_diff_2
  winc_diff_3 =~ 1*inc_diff_3
  winc_diff_4 =~ 1*inc_diff_4
  winc_diff_5 =~ 1*inc_diff_5
  winc_diff_6 =~ 1*inc_diff_6
  winc_diff_7 =~ 1*inc_diff_7
  winc_diff_8 =~ 1*inc_diff_8
  winc_diff_9 =~ 1*inc_diff_9
  winc_diff_10 =~ 1*inc_diff_10
  winc_diff_11 =~ 1*inc_diff_11 
  
  # Estimate the lagged effects (constrained)
  winc_diff_2   ~ a*winc_diff_1 + b*wFeduc_a_1
  winc_diff_3   ~ a*winc_diff_2 + b*wFeduc_a_2
  winc_diff_4   ~ a*winc_diff_3 + b*wFeduc_a_3
  winc_diff_5   ~ a*winc_diff_4 + b*wFeduc_a_4
  winc_diff_6   ~ a*winc_diff_5 + b*wFeduc_a_5
  winc_diff_7   ~ a*winc_diff_6 + b*wFeduc_a_6
  winc_diff_8   ~ a*winc_diff_7 + b*wFeduc_a_7
  winc_diff_9   ~ a*winc_diff_8 + b*wFeduc_a_8
  winc_diff_10  ~ a*winc_diff_9 + b*wFeduc_a_9
  winc_diff_11  ~ a*winc_diff_10 + b*wFeduc_a_10
  
  
  wFeduc_a_2  ~ c*winc_diff_1 + d*wFeduc_a_1
  wFeduc_a_3  ~ c*winc_diff_2 + d*wFeduc_a_2
  wFeduc_a_4  ~ c*winc_diff_3 + d*wFeduc_a_3
  wFeduc_a_5  ~ c*winc_diff_4 + d*wFeduc_a_4
  wFeduc_a_6  ~ c*winc_diff_5 + d*wFeduc_a_5
  wFeduc_a_7  ~ c*winc_diff_6 + d*wFeduc_a_6
  wFeduc_a_8  ~ c*winc_diff_7 + d*wFeduc_a_7
  wFeduc_a_9  ~ c*winc_diff_8 + d*wFeduc_a_8
  wFeduc_a_10  ~ c*winc_diff_9 + d*wFeduc_a_9
  wFeduc_a_11  ~ c*winc_diff_10 + d*wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  winc_diff_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  winc_diff_2 ~~ cov*wFeduc_a_2
  winc_diff_3 ~~ cov*wFeduc_a_3
  winc_diff_4 ~~ cov*wFeduc_a_4
  winc_diff_5 ~~ cov*wFeduc_a_5
  winc_diff_6 ~~ cov*wFeduc_a_6
  winc_diff_7 ~~ cov*wFeduc_a_7
  winc_diff_8 ~~ cov*wFeduc_a_8
  winc_diff_9 ~~ cov*wFeduc_a_9
  winc_diff_10 ~~ cov*wFeduc_a_10
  winc_diff_11 ~~ cov*wFeduc_a_11
  
  # Estimate the variance 
  winc_diff_1 ~~ winc_diff_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  winc_diff_2 ~~ vy*winc_diff_2 
  wFeduc_a_2 ~~ vx*wFeduc_a_2
  winc_diff_3 ~~ vy*winc_diff_3
  wFeduc_a_3 ~~ vx*wFeduc_a_3
  winc_diff_4 ~~ vy*winc_diff_4 
  wFeduc_a_4 ~~ vx*wFeduc_a_4
  winc_diff_5 ~~ vy*winc_diff_5
  wFeduc_a_5 ~~ vx*wFeduc_a_5
  winc_diff_6 ~~ vy*winc_diff_6 
  wFeduc_a_6 ~~ vx*wFeduc_a_6
  winc_diff_7 ~~ vy*winc_diff_7 
  wFeduc_a_7 ~~ vx*wFeduc_a_7
  winc_diff_8 ~~ vy*winc_diff_8 
  wFeduc_a_8 ~~ vx*wFeduc_a_8
  winc_diff_9 ~~ vy*winc_diff_9 
  wFeduc_a_9 ~~ vx*wFeduc_a_9
  winc_diff_10 ~~ vy*winc_diff_10 
  wFeduc_a_10 ~~ vx*wFeduc_a_10
  winc_diff_11 ~~ vy*winc_diff_11 
  wFeduc_a_11 ~~ vx*wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*winc_diff_1

