# testpanelGroupBreak: A Test for the Group-level Break using a Multivariate Linear... In MCMCpack: Markov Chain Monte Carlo (MCMC) Package

 testpanelGroupBreak R Documentation

## A Test for the Group-level Break using a Multivariate Linear Regression Model with Breaks

### Description

testpanelGroupBreak fits a multivariate linear regression model with parametric breaks using panel residuals to test the existence of group-level breaks in panel residuals. The details are discussed in Park (2011).

### Usage

testpanelGroupBreak(
subject.id,
time.id,
resid,
m = 1,
mcmc = 1000,
burnin = 1000,
thin = 1,
verbose = 0,
b0,
B0,
c0,
d0,
a = NULL,
b = NULL,
seed = NA,
marginal.likelihood = c("none", "Chib95"),
...
)


### Arguments

 subject.id A numeric vector indicating the group number. It should start from 1. time.id A numeric vector indicating the time unit. It should start from 1. resid A vector of panel residuals m The number of changepoints. mcmc The number of MCMC iterations after burn-in. burnin The number of burn-in iterations for the sampler. thin The thinning interval used in the simulation. The number of MCMC iterations must be divisible by this value. verbose A switch which determines whether or not the progress of the sampler is printed to the screen. If verbose is greater than 0, the iteration number and the posterior density samples are printed to the screen every verboseth iteration. b0 The prior mean of the residual mean. B0 The prior precision of the residual variance c0 c_0/2 is the shape parameter for the inverse Gamma prior on σ^2. The amount of information in the inverse Gamma prior is something like that from c_0 pseudo-observations. d0 d_0/2 is the scale parameter for the inverse Gamma prior on σ^2. a a is the shape1 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states. b b is the shape2 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states. seed The seed for the random number generator. If NA, current R system seed is used. marginal.likelihood How should the marginal likelihood be calculated? Options are: none in which case the marginal likelihood will not be calculated and Chib95 in which case the method of Chib (1995) is used. ... further arguments to be passed

### Details

testpanelGroupBreak fits a multivariate linear regression model with parametric breaks using panel residuals to detect the existence of system-level breaks in unobserved factors as discussed in Park (2011).

The model takes the following form:

e_{i} \sim \mathcal{N}(β_{m}, σ^2_m I)\;\; m = 1, …, M

We assume standard, semi-conjugate priors:

β \sim \mathcal{N}(b0, B0)

And:

σ^{-2} \sim \mathcal{G}amma(c_0/2, d_0/2)

Where β and σ^{-2} are assumed a priori independent.

And:

p_{mm} \sim \mathcal{B}eta(a, b),\;\; m = 1, …, M

Where M is the number of states.

### Value

An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package. The object contains an attribute prob.state storage matrix that contains the probability of state_i for each period, and the log-marginal likelihood of the model (logmarglike).

### References

Jong Hee Park, 2012. “Unified Method for Dynamic and Cross-Sectional Heterogeneity: Introducing Hidden Markov Panel Models.” American Journal of Political Science.56: 1040-1054. <doi: 10.1111/j.1540-5907.2012.00590.x>

Siddhartha Chib. 1998. “Estimation and comparison of multiple change-point models.” Journal of Econometrics. 86: 221-241. <doi: 10.1080/01621459.1995.10476635>

### Examples


## Not run:
## data generating
set.seed(1977)
Q <- 3
true.beta1   <-  c(1, 1, 1) ; true.beta2   <-  c(1, -1, -1)
true.sigma2 <-  c(1, 3); true.D1 <- diag(.5, Q); true.D2 <- diag(2.5, Q)
N=20; T=100;
NT <- N*T
x1 <- rnorm(NT)
x2 <- runif(NT, 5, 10)
X <- cbind(1, x1, x2);   W <- X;   y <- rep(NA, NT)

## true break numbers are one and at the center
break.point = rep(T/2, N); break.sigma=c(rep(1, N));
break.list <- rep(1, N)
id  <-  rep(1:N, each=NT/N)
K <-  ncol(X);
ruler <- c(1:T)

## compute the weight for the break
W.mat <- matrix(NA, T, N)
for (i in 1:N){
W.mat[, i] <- pnorm((ruler-break.point[i])/break.sigma[i])
}
Weight <- as.vector(W.mat)

## data generating by weighting two means and variances
j = 1
for (i in 1:N){
Xi <- X[j:(j+T-1), ]
Wi <- W[j:(j+T-1), ]
true.V1 <- true.sigma2[1]*diag(T) + Wi%*%true.D1%*%t(Wi)
true.V2 <- true.sigma2[2]*diag(T) + Wi%*%true.D2%*%t(Wi)
true.mean1 <- Xi%*%true.beta1
true.mean2 <- Xi%*%true.beta2
weight <- Weight[j:(j+T-1)]
y[j:(j+T-1)] <- (1-weight)*true.mean1 + (1-weight)*chol(true.V1)%*%rnorm(T) +
weight*true.mean2 + weight*chol(true.V2)%*%rnorm(T)
j <- j + T
}
## model fitting
subject.id <- c(rep(1:N, each=T))
time.id <- c(rep(1:T, N))

resid <- rstandard(lm(y ~X-1 + as.factor(subject.id)))
G <- 100
out0 <- testpanelGroupBreak(subject.id, time.id, resid, m=0,
mcmc=G, burnin=G, thin=1, verbose=G,
b0=0, B0=1/100, c0=2, d0=2, marginal.likelihood = "Chib95")
out1 <- testpanelGroupBreak(subject.id, time.id, resid, m=1,
mcmc=G, burnin=G, thin=1, verbose=G,
b0=0, B0=1/100, c0=2, d0=2, marginal.likelihood = "Chib95")
out2 <- testpanelGroupBreak(subject.id, time.id, resid, m=2,
mcmc=G, burnin=G, thin=1, verbose=G,
b0=0, B0=1/100, c0=2, d0=2, marginal.likelihood = "Chib95")
out3 <- testpanelGroupBreak(subject.id, time.id, resid, m=3,
mcmc=G, burnin=G, thin=1, verbose=G,
b0=0, B0=1/100, c0=2, d0=2, marginal.likelihood = "Chib95")

## Note that the code is for a hypothesis test of no break in panel residuals.
## When breaks exist, the estimated number of break in the mean and variance of panel residuals
## tends to be larger than the number of break in the data generating process.
## This is due to the difference in parameter space, not an error of the code.
BayesFactor(out0, out1, out2, out3)

## In order to identify the number of breaks in panel parameters,