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Comparing Two-Profile RILTA and CULTA Models

Ivan Jacob Agaloos Pesigan

Source: vignettes/sim-rilta-2-profiles.Rmd
sim-rilta-2-profiles.Rmd

We generate data using the CULTA model with two latent profiles, where profile membership depends on a covariate and profile transitions follow a multinomial structure. However, for model fitting, we impose a simpler structure by fitting a random intercept latent transition analysis (RILTA) model. We then compare this misspecified model to the correctly specified two-profile CULTA model.

Data Generation 

# complete list of R function arguments

# random seed for reproducibility
set.seed(42)

# dimensions
n # number of individuals
#> [1] 10000
m # measurement occasions
#> [1] 6
p # number of items
#> [1] 4
q # common trait dimension
#> [1] 1

# covariate parameters
mu_x 
#> [1] 11.4009
sigma_x
#> [1] 24.67566

# profile membership and transition parameters
nu_0
#> [1] -3.563
kappa_0
#> [1] 0.122
alpha_0
#> [1] -3.586
beta_00
#> [1] 2.25
gamma_00
#> [1] 0.063
gamma_10
#> [1] 0.094

# trait parameters
psi_t
#>      [,1]
#> [1,]  0.1
mu_t
#> [1] 0
psi_p
#>      [,1] [,2] [,3] [,4]
#> [1,]  0.1  0.0  0.0  0.0
#> [2,]  0.0  0.1  0.0  0.0
#> [3,]  0.0  0.0  0.5  0.0
#> [4,]  0.0  0.0  0.0  0.5
mu_p
#> [1] 0 0 0 0
common_trait_loading
#>      [,1]
#> [1,]    1
#> [2,]    1
#> [3,]    1
#> [4,]    1

# state parameters
common_state_loading
#>      [,1]
#> [1,]    1
#> [2,]    1
#> [3,]    1
#> [4,]    1
phi_0
#> [1] 0
phi_1
#> [1] 0.311
psi_s0
#> [1] 1
psi_s
#> [1] 0.25
theta
#>      [,1] [,2] [,3] [,4]
#> [1,] 0.15 0.00 0.00 0.00
#> [2,] 0.00 0.15 0.00 0.00
#> [3,] 0.00 0.00 0.15 0.00
#> [4,] 0.00 0.00 0.00 0.15

# profile-specific means
mu_profile
#>       [,1]   [,2]
#> [1,] 2.253 -0.278
#> [2,] 1.493 -0.165
#> [3,] 1.574 -0.199
#> [4,] 1.117 -0.148
data <- GenCULTA2Profiles(
  n = n,
  m = m,
  mu_x = mu_x,
  sigma_x = sigma_x,
  nu_0 = nu_0,
  kappa_0 = kappa_0,
  alpha_0 = alpha_0,
  beta_00 = beta_00,
  gamma_00 = gamma_00,
  gamma_10 = gamma_10,
  mu_t = mu_t,
  psi_t = psi_t,
  mu_p = mu_p,
  psi_p = psi_p,
  common_trait_loading = common_trait_loading,
  common_state_loading = common_state_loading,
  phi_0 = phi_0,
  phi_1 = phi_1,
  psi_s0 = psi_s0,
  psi_s = psi_s,
  theta = theta, 
  mu_profile = mu_profile
)

Model Fitting

The FitLTA2Profiles function fits the misspecified two-profile RILTA model using Mplus. Note: This function requires that Mplus is already installed on the system.

rilta <- FitRILTA2Profiles(data = data)

The FitCULTA2Profiles function fits the correct two-profile model using Mplus. Note: This function requires that Mplus is already installed on the system. To speed up model fitting, consider using the ncores argument to leverage multiple cores.

culta <- FitCULTA2Profiles(data = data)

Model Comparison

The anova function can be used to compare the two fitted models.

anova(rilta, culta)
#> $fit
#>                    logLik df correction      AIC      BIC     aBIC   entropy
#> 2-profile RILTA -309109.4 22   2.679461 618262.7 618421.3 618351.4 0.8920079
#> 2-profile CULTA -237508.2 33   1.000768 475082.4 475320.3 475215.5 0.9367669
#> 
#> $test
#>  chi_diff   df_diff   p_value 
#> -60765.98     11.00      1.00

Parameter Recovery

Parameter recovery was assessed by calculating the differences between the population values and the estimated profile-specific means and log-odds.

Parameter Recovery
Parameter RILTA Estimate Difference CULTA Estimate Difference
mu_10 2.253 1.5255399 0.7274601 2.2689973 -0.0159973
mu_20 1.493 1.2540192 0.2389808 1.5140045 -0.0210045
mu_30 1.574 1.3511744 0.2228256 1.6057853 -0.0317853
mu_40 1.117 0.9648591 0.1521409 1.1275251 -0.0105251
mu_11 -0.278 -0.5080130 0.2300130 -0.2779016 -0.0000984
mu_21 -0.165 -0.3956839 0.2306839 -0.1652498 0.0002498
mu_31 -0.199 -0.4362505 0.2372505 -0.1829942 -0.0160058
mu_41 -0.148 -0.3389233 0.1909233 -0.1515997 0.0035997
nu_0 -3.563 -1.2267252 -2.3362748 -3.6910557 0.1280557
alpha_0 -3.586 -2.5248986 -1.0611014 -3.5634025 -0.0225975
kappa_0 0.122 0.0357181 0.0862819 0.1273813 -0.0053813
beta_00 2.250 2.7720950 -0.5220950 2.1225611 0.1274389
gamma_00 0.063 -0.0014707 0.0644707 0.0676685 -0.0046685
gamma_10 0.094 0.0595538 0.0344462 0.0942463 -0.0002463

Mplus Script Used

The RILTA model was estimated using the following Mplus script.

Error: object 'lta' not found