residuals {HiddenMarkov}

Residuals of Hidden Markov Model

Description

Provides methods for the generic function residuals. There is currently no method for objects of class "mmpp".

Usage

## S3 method for class 'dthmm'
residuals(object, ...)
## S3 method for class 'mmglm0'
residuals(object, ...)
## S3 method for class 'mmglm1'
residuals(object, ...)
## S3 method for class 'mmglmlong1'
residuals(object, ...)

Arguments

object

an object with class dthmm, mmglm0, mmglm1 or mmglmlong1.

...

other arguments.

Details

The calculated residuals are pseudo residuals. Under satisfactory conditions they have an approximate standard normal distribution. Initially the function probhmm is called. If the model fits satisfactorily, the returned values should be approximately uniformly distributed. Hence by applying the function qnorm, the resultant “residuals” should have an approximate standard normal distribution.

A continuity adjustment is made when the observed distribution is discrete. In the case of count distributions (e.g. binomial and Poisson) where the observed count is close to or on the boundary of the domain (e.g. binomial or Poisson count is zero, or binomial count is “n”), the pseudo residuals will give a very poor indication of the models goodness of fit; see the Poisson example below.

The code for the methods "dthmm", "mmglm0", "mmglm1" and "mmglmlong1" can be viewed by appending residuals.dthmm, residuals.mmglm0, residuals.mmglm1 or residuals.mmglmlong1, respectively, to HiddenMarkov:::, on the R command line; e.g. HiddenMarkov:::dthmm. The three colons are needed because these method functions are not in the exported NAMESPACE.

Value

A vector containing the pseudo residuals.

Examples

#   Example Using Beta Distribution

Pi <- matrix(c(0.8, 0.2,
               0.3, 0.7),
             byrow=TRUE, nrow=2)

n <- 2000

x <- dthmm(NULL, Pi, c(0,1), "beta",
           list(shape1=c(2, 6), shape2=c(6, 2)))

x <- simulate(x, nsim=n, seed=5)

y <- residuals(x) 

w <- hist(y, main="Beta HMM: Pseudo Residuals")
z <- seq(-3, 3, 0.01)
points(z, dnorm(z)*n*(w$breaks[2]-w$breaks[1]), col="red", type="l")
box()

qqnorm(y, main="Beta HMM: Q-Q Plot of Pseudo Residuals")
abline(a=0, b=1, lty=3)
abline(h=seq(-2, 2, 1), lty=3)
abline(v=seq(-2, 2, 1), lty=3)


#-----------------------------------------------
#   Example Using Gaussian Distribution

Pi <- matrix(c(1/2, 1/2,   0,   0,   0,
               1/3, 1/3, 1/3,   0,   0,
                 0, 1/3, 1/3, 1/3,   0,
                 0,   0, 1/3, 1/3, 1/3,
                 0,   0,   0, 1/2, 1/2),
             byrow=TRUE, nrow=5)

x <- dthmm(NULL, Pi, c(0, 1, 0, 0, 0), "norm",
           list(mean=c(1, 4, 2, 5, 3), sd=c(0.5, 1, 1, 0.5, 0.1)))

n <- 2000
x <- simulate(x, nsim=n, seed=5)

y <- residuals(x) 

w <- hist(y, main="Gaussian HMM: Pseudo Residuals")
z <- seq(-3, 3, 0.01)
points(z, dnorm(z)*n*(w$breaks[2]-w$breaks[1]), col="red", type="l")
box()

qqnorm(y, main="Gaussian HMM: Q-Q Plot of Pseudo Residuals")
abline(a=0, b=1, lty=3)
abline(h=seq(-2, 2, 1), lty=3)
abline(v=seq(-2, 2, 1), lty=3)


#-----------------------------------------------
#   Example Using Poisson Distribution  

Pi <- matrix(c(0.8, 0.2,
               0.3, 0.7),
             byrow=TRUE, nrow=2)

x <- dthmm(NULL, Pi, c(0, 1), "pois",
           list(lambda=c(1, 5)), discrete=TRUE)

n <- 2000
x <- simulate(x, nsim=n, seed=5)

y <- residuals(x) 

w <- hist(y, main="Poisson HMM: Pseudo Residuals")
z <- seq(-3, 3, 0.01)
points(z, dnorm(z)*n*(w$breaks[2]-w$breaks[1]), col="red", type="l")
box()

qqnorm(y, main="Poisson HMM: Q-Q Plot of Pseudo Residuals")
abline(a=0, b=1, lty=3)
abline(h=seq(-2, 2, 1), lty=3)
abline(v=seq(-2, 2, 1), lty=3)