gather collection of complicated SEM models to guide users in their specification

[aaronpeikert]

LGCM

using StenoGraphs, StructuralEquationModels
ts = 1:100
obs = Symbol.("vf_t", lpad.(ts, 3, "0"))
@declare_nodes i s # same as i, s = Node.((:i, :s))
m = Node(Symbol("1"))
graph = StenoGraph(
    i → [fixed(1)] .* obs,
    s → fixed.(ts .- 1) .* obs,
    obs ↔ obs,
    m → [s i],
    [s i] ⇔ [s i]
)

BigFive

IPIP120/300 PIP 300/120 https://osf.io/wxvth

Methods Factor

from https://www.sciencedirect.com/science/article/pii/S2589958923000403

Dual Change Score Model

https://thechangelab.stanford.edu/tutorials/growth-modeling/multivariate-latent-change-score-models/

bdcm_lavaan <- ' #opening quote
#MATHEMATICS
  #latent true scores (loadings = 1)
    lm1 =~ 1*math2
    lm2 =~ 1*math3
    lm3 =~ 1*math4
    lm4 =~ 1*math5
    lm5 =~ 1*math6
    lm6 =~ 1*math7
    lm7 =~ 1*math8

  #latent true score means (initial free, others = 0)  
    lm1 ~ 1
    lm2 ~ 0*1
    lm3 ~ 0*1
    lm4 ~ 0*1
    lm5 ~ 0*1
    lm6 ~ 0*1
    lm7 ~ 0*1

  #latent true score variances (initial free, others = 0)
    lm1 ~~ start(15)*lm1
    lm2 ~~ 0*lm2
    lm3 ~~ 0*lm3
    lm4 ~~ 0*lm4
    lm5 ~~ 0*lm5
    lm6 ~~ 0*lm6
    lm7 ~~ 0*lm7

  #observed intercepts (fixed to 0)
    math2 ~ 0*1
    math3 ~ 0*1
    math4 ~ 0*1
    math5 ~ 0*1
    math6 ~ 0*1
    math7 ~ 0*1
    math8 ~ 0*1

  #observed residual variances (constrained to equality)
    math2 ~~ sigma2_u*math2
    math3 ~~ sigma2_u*math3
    math4 ~~ sigma2_u*math4
    math5 ~~ sigma2_u*math5
    math6 ~~ sigma2_u*math6
    math7 ~~ sigma2_u*math7
    math8 ~~ sigma2_u*math8

  #autoregressions (fixed = 1)
    lm2 ~ 1*lm1
    lm3 ~ 1*lm2
    lm4 ~ 1*lm3
    lm5 ~ 1*lm4
    lm6 ~ 1*lm5
    lm7 ~ 1*lm6

  #latent change scores (fixed = 1)
    dm2 =~ 1*lm2
    dm3 =~ 1*lm3
    dm4 =~ 1*lm4
    dm5 =~ 1*lm5
    dm6 =~ 1*lm6
    dm7 =~ 1*lm7

  #latent change score means (constrained to 0)  
    dm2 ~ 0*1
    dm3 ~ 0*1
    dm4 ~ 0*1
    dm5 ~ 0*1
    dm6 ~ 0*1
    dm7 ~ 0*1

  #latent change score variances (constrained to 0)  
    dm2 ~~ 0*dm2
    dm3 ~~ 0*dm3
    dm4 ~~ 0*dm4
    dm5 ~~ 0*dm5
    dm6 ~~ 0*dm6
    dm7 ~~ 0*dm7

  #constant change factor (loadings = 1)
    g2 =~ 1*dm2 + 
          1*dm3 + 
          1*dm4 + 
          1*dm5 + 
          1*dm6 + 
          1*dm7 

  #constant change factor mean  
    g2 ~ start(15)*1

  #constant change factor variance
    g2 ~~ g2

  #constant change factor covariance with the initial true score
    g2 ~~ lm1

  #proportional effects (constrained equal)
    dm2 ~ start(-.2)*pi_m * lm1
    dm3 ~ start(-.2)*pi_m * lm2
    dm4 ~ start(-.2)*pi_m * lm3
    dm5 ~ start(-.2)*pi_m * lm4
    dm6 ~ start(-.2)*pi_m * lm5
    dm7 ~ start(-.2)*pi_m * lm6

#READING RECOGNITION
  #latent true scores (loadings = 1)
    lr1 =~ 1*rec2
    lr2 =~ 1*rec3
    lr3 =~ 1*rec4
    lr4 =~ 1*rec5
    lr5 =~ 1*rec6
    lr6 =~ 1*rec7
    lr7 =~ 1*rec8

