# demo/MILinearDiscrete.R In dynr: Dynamic Models with Regime-Switching

```#---------------------------------------------------------------------
# Author: Yanling Li and Linying Ji
# Date: 2019-09-29
# Filename: MILinearDiscrete.R
# Purpose: An illustrative example of using dynr.mi to implement
# multiple imputation with a vector autoregressive model
#---------------------------------------------------------------------

#---------------------------------------------------------------------

require(dynr)

#---------------------------------------------------------------------
# The data were generated from a vector autogressive (VAR) model
# with two observed dependent variables (i.e., wp and hp) and
# two covariates (i.e., ca and cn).
# x1 and x2 are two auxiliary varialbes used in the generation of missing data.
# The data contain 100 subjects (N = 100) and 100 time points (T = 100) for each subject.
# Missing data were under missing at random (MAR) condtion with around 30% missing rate.
# The true parameters used to generate the data:
# auto-regression parameters
a=0.4; a1=0.3;
# cross-regression parameters
b=-0.3; b1=-0.2;

# coefficients of covariates
c=0.3; c1=0.3;
d=-0.5; d1=-0.4;

# noise variance and covariance
v_wp = 1
c_hw = 0.3
v_hp = 1

data(VARsim)
VARsim\$ca <- as.factor(VARsim\$ca)

# Declare the data with the dynr.data() function
rawdata <- dynr.data(VARsim, id="ID", time="Time",
observed=c("wp","hp"),covariates=c("ca","cn"))

# Define elements of the measurement model
meas <- prep.measurement(
0,1),ncol=2,byrow=T),
state.names=c("eta_wp","eta_hp"),
obs.names=c("wp","hp")
)

# Define elements of the dynamic model
formula =list(eta_wp ~ a*eta_wp + b*eta_hp + c*ca + d*cn,
eta_hp ~ a1*eta_hp + b1*eta_wp +c1*ca + d1*cn)

startval=c(a = .4, b = -.3, b1=-.2, a1=.3,
c = .3, c1=.3, d=-.5, d1=-.4
), isContinuousTime=FALSE)

# Define the initial conditions of the model
initial <- prep.initial(
values.inistate=c(.15,.15),
params.inistate=c('mu_wp', 'mu_hp'),
values.inicov=matrix(c(1,.1,
.1,1),byrow=T,ncol=2),
params.inicov=matrix(c("v_11","c_21",
"c_21","v_22"),byrow=T,ncol=2))

# Define the covariance structures of the measurement noise
# covariance matrix and the dynamic noise covariance matrix
mdcov <- prep.noise(
values.latent=matrix(c(1,.3,
.3,1),byrow=T,ncol=2),
params.latent=matrix(c("v_wp","c_hw",
"c_hw","v_hp"),byrow=T,ncol=2),
values.observed=diag(rep(0,2)),
params.observed=diag(c('fixed','fixed'),2))

# Pass data and submodels to dynrModel object
model <- dynr.model(dynamics=dynm, measurement=meas,
noise=mdcov, initial=initial, data=rawdata,
outfile=paste("trial.c",sep=""))

# Plot the Formula
printex(model, ParameterAs = model\$param.names, printInit = TRUE, printRS = FALSE,
outFile = "MILinearDiscrete.tex")

plotFormula(model, ParameterAs = model\$param.names, printDyn = TRUE, printMeas = TRUE)

# An example of using dynr.mi() function to implement multiple imputation and parameter estimation procedures
result <- dynr.mi(model, which.aux=c("x1","x2"),
which.lag=c("wp","hp"), lag=1,
m=5, iter=10,
imp.obs=FALSE, imp.exo=TRUE,
diag = TRUE, Rhat=1.1,
conf.level=0.95,
verbose=FALSE, seed=12345)

# Compare true parameters to estimated ones
truep <- c(a=0.4, b=-0.3, b1=-0.2, a1=0.3,
c=0.3, c1=0.3, d=-0.5, d1=-0.4,
v_wp = 1, c_hw = 0.3,v_hp = 1)
estp <- result\$estimation.result[1:11, ]
data.frame(truep, estp)

# Convergence diagnostic check
# Rhat plot
result\$Rhat.plot
```

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dynr documentation built on Oct. 17, 2022, 9:06 a.m.