Zero-Inflated Models for Count Time Series with Excess Zeros

Description

Fits observation-driven and parameter-driven models for count time series with excess zeros.

Details

The package ZIM contains functions to fit statistical models for count time series with excess zeros (Yang et al., 2013, 2015). The main function for fitting observation-driven models is zim, and the main function for fitting parameter-driven models is dzim.

Note

The observation-driven models for zero-inflated count time series can also be fit using the function zeroinfl from the pscl package (Zeileis et al., 2008). Fitting parameter-driven models is based on sequential Monte Carlo (SMC) methods, which are computer intensive and could take several hours to estimate the model parameters.

References

Yang, M., Cavanaugh, J. E., and Zamba, G. K. D. (2015). State-space models for count time series with excess zeros. Statistical Modelling, 15:70-90

Yang, M., Zamba, G. K. D., and Cavanaugh, J. E. (2013). Markov regression models for count time series with excess zeros: A partial likelihood approach. Statistical Methodology, 14:26-38.

Zeileis, A., Kleiber, C., and Jackman, S. (2008). Regression models for count data in R. Journal of Statistical Software, 27(8).

The Zero-Inflated Negative Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the zero-inflated negative binomial (ZINB) distribution with parameters k, lambda, and omega.

Usage

dzinb(x, k, lambda, omega, log = FALSE)
pzinb(q, k, lambda, omega, lower.tail = TRUE, log.p = FALSE)
qzinb(p, k, lambda, omega, lower.tail = TRUE, log.p = FALSE)
rzinb(n, k, lambda, omega)

Arguments

Value

dzinb gives the density, pzinb gives the distribution function, qzinb gives the quantile function, and rzinb generates random deviates.

See Also

dzip, pzip, qzip, and rzip for the zero-inflated Poisson (ZIP) distribution.

Examples

dzinb(x = 0:10, k = 1, lambda = 1, omega = 0.5)
pzinb(q = c(1, 5, 9), k = 1, lambda = 1, omega = 0.5)
qzinb(p = c(0.25, 0.50, 0.75), k = 1, lambda = 1, omega = 0.5)
set.seed(123)
rzinb(n = 100, k = 1, lambda = 1, omega = 0.5)

The Zero-Inflated Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the zero-inflated Poisson (ZIP) distribution with parameters lambda and omega.

Usage

dzip(x, lambda, omega, log = FALSE)
pzip(q, lambda, omega, lower.tail = TRUE, log.p = FALSE)
qzip(p, lambda, omega, lower.tail = TRUE, log.p = FALSE)
rzip(n, lambda, omega)

Arguments

Value

dzip gives the density, pzip gives the distribution function, qzip gives the quantile function, and rzip generates random deviates.

See Also

dzinb, pzinb, qzinb, and rzinb for the zero-inflated negative binomial (ZINB) distribution.

Examples

dzip(x = 0:10, lambda = 1, omega = 0.5)
pzip(q = c(1, 5, 9), lambda = 1, omega = 0.5)
qzip(p = c(0.25, 0.50, 0.75), lambda = 1, omega = 0.5)
set.seed(123)
rzip(n = 100, lambda = 1, omega = 0.5)

Backshift Operator

Description

Apply the backshift operator or lag operator to a time series objective.

Usage

bshift(x, k = 1)

Arguments

See Also

lag, zlag

Examples

x <- arima.sim(model = list(ar = 0.8, sd = 0.5), n = 120)
bshift(x, k = 12)

Fitting Dynamic Zero-Inflated Models

Description

dzim is used to fit dynamic zero-inflated models.

Usage

dzim(formula, data, subset, na.action, weights = 1, offset = 0,
  control = dzim.control(...), ...)

Arguments

See Also

dzim.fit, dzim.filter, dzim.smooth, dzim.control, dzim.sim, dzim.plot

Auxiliary for Controlling DZIM Fitting

Description

Auxiliary function for dzim fitting. Typically only used internally by dzim.fit, but may be used to construct a control argument for either function.

Usage

dzim.control(dist = c("poisson", "nb", "zip", "zinb"), trace = FALSE,
  start = NULL, order = 1, mu0 = rep(0, order), Sigma0 = diag(1,
  order), N = 1000, R = 1000, niter = 500)

Arguments

Note

The default values of N, R, and niter are chosen based on our experience. In some cases, N = 500, R = 500, and niter = 200 might be sufficient. The dzim.plot function should always be used for convergence diagnostics.