'

inc_diff_model1_constrained_lag_means <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1* Feduc_a_1 + 1* Feduc_a_2 + 1*Feduc_a_3 + 1*Feduc_a_4 + 1*Feduc_a_5 + 1*Feduc_a_6 + 1*Feduc_a_7 + 1*Feduc_a_8 + 1*Feduc_a_9 + 1*Feduc_a_10 + 1*Feduc_a_11
  RIy =~  1*inc_diff_1 + 1*inc_diff_2 + 1*inc_diff_3 + 1*inc_diff_4 + 1*inc_diff_5 + 1*inc_diff_6 + 1*inc_diff_7 + 1*inc_diff_8 + 1*inc_diff_9 + 1*inc_diff_10 + 1*inc_diff_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feduc_a_1 ~~ 0*Feduc_a_1
  Feduc_a_2 ~~ 0*Feduc_a_2
  Feduc_a_3 ~~ 0*Feduc_a_3
  Feduc_a_4 ~~ 0*Feduc_a_4
  Feduc_a_5 ~~ 0*Feduc_a_5
  Feduc_a_6 ~~ 0*Feduc_a_6
  Feduc_a_7 ~~ 0*Feduc_a_7
  Feduc_a_8 ~~ 0*Feduc_a_8
  Feduc_a_9 ~~ 0*Feduc_a_9
  Feduc_a_10 ~~ 0*Feduc_a_10
  Feduc_a_11 ~~ 0*Feduc_a_11
  
    # Regression of random intercepts on z1
  RIx + RIy ~ between_educ + between_age + between_origin + between_female# Constrained over time.

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeduc_a_1 =~ 1*Feduc_a_1
  wFeduc_a_2 =~ 1*Feduc_a_2
  wFeduc_a_3 =~ 1*Feduc_a_3
  wFeduc_a_4 =~ 1*Feduc_a_4
  wFeduc_a_5 =~ 1*Feduc_a_5
  wFeduc_a_6 =~ 1*Feduc_a_6
  wFeduc_a_7 =~ 1*Feduc_a_7
  wFeduc_a_8 =~ 1*Feduc_a_8
  wFeduc_a_9 =~ 1*Feduc_a_9
  wFeduc_a_10 =~ 1*Feduc_a_10
  wFeduc_a_11 =~ 1*Feduc_a_11
  winc_diff_1 =~ 1*inc_diff_1
  winc_diff_2 =~ 1*inc_diff_2
  winc_diff_3 =~ 1*inc_diff_3
  winc_diff_4 =~ 1*inc_diff_4
  winc_diff_5 =~ 1*inc_diff_5
  winc_diff_6 =~ 1*inc_diff_6
  winc_diff_7 =~ 1*inc_diff_7
  winc_diff_8 =~ 1*inc_diff_8
  winc_diff_9 =~ 1*inc_diff_9
  winc_diff_10 =~ 1*inc_diff_10
  winc_diff_11 =~ 1*inc_diff_11 
  
