---
title: "Examples of Multivariate Longitudinal Models"
output: rmarkdown::html_vignette
description: > 
  This vignette provides a comprehensive exploration and practical demonstrations of the `getMGM()` function. This function is designed to construct multivariate Latent Growth Curve Models (LGCMs) or Latent Change Score Models (LCSMs). The supported functional forms of LGCMs include linear, quadratic, negative exponential, Jenss-Bayley, and bilinear spline. LCSMs support quadratic, negative exponential, Jenss-Bayley, and nonparametric functions. Notably, the negative exponential and Jenss-Bayley LGCMs/LCSMs, as well as bilinear spline LGCMs, can be fitted as intrinsically nonlinear models. 
vignette: >
  %\VignetteIndexEntry{getMGM_examples}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## Load nlpsem package, dependent packages and set CSOLNP as the optimizer
```{r, message = FALSE}
library(nlpsem)
mxOption(model = NULL, key = "Default optimizer", "CSOLNP", reset = FALSE)
```

## Load pre-computed models
```{r, message = FALSE}
load(system.file("extdata", "getMGM_examples.RData", package = "nlpsem"))
```

## Load example data and preprocess data
```{r, message = FALSE, eval = FALSE}
# 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. 
```{r, message = FALSE, eval = FALSE}
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
  )
```

```{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")
)
show(Figure1)
```

## Example 2: Fit multivariate bilinear spline LGCMs with random knots to evaluate the development of reading and mathematics ability from Kindergarten to Grade 5. 
```{r, message = FALSE, eval = FALSE}
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
  )
```

```{r}
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")
)
show(Figure2)
```