See Also

dzim, dzim.fit, dzim.filter, dzim.smooth, dzim.sim, dzim.plot

Particle Filtering for DZIM

Description

Function to implement the particle filtering method proposed by Gordsill et al. (1993).

Usage

dzim.filter(y, X, w, para, control)

Arguments

References

Gordon, N. J., Salmond, D. J., and Smith, A. F. M. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEEE Proceedings, 140, 107-113.

See Also

dzim, dzim.fit, dzim.smooth, dzim.control, dzim.sim, dzim.plot

Fitter Function for Dynamic Zero-Inflated Models

Description

dzim.fit is the basic computing engine called by dzim used to fit dynamic zero-inflated models. This should usually not be used directly unless by experienced users.

Usage

dzim.fit(y, X, offset = rep(0, n), control = dzim.control(...), ...)

Arguments

See Also

dzim, dzim.control, dzim.filter, dzim.smooth, dzim.sim, dzim.plot

Trace Plots from DZIM

Description

Function to display trace plots from a dynamic zero-inflated model.

Usage

dzim.plot(object, k.inv = FALSE, sigma.sq = FALSE, ...)

Arguments

Simulate Data from DZIM

Description

Simulate data from a dynamic zero-inflated model.

Usage

dzim.sim(X, w, omega, k, beta, phi, sigma, mu0, Sigma0)

Arguments

See Also

dzim, dzim.fit, dzim.filter, dzim.smooth, dzim.control, dzim.plot

Particle Smoothing for DZIM

Description

Function to implement the particle smoothing method proposed by Gordsill et al. (2004).

Usage

dzim.smooth(y, X, w, para, control)

Arguments

References

Gordsill, S. J., Doucet, A., and West, M. (2004). Monte Carlo smoothing for nonlinear time series. Journal of the American Statistical Association, 99, 156-168.

See Also

dzim, dzim.fit, dzim.filter, dzim.control, dzim.sim, dzim.plot

Example: Injury Series from Occupational Health

Description

Monthly number of injuries in hospitals from July 1988 to October 1995.

Source

Numbers from Figure 1 of Yau et al. (2004).

References

Yau, K. K. W., Lee, A. H. and Carrivick, P. J. W. (2004). Modeling zero-inflated count series with application to occupational health. Computer Methods and Programs in Biomedicine, 74, 47-52.

Examples

data(injury)
plot(injury, type = "o", pch = 20, xaxt = "n", yaxt = "n", ylab = "Injury Count")
  axis(side = 1, at = seq(1, 96, 8))
  axis(side = 2, at = 0:9)
  abline(v = 57, lty = 2)
  mtext("Pre-intervention",  line = 1, at = 25, cex = 1.5)
  mtext("Post-intervention", line = 1, at = 80, cex = 1.5)

Function to Compute P-value.

Description

Function to compute p-value based on a t-statistic.

Usage

pvalue(t, df = Inf, alternative = c("two.sided", "less", "greater"))

Arguments

Examples

pvalue(1.96, alternative = "greater")

Example: Syphilis Series

Description

Weekly number of syphilis cases in the United States from 2007 to 2010.

Format

A data frame with 209 observations on the following 69 variables.

Note

C.N.M.I.: Commonwealth of Northern Mariana Islands.

Source

CDC Morbidity and Mortality Weekly Report (http://www.cdc.gov/MMWR/).

Examples

data(syph)
plot(ts(syph$a33), main = "Maryland")

Fitting Zero-Inflated Models

Description

zim is used to fit zero-inflated models.

Usage

zim(formula, data, subset, na.action, weights = 1, offset = 0,
  control = zim.control(...), ...)

Arguments

Note

zim is very similar to zeroinfl from the pscl package. Both functions can be used to fit observation-driven models for zero-inflated time series.

See Also

zim.fit, zim.control

Auxiliary for Controlling ZIM Fitting

Description

Auxiliary function for zim fitting. Typically only used internally by zim.fit, but may be used to construct a control argument for either function.

Usage

zim.control(dist = c("zip", "zinb"), method = c("EM-NR", "EM-FS"),
  type = c("solve", "ginv"), robust = FALSE, trace = FALSE,
  start = NULL, minit = 10, maxit = 10000, epsilon = 1e-08)

Arguments

See Also

zim, zim.fit

Fitter Function for Zero-Inflated Models

Description

zim.fit is the basic computing engine called by zim used to fit zero-inflated models. This should usually not be used directly unless by experienced users.

Usage

zim.fit(y, X, Z, weights = rep(1, nobs), offset = rep(0, nobs),
  control = zim.control(...), ...)

Arguments

See Also

zim, zim.control