  # Estimate the lagged effects (constrained)
  winc_diff_2   ~ a*winc_diff_1 + b*wFeduc_a_1
  winc_diff_3   ~ a*winc_diff_2 + b*wFeduc_a_2
  winc_diff_4   ~ a*winc_diff_3 + b*wFeduc_a_3
  winc_diff_5   ~ a*winc_diff_4 + b*wFeduc_a_4
  winc_diff_6   ~ a*winc_diff_5 + b*wFeduc_a_5
  winc_diff_7   ~ a*winc_diff_6 + b*wFeduc_a_6
  winc_diff_8   ~ a*winc_diff_7 + b*wFeduc_a_7
  winc_diff_9   ~ a*winc_diff_8 + b*wFeduc_a_8
  winc_diff_10  ~ a*winc_diff_9 + b*wFeduc_a_9
  winc_diff_11  ~ a*winc_diff_10 + b*wFeduc_a_10
  
  
  wFeduc_a_2  ~ c*winc_diff_1 + d*wFeduc_a_1
  wFeduc_a_3  ~ c*winc_diff_2 + d*wFeduc_a_2
  wFeduc_a_4  ~ c*winc_diff_3 + d*wFeduc_a_3
  wFeduc_a_5  ~ c*winc_diff_4 + d*wFeduc_a_4
  wFeduc_a_6  ~ c*winc_diff_5 + d*wFeduc_a_5
  wFeduc_a_7  ~ c*winc_diff_6 + d*wFeduc_a_6
  wFeduc_a_8  ~ c*winc_diff_7 + d*wFeduc_a_7
  wFeduc_a_9  ~ c*winc_diff_8 + d*wFeduc_a_8
  wFeduc_a_10  ~ c*winc_diff_9 + d*wFeduc_a_9
  wFeduc_a_11  ~ c*winc_diff_10 + d*wFeduc_a_10
  
  # Estimate the covariance at the first wave. 
  winc_diff_1 ~~ wFeduc_a_1 # Covariance

  # Estimate the covariances between the residuals
  winc_diff_2 ~~ cov*wFeduc_a_2
  winc_diff_3 ~~ cov*wFeduc_a_3
  winc_diff_4 ~~ cov*wFeduc_a_4
  winc_diff_5 ~~ cov*wFeduc_a_5
  winc_diff_6 ~~ cov*wFeduc_a_6
  winc_diff_7 ~~ cov*wFeduc_a_7
  winc_diff_8 ~~ cov*wFeduc_a_8
  winc_diff_9 ~~ cov*wFeduc_a_9
  winc_diff_10 ~~ cov*wFeduc_a_10
  winc_diff_11 ~~ cov*wFeduc_a_11
  
  # Estimate the variance 
  winc_diff_1 ~~ winc_diff_1 
  wFeduc_a_1 ~~ wFeduc_a_1
  
  # Estimate the residual variance
  winc_diff_2 ~~ vy*winc_diff_2 
  wFeduc_a_2 ~~ vx*wFeduc_a_2
  winc_diff_3 ~~ vy*winc_diff_3
  wFeduc_a_3 ~~ vx*wFeduc_a_3
  winc_diff_4 ~~ vy*winc_diff_4 
  wFeduc_a_4 ~~ vx*wFeduc_a_4
  winc_diff_5 ~~ vy*winc_diff_5
  wFeduc_a_5 ~~ vx*wFeduc_a_5
  winc_diff_6 ~~ vy*winc_diff_6 
  wFeduc_a_6 ~~ vx*wFeduc_a_6
  winc_diff_7 ~~ vy*winc_diff_7 
  wFeduc_a_7 ~~ vx*wFeduc_a_7
  winc_diff_8 ~~ vy*winc_diff_8 
  wFeduc_a_8 ~~ vx*wFeduc_a_8
  winc_diff_9 ~~ vy*winc_diff_9 
  wFeduc_a_9 ~~ vx*wFeduc_a_9
  winc_diff_10 ~~ vy*winc_diff_10 
  wFeduc_a_10 ~~ vx*wFeduc_a_10
  winc_diff_11 ~~ vy*winc_diff_11 
  wFeduc_a_11 ~~ vx*wFeduc_a_11
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeduc_a_1 + 0*winc_diff_1
  
