# Examples of Multivariate Longitudinal Models

## 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", "getMGM_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
    xstarts <- mean(baseT)

## Example 1: Fit multivariate bilinear spline LGCMs fixed knots to evaluate the development of reading and mathematics ability from Kindergarten to Grade 5.

    paraBLS_PLGCM.r <- c(
      "Y_mueta0", "Y_mueta1", "Y_mueta2", "Y_knot",
      paste0("Y_psi", c("00", "01", "02", "11", "12", "22")), "Y_res",
      "Z_mueta0", "Z_mueta1", "Z_mueta2", "Z_knot",
      paste0("Z_psi", c("00", "01", "02", "11", "12", "22")), "Z_res",
      paste0("YZ_psi", c("00", "10", "20", "01", "11", "21", "02", "12", "22")),
      "YZ_res"
      )
    RM_PLGCM.r <- getMGM(
      dat = RMS_dat0, t_var = c("T", "T"), y_var = c("R", "M"), curveFun = "BLS",
      intrinsic = FALSE, records = list(1:9, 1:9), y_model = "LGCM", res_scale = c(0.1, 0.1),
      res_cor = 0.3, paramOut = TRUE, names = paraBLS_PLGCM.r
      )

    Figure1 <- getFigure(
      model = RM_PLGCM.r@mxOutput, sub_Model = "MGM", y_var = c("R", "M"), curveFun = "BLS",
      y_model = "LGCM", t_var = c("T", "T"), records = list(1:9, 1:9), xstarts = xstarts,
      xlab = "Month", outcome = c("Reading", "Mathematics")
    )
    #> Treating first argument as an object that stores a character
    #> Treating first argument as an object that stores a character
    show(Figure1)
    #> figOutput Object
    #> --------------------
    #> Trajectories: 2
    #>
    #> Trajectory 1 :
    #>   Figure 1:
    #> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

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

## Example 2: Fit multivariate bilinear spline LGCMs with random knots to evaluate the development of reading and mathematics ability from Kindergarten to Grade 5.

    paraBLS_PLGCM_f <- c(
      "Y_mueta0", "Y_mueta1", "Y_mueta2", "Y_knot",
      paste0("Y_psi", c("00", "01", "02", "0g", "11", "12", "1g", "22", "2g", "gg")), "Y_res",
      "Z_mueta0", "Z_mueta1", "Z_mueta2", "Z_knot",
      paste0("Z_psi", c("00", "01", "02", "0g", "11", "12", "1g", "22", "2g", "gg")), "Z_res",
      paste0("YZ_psi", c(c("00", "10", "20", "g0", "01", "11", "21", "g1",
                           "02", "12", "22", "g2", "0g", "1g", "2g", "gg"))),
      "YZ_res"
      )
    RM_PLGCM.f <- getMGM(
      dat = RMS_dat0, t_var = c("T", "T"), y_var = c("R", "M"), curveFun = "BLS",
      intrinsic = TRUE, records = list(1:9, 1:9), y_model = "LGCM", res_scale = c(0.1, 0.1),
      res_cor = 0.3, paramOut = TRUE, names = paraBLS_PLGCM_f
      )

    Figure2 <- getFigure(
      model = RM_PLGCM.f@mxOutput, sub_Model = "MGM", y_var = c("R", "M"), curveFun = "BLS",
      y_model = "LGCM", t_var = c("T", "T"), records = list(1:9, 1:9), xstarts = xstarts,
      xlab = "Month", outcome = c("Reading", "Mathematics")
    )
    #> Treating first argument as an object that stores a character
    #> Treating first argument as an object that stores a character
    show(Figure2)
    #> figOutput Object
    #> --------------------
    #> Trajectories: 2
    #>
    #> Trajectory 1 :
    #>   Figure 1:
    #> `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

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