  #latent true score means (initial free, others = 0)    
    lr1 ~ 1
    lr2 ~ 0*1
    lr3 ~ 0*1
    lr4 ~ 0*1
    lr5 ~ 0*1
    lr6 ~ 0*1
    lr7 ~ 0*1

  #latent true score variances (initial free, others = 0)
    lr1 ~~ start(15)*lr1
    lr2 ~~ 0*lr2
    lr3 ~~ 0*lr3
    lr4 ~~ 0*lr4
    lr5 ~~ 0*lr5
    lr6 ~~ 0*lr6
    lr7 ~~ 0*lr7

  #observed intercept variances (fixed = 0)
    rec2 ~ 0*1
    rec3 ~ 0*1
    rec4 ~ 0*1
    rec5 ~ 0*1
    rec6 ~ 0*1
    rec7 ~ 0*1
    rec8 ~ 0*1

  #observed residual variances (constrained to eqaulity)
    rec2 ~~ sigma2_s*rec2
    rec3 ~~ sigma2_s*rec3
    rec4 ~~ sigma2_s*rec4
    rec5 ~~ sigma2_s*rec5
    rec6 ~~ sigma2_s*rec6
    rec7 ~~ sigma2_s*rec7
    rec8 ~~ sigma2_s*rec8

  #autoregressions (fixed = 1)
    lr2 ~ 1*lr1
    lr3 ~ 1*lr2
    lr4 ~ 1*lr3
    lr5 ~ 1*lr4
    lr6 ~ 1*lr5
    lr7 ~ 1*lr6

  #latent change scores (ficed = 1)
    dr2 =~ 1*lr2
    dr3 =~ 1*lr3
    dr4 =~ 1*lr4
    dr5 =~ 1*lr5
    dr6 =~ 1*lr6
    dr7 =~ 1*lr7

  #latent change score means (fixed = 0)  
    dr2 ~ 0*1
    dr3 ~ 0*1
    dr4 ~ 0*1
    dr5 ~ 0*1
    dr6 ~ 0*1
    dr7 ~ 0*1

  #latent change score variances (fixed = 0)
    dr2 ~~ 0*dr2
    dr3 ~~ 0*dr3
    dr4 ~~ 0*dr4
    dr5 ~~ 0*dr5
    dr6 ~~ 0*dr6
    dr7 ~~ 0*dr7

  #constant change factor (fixed = 1)
    j2 =~ 1*dr2 + 
          1*dr3 + 
          1*dr4 + 
          1*dr5 + 
          1*dr6 + 
          1*dr7 

  #constant change factor mean  
    j2 ~ start(10)*1

  #constant change factor variance
    j2 ~~ j2

  #constant change factor covariance with the initial true score
    j2 ~~ lr1

  #proportional effects (constrained to equality)
    dr2 ~ start(-.2)*pi_r * lr1 
    dr3 ~ start(-.2)*pi_r * lr2 
    dr4 ~ start(-.2)*pi_r * lr3 
    dr5 ~ start(-.2)*pi_r * lr4 
    dr6 ~ start(-.2)*pi_r * lr5 
    dr7 ~ start(-.2)*pi_r * lr6 

#BIVARIATE INFORMATION

  #covariances between the latent growth factors
    lm1 ~~ lr1
    lm1 ~~ j2
    lr1 ~~ g2
    j2 ~~ g2 


  #residual covariances
    math2 ~~ sigma_su*rec2
    math3 ~~ sigma_su*rec3
    math4 ~~ sigma_su*rec4
    math5 ~~ sigma_su*rec5
    math6 ~~ sigma_su*rec6
    math7 ~~ sigma_su*rec7

#COUPLING PARMETERS
  
  #math to changes in reading
    dr2 ~ delta_r*lm1
    dr3 ~ delta_r*lm2
    dr4 ~ delta_r*lm3
    dr5 ~ delta_r*lm4
    dr6 ~ delta_r*lm5
    dr7 ~ delta_r*lm6

  #reading to changes in math
    dm2 ~ delta_m*lr1
    dm3 ~ delta_m*lr2
    dm4 ~ delta_m*lr3
    dm5 ~ delta_m*lr4
    dm6 ~ delta_m*lr5
    dm7 ~ delta_m*lr6
' #closing quote

Bivariate LGCM

tbd

[aaronpeikert]

#270 #277 aaronpeikert/StenoGraphs.jl#68 aaronpeikert/StenoGraphs.jl#67