  
  #constrain grand means over time
  inc_diff_1 + inc_diff_2 + inc_diff_3 + inc_diff_4 + inc_diff_5 + inc_diff_6 + inc_diff_7 + inc_diff_8 + inc_diff_9 + inc_diff_10 + inc_diff_11 ~ my*1
  
  Feduc_a_1 + Feduc_a_2 + Feduc_a_3 + Feduc_a_4 + Feduc_a_5 + Feduc_a_6 + Feduc_a_7 + Feduc_a_8 + Feduc_a_9 + Feduc_a_10 + Feduc_a_11 ~ mx*1

'


#save model specifications in list
inc_diff_lavaan_models <- list(inc_diff_model1_unconstrained,
     inc_diff_model1_constrained_lag,
     inc_diff_model1_constrained_lag_means
     )

Main analysis: estimate models (ML/ FIML)

lavaan_models_main <- list(eu_lavaan_models,
                           cult_lavaan_models,
                           inc_diff_lavaan_models)

# paralellize the estimation
numCores <- detectCores()
registerDoParallel(core = 3)

#initialize foreach loop
main_results <- foreach(a = 1:3) %:%
  foreach(b = 1:3, .packages = c("tidyverse",
                                 "lavaan")) %dopar% {
                                   lavaan(
                                     lavaan_models_main[[a]][[b]],
                                     data = MyData,
                                     missing = 'ML', 
                                     meanstructure = T, 
                                     int.ov.free = T
                                   )
                                 }
#stop parralellization
stopImplicitCluster()

#parallel computing
registerDoParallel(core = 3)

#store fit stats of all models
fit_list <- foreach(a=1:3) %:%
  foreach(b=1:3,
          .combine = rbind,
          .packages = "lavaan") %dopar% {
            lavInspect(main_results[[a]][[b]], what = "fit")
          }

names(fit_list) <- c("EU models", "Cultural Inclusion models", "Income Difference models")

#stop parralellization
stopImplicitCluster()

Main analysis: estimate models (MLR)

# paralellize the estimation
numCores <- detectCores()
registerDoParallel(core = 3)

#initialize foreach loop
main_results_MLR <- foreach(a = 1:3) %:%
  foreach(b = 1:3, .packages = c("tidyverse",
                                 "lavaan")) %dopar% {
                                   lavaan(
                                     lavaan_models_main[[a]][[b]],
                                     data = MyData,
                                     estimator = 'MLR',
                                     missing = "ML",
                                     meanstructure = T, 
                                     int.ov.free = T
                                   )
                                 }


main_results_MLF <- foreach(a = 1:3) %:%
  foreach(b = 1:3, .packages = c("tidyverse",
                                 "lavaan")) %dopar% {
                                   lavaan(
                                     lavaan_models_main[[a]][[b]],
                                     data = MyData,
                                     estimator = 'MLF',
                                     missing = "ML",
                                     meanstructure = T, 
                                     int.ov.free = T
                                   )
                                 }
#stop parralellization
stopImplicitCluster()


#parallel computing
registerDoParallel(core = 3)

#store fit stats of all models
fit_list_MLR <- foreach(a=1:3) %:%
  foreach(b=1:3,
          .combine = rbind,
          .packages = "lavaan") %dopar% {
            lavInspect(main_results_MLR[[a]][[b]], what = "fit")
          }

names(fit_list_MLR) <- c("EU models", "Cultural Inclusion models", "Income Difference models")

#stop parralellization
stopImplicitCluster()

Export results

main_lavaan_results <- list(main_results_MLR,
                            lavaan_models_main, 
                            fit_list_MLR)

names(main_lavaan_results) <- c("Main lavaan results",
                                "Lavaan model objects",
                                "Fit statistics (extracted)")

save(main_lavaan_results,
     file = "results/riclpm/240816_lavaan-main-results.Rdata")

---

Copyright © 2024 Jeroense Thijmen