Examples of Latent Change Score Models

Load nlpsem package, dependent packages and set CSOLNP as the optimizer

library(OpenMx)
library(dplyr)
library(tidyr)
library(stringr)
library(ggplot2)
library(nlpsem)
mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)

Load pre-computed models

load(system.file("extdata", "getLCSM_examples.RData", package = "nlpsem"))

Load example data and preprocess data

# Load ECLS-K (2011) data
data("RMS_dat")
RMS_dat0 <- RMS_dat
# Re-baseline the data so that the estimated initial status is for the
# starting point of the study
baseT <- RMS_dat0$T1
RMS_dat0$T1 <- (RMS_dat0$T1 - baseT)/12
RMS_dat0$T2 <- (RMS_dat0$T2 - baseT)/12
RMS_dat0$T3 <- (RMS_dat0$T3 - baseT)/12
RMS_dat0$T4 <- (RMS_dat0$T4 - baseT)/12
RMS_dat0$T5 <- (RMS_dat0$T5 - baseT)/12
RMS_dat0$T6 <- (RMS_dat0$T6 - baseT)/12
RMS_dat0$T7 <- (RMS_dat0$T7 - baseT)/12
RMS_dat0$T8 <- (RMS_dat0$T8 - baseT)/12
RMS_dat0$T9 <- (RMS_dat0$T9 - baseT)/12
# Standardize time-invariant covariates (TICs)
## ex1 and ex2 are standardized growth TICs in models
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)
xstarts <- mean(baseT)/12

Example 1: Fit nonparametric LCSMs to assess the development of reading ability from Kindergarten to Grade 5, both with and without incorporating baseline teacher-reported approach to learning and attentional focus. The getSummary() function is used to generate a comprehensive summary table for these two models. Additionally, the visual representations of the growth rate and change from the baseline for both models.

paraNonP_LCSM <- c(
  c("mueta0", "mueta1", paste0("psi", c("00", "01", "11")), paste0("rel_rate", 2:8),
    "residuals", paste0("slp_val_est", 1:8), paste0("slp_var_est", 1:8),
    paste0("chg_inv_val_est", 1:8), paste0("chg_inv_var_est", 1:8),
    paste0("chg_bl_val_est", 1:8), paste0("chg_bl_var_est", 1:8))
  )
Read_LCSM_NonP <- getLCSM(
  dat = RMS_dat0, t_var = "T", y_var = "R", curveFun = "nonparametric",
  intrinsic = FALSE, records = 1:9, growth_TIC = NULL, res_scale = 0.1, 
  paramOut = TRUE, names = paraNonP_LCSM
  )
paraNonP_LCSM_TIC <- c(
  c("alpha0", "alpha1", paste0("psi", c("00", "01", "11")), paste0("rel_rate", 2:8),
    "residuals", paste0("beta1", c(0:1)), paste0("beta2", c(0:1)),
    paste0("mux", 1:2), paste0("phi", c("11", "12", "22")), "mueta0", "mueta1",
    paste0("slp_val_est", 1:8), paste0("slp_var_est", 1:8),
    paste0("chg_inv_val_est", 1:8), paste0("chg_inv_var_est", 1:8),
    paste0("chg_bl_val_est", 1:8), paste0("chg_bl_var_est", 1:8))
  )
Read_LCSM_NonP_TIC <- getLCSM(
  dat = RMS_dat0, t_var = "T", y_var = "R", curveFun = "nonparametric",
  intrinsic = FALSE, records = 1:9, growth_TIC = c("ex1", "ex2"), res_scale = 0.1, 
  paramOut = TRUE, names = paraNonP_LCSM_TIC
  )
getSummary(model_list = list(Read_LCSM_NonP[[1]], Read_LCSM_NonP_TIC[[1]]))
#>    Model No_Params     -2ll      AIC      BIC Y_residuals
#> 1 Model1        13 32288.39 32314.39 32369.18     45.1379
#> 2 Model2        22 34575.48 34619.48 34712.20     45.1410
Figure1 <- getFigure(
  model = Read_LCSM_NonP[[1]], sub_Model = "LCSM", y_var = "R", curveFun = "NonP", 
  y_model = "LCSM", t_var = "T", records = 1:9, xstarts = xstarts, xlab = "Year",
  outcome = "Reading"
)
#> Treating first argument as an object that stores a character
#> Treating first argument as an object that stores a character
#> Treating first argument as an object that stores a character
print(Figure1[[1]])
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

print(Figure1[[2]])

Figure2 <- getFigure(
  model = Read_LCSM_NonP_TIC[[1]], sub_Model = "LCSM", y_var = "R", curveFun = "NonP", 
  y_model = "LCSM", t_var = "T", records = 1:9, xstarts = xstarts, xlab = "Year",
  outcome = "Reading"
)
#> Treating first argument as an object that stores a character
#> Treating first argument as an object that stores a character
#> Treating first argument as an object that stores a character
print(Figure2[[1]])
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

print(Figure2[[2]])

Example 2: Fit LCSMs with quadratic, negative exponential and Jenss-Bayley functional forms. Additionally, the visual representations change from the baseline for three models.

Read_LCSM_QUAD <- getLCSM(
  dat = RMS_dat0, t_var = "T", y_var = "R", curveFun = "quadratic", intrinsic = FALSE,
  records = 1:9, res_scale = 0.1
  )
set.seed(20191029)
Read_LCSM_EXP_r <- getLCSM(
  dat = RMS_dat0, t_var = "T", y_var = "R", curveFun = "negative exponential",
  intrinsic = FALSE, records = 1:9, res_scale = 0.1, tries = 10
  )
set.seed(20191029)
Read_LCSM_JB_r <- getLCSM(
  dat = RMS_dat0, t_var = "T", y_var = "R", curveFun = "Jenss-Bayley",
  intrinsic = FALSE, records = 1:9, res_scale = 0.1, tries = 10
  )
Figure3 <- getFigure(
  model = Read_LCSM_QUAD, sub_Model = "LCSM", y_var = "R", curveFun = "QUAD", 
  y_model = "LCSM", t_var = "T", records = 1:9, xstarts = xstarts, xlab = "Year",
  outcome = "Reading"
)
#> Treating first argument as an object that stores a character
print(Figure3[[1]])
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Figure4 <- getFigure(
  model = Read_LCSM_EXP_r, sub_Model = "LCSM", y_var = "R", curveFun = "EXP", 
  y_model = "LCSM", t_var = "T", records = 1:9, xstarts = xstarts, xlab = "Year",
  outcome = "Reading"
)
#> Treating first argument as an object that stores a character
print(Figure4[[1]])
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Figure5 <- getFigure(
  model = Read_LCSM_JB_r, sub_Model = "LCSM", y_var = "R", curveFun = "JB", 
  y_model = "LCSM", t_var = "T", records = 1:9, xstarts = xstarts, xlab = "Year",
  outcome = "Reading"
)
#> Treating first argument as an object that stores a character
print(Figure5[[1]])
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'