Examples of Longitudinal Mixture Models

The saved examples below were generated with nlpsem 1.0.0.9006; extdata/REGENERATED.txt records the versions and how the fits compare with the previous ones. Rendering this guide does not refit its disabled model-fitting chunks. Refit with the current version for a new analysis, use getDiagnostics() to check admissibility and uncertainty, and compare multiple starts for difficult nonlinear or mixture models. These examples are not evidence of numerical qualification.

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

library(nlpsem)
mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)

Load pre-computed models

load(system.file("extdata", "getMIX_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$T1 - baseT
RMS_dat0$T2 <- RMS_dat0$T2 - baseT
RMS_dat0$T3 <- RMS_dat0$T3 - baseT
RMS_dat0$T4 <- RMS_dat0$T4 - baseT
RMS_dat0$T5 <- RMS_dat0$T5 - baseT
RMS_dat0$T6 <- RMS_dat0$T6 - baseT
RMS_dat0$T7 <- RMS_dat0$T7 - baseT
RMS_dat0$T8 <- RMS_dat0$T8 - baseT
RMS_dat0$T9 <- RMS_dat0$T9 - baseT
# Standardize time-invariant covariates (TICs)
## ex1 and ex2 are standardized growth TICs in models
RMS_dat0$ex1 <- scale(RMS_dat0$Approach_to_Learning)
RMS_dat0$ex2 <- scale(RMS_dat0$Attention_focus)
## gx1 and gx2 are standardized cluster TICs in models
RMS_dat0$gx1 <- scale(RMS_dat0$INCOME)
RMS_dat0$gx2 <- scale(RMS_dat0$EDU)
xstarts <- mean(baseT)

Example 1: Fit bilinear spline LGCMs with 1-, 2-, and 3- latent classes to examine the heterogeneity in the development of mathematics skills. The enumeration process is conducted using the `getSummary()` function, with `HetModels = TRUE` specified.

Math_BLS_LGCM1 <- getLGCM(
  dat = RMS_dat0, t_var = "T", y_var = "M", curveFun = "BLS", intrinsic = FALSE,
  records = 1:9, tries = 10
  )
Math_BLS_LGCM2 <- getMIX(
  dat = RMS_dat0, prop_starts = c(0.45, 0.55), sub_Model = "LGCM", y_var = "M",
  t_var = "T", records = 1:9, curveFun = "BLS", intrinsic = FALSE, tries = 10
)
set.seed(20191029)
Math_BLS_LGCM3 <- getMIX(
  dat = RMS_dat0, prop_starts = c(0.30, 0.40, 0.30), sub_Model = "LGCM", y_var = "M",
  t_var = "T", records = 1:9, curveFun = "BLS", intrinsic = FALSE, tries = 10
)

Figure1 <- getFigure(
  model = Math_BLS_LGCM1@mxOutput, nClass = NULL, cluster_TIC = NULL, sub_Model = "LGCM",
  y_var = "M", curveFun = "BLS", y_model = "LGCM", t_var = "T", records = 1:9,
  m_var = NULL, x_var = NULL, x_type = NULL, xstarts = xstarts, xlab = "Month",
  outcome = "Mathematics"
)
show(Figure1)
#> figOutput Object
#> --------------------
#> Trajectories: 1 
#> Figure 1:
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Mathematics mean trajectory over months from a one-class bilinear spline growth model, comparing the fitted mean and smoothed observed mean with pointwise 95 percent confidence limits.

Figure2 <- getFigure(
  model = Math_BLS_LGCM2@mxOutput, nClass = 2, cluster_TIC = NULL, sub_Model = "LGCM",
  y_var = "M", curveFun = "BLS", y_model = "LGCM", t_var = "T", records = 1:9,
  m_var = NULL, x_var = NULL, x_type = NULL, xstarts = xstarts, xlab = "Month",
  outcome = "Mathematics"
)
show(Figure2)
#> figOutput Object
#> --------------------
#> Trajectories: 1 
#> Figure 1:
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Mathematics mean trajectory over months from a two-class bilinear spline growth model, comparing the fitted mean and smoothed observed mean with pointwise 95 percent confidence limits.

Figure3 <- getFigure(
  model = Math_BLS_LGCM3@mxOutput, nClass = 3, cluster_TIC = NULL, sub_Model = "LGCM",
  y_var = "M", curveFun = "BLS", y_model = "LGCM", t_var = "T", records = 1:9,
  m_var = NULL, x_var = NULL, x_type = NULL, xstarts = xstarts, xlab = "Month",
  outcome = "Mathematics"
)
show(Figure3)
#> figOutput Object
#> --------------------
#> Trajectories: 1 
#> Figure 1:
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Mathematics mean trajectory over months from a three-class bilinear spline growth model, comparing the fitted mean and smoothed observed mean with pointwise 95 percent confidence limits.

getSummary(model_list = list(Math_BLS_LGCM1@mxOutput, Math_BLS_LGCM2@mxOutput, Math_BLS_LGCM3@mxOutput),
           HetModels = TRUE)
#>    Model No_Params     -2ll      AIC      BIC Y_res_c1 %Class1 Y_res_c2 %Class2
#> 1 Model1        11 31347.39 31369.39 31415.75  34.0030    100%       NA    <NA>
#> 2 Model2        23 31134.61 31180.61 31277.55  34.2368   67.4%  31.5801   32.6%
#> 3 Model3        35 31022.74 31092.74 31240.25  25.9356     20%  32.4419   42.2%
#>   Y_res_c3 %Class3
#> 1       NA    <NA>
#> 2       NA    <NA>
#> 3  31.5999   37.8%

getDiagnostics() reports slightly indefinite class-specific covariance matrices of the growth factors in the saved two-class solution (class 2) and three-class solution (classes 1 and 3), so refitting these calls returns them with a warning. Weigh the class enumeration with this in mind.

Example 2: Fit reduced bilinear spline bivariate LGCMs with three latent classes to analyze the heterogeneity in the co-development of reading and mathematics skills.

set.seed(20191029)
RM_BLS_PLGCM3 <- getMIX(
  dat = RMS_dat0, prop_starts = c(0.30, 0.40, 0.30), sub_Model = "MGM",
  cluster_TIC = c("gx1", "gx2"), t_var = c("T", "T"), y_var = c("R", "M"),
  curveFun = "BLS", intrinsic = FALSE, records = list(1:9, 1:9),
  y_model = "LGCM", tries = 10, paramOut = TRUE
  )

Figure4 <- getFigure(
  model = RM_BLS_PLGCM3@mxOutput, nClass = 3, cluster_TIC = c("gx1", "gx2"), 
  sub_Model = "MGM", y_var = c("R", "M"), curveFun = "BLS", y_model = "LGCM",
  t_var = c("T", "T"), records = list(1:9, 1:9), m_var = NULL, x_var = NULL, 
  x_type = NULL, xstarts = xstarts, xlab = "Month", 
  outcome = c("Reading", "Mathematics")
)
show(Figure4)
#> figOutput Object
#> --------------------
#> Trajectories: 2 
#> 
#> Trajectory 1 :
#>   Figure 1:
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Reading mean trajectory over months from a three-class bivariate bilinear spline growth model, comparing the fitted mean and smoothed observed mean with pointwise 95 percent confidence limits.

#> 
#> Trajectory 2 :
#>   Figure 1:
#> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Mathematics mean trajectory over months from a three-class bivariate bilinear spline growth model, comparing the fitted mean and smoothed observed mean with pointwise 95 percent confidence limits.