| Title: | Zero-Inflated Models (ZIM) for Count Time Series with Excess Zeros |
|---|---|
| Description: | Analyze count time series with excess zeros. Two types of statistical models are supported: Markov regression by Yang et al. (2013) <doi:10.1016/j.stamet.2013.02.001> and state-space models by Yang et al. (2015) <doi:10.1177/1471082X14535530>. They are also known as observation-driven and parameter-driven models respectively in the time series literature. The functions used for Markov regression or observation-driven models can also be used to fit ordinary regression models with independent data under the zero-inflated Poisson (ZIP) or zero-inflated negative binomial (ZINB) assumption. Besides, the package contains some miscellaneous functions to compute density, distribution, quantile, and generate random numbers from ZIP and ZINB distributions. |
| Authors: | Ming Yang [aut, cre], Gideon Zamba [aut], Joseph Cavanaugh [aut] |
| Maintainer: | Ming Yang <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1.0.1809 |
| Built: | 2025-01-29 03:20:00 UTC |
| Source: | https://github.com/mingstat/zim |
Fits observation-driven and parameter-driven models for count time series with excess zeros.
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.
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.
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).
Backshift Operator
Apply the backshift operator or lag operator to a time series objective.
bshift(x, k = 1)bshift(x, k = 1)
x |
univariate or multivariate time series. |
k |
number of lags. |
x <- arima.sim(model = list(ar = 0.8, sd = 0.5), n = 120) bshift(x, k = 12)x <- arima.sim(model = list(ar = 0.8, sd = 0.5), n = 120) bshift(x, k = 12)
dzim is used to fit dynamic zero-inflated models.
dzim(formula, data, subset, na.action, weights = 1, offset = 0, control = dzim.control(...), ...)dzim(formula, data, subset, na.action, weights = 1, offset = 0, control = dzim.control(...), ...)
formula |
an objective of class " |
data |
an optional dataframe, list or environment containing the variables in the model. |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
na.action |
a function which indicates what should happen when the data contain |
weights |
an optional vector of 'prior weights' to be used in the fitting process. |
offset |
this can be used to specify a priori known component to be included in the linear predictor during fitting. |
control |
control arguments from |
... |
additional arguments |
dzim.fit,
dzim.filter,
dzim.smooth,
dzim.control,
dzim.sim,
dzim.plot
Auxiliary function for dzim fitting. Typically only used internally by
dzim.fit, but may be used to construct a control argument for either function.
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)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)
dist |
count model family |
trace |
logical; if TRUE, display iteration history. |
start |
initial parameter values. |
order |
autoregressive order. |
mu0 |
mean vector for initial state. |
Sigma0 |
covariance matrix for initial state. |
N |
number of particiles in particle filtering. |
R |
number of replications in particle smoothing. |
niter |
number of iterations. |
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.
dzim,
dzim.fit,
dzim.filter,
dzim.smooth,
dzim.sim,
dzim.plot
Function to implement the particle filtering method proposed by Gordsill et al. (1993).
dzim.filter(y, X, w, para, control)dzim.filter(y, X, w, para, control)
y |
response variable. |
X |
design matrix. |
w |
|
para |
model parameters. |
control |
control arguments. |
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.
dzim,
dzim.fit,
dzim.smooth,
dzim.control,
dzim.sim,
dzim.plot
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.
dzim.fit(y, X, offset = rep(0, n), control = dzim.control(...), ...)dzim.fit(y, X, offset = rep(0, n), control = dzim.control(...), ...)
y |
response variable. |
X |
design matrix. |
offset |
offset variable. |
control |
control arguments. |
... |
additional arguments. |
dzim,
dzim.control,
dzim.filter,
dzim.smooth,
dzim.sim,
dzim.plot
Function to display trace plots from a dynamic zero-inflated model.
dzim.plot(object, k.inv = FALSE, sigma.sq = FALSE, ...)dzim.plot(object, k.inv = FALSE, sigma.sq = FALSE, ...)
object |
|
k.inv |
logical; indicating whether an inverse transformation is needed for the dispersion parameter. |
sigma.sq |
logical; indicating whether a square transformation is needed for the standard deviation parameter. |
... |
additional arguments. |
Simulate data from a dynamic zero-inflated model.
dzim.sim(X, w, omega, k, beta, phi, sigma, mu0, Sigma0)dzim.sim(X, w, omega, k, beta, phi, sigma, mu0, Sigma0)
X |
design matrix. |
w |
|
omega |
zero-inflation parameter. |
k |
dispersion parameter. |
beta |
regression coefficients. |
phi |
autoregressive coefficients. |
sigma |
standard deviation. |
mu0 |
mean vector of initial state. |
Sigma0 |
covariance matrix of initial state. |
dzim,
dzim.fit,
dzim.filter,
dzim.smooth,
dzim.control,
dzim.plot
Function to implement the particle smoothing method proposed by Gordsill et al. (2004).
dzim.smooth(y, X, w, para, control)dzim.smooth(y, X, w, para, control)
y |
response variable. |
X |
design matrix. |
w |
|
para |
model parameters. |
control |
control arguments. |
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.
dzim,
dzim.fit,
dzim.filter,
dzim.control,
dzim.sim,
dzim.plot
Monthly number of injuries in hospitals from July 1988 to October 1995.
Numbers from Figure 1 of Yau et al. (2004).
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.
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)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 based on a t-statistic.
pvalue(t, df = Inf, alternative = c("two.sided", "less", "greater"))pvalue(t, df = Inf, alternative = c("two.sided", "less", "greater"))
t |
t-statistic. |
df |
degree of freedoms. |
alternative |
type of alternatives. |
pvalue(1.96, alternative = "greater")pvalue(1.96, alternative = "greater")
Weekly number of syphilis cases in the United States from 2007 to 2010.
A data frame with 209 observations on the following 69 variables.
year |
Year |
week |
Week |
a1 |
United States |
a2 |
New England |
a3 |
Connecticut |
a4 |
Maine |
a5 |
Massachusetts |
a6 |
New Hampshire |
a7 |
Rhode Island |
a8 |
Vermont |
a9 |
Mid. Atlantic |
a10 |
New Jersey |
a11 |
New York (Upstate) |
a12 |
New York City |
a13 |
Pennsylvania |
a14 |
E.N. Central |
a15 |
Illinois |
a16 |
Indiana |
a17 |
Michigan |
a18 |
Ohio |
a19 |
Wisconsin |
a20 |
W.N. Central |
a21 |
Iowa |
a22 |
Kansas |
a23 |
Minnesota |
a24 |
Missouri |
a25 |
Nebraska |
a26 |
North Dakota |
a27 |
South Dakota |
a28 |
S. Atlantic |
a29 |
Delaware |
a30 |
District of Columbia |
a31 |
Florida |
a32 |
Georgia |
a33 |
Maryland |
a34 |
North Carolina |
a35 |
South Carolina |
a36 |
Virginia |
a37 |
West Virginia |
a38 |
E.S. Central |
a39 |
Alabama |
a40 |
Kentucky |
a41 |
Mississippi |
a42 |
Tennessee |
a43 |
W.S. Central |
a44 |
Arkansas |
a45 |
Louisana |
a46 |
Oklahoma |
a47 |
Texas |
a48 |
Moutain |
a49 |
Arizona |
a50 |
Colorado |
a51 |
Idaho |
a52 |
Montana |
a53 |
Nevada |
a54 |
New Mexico |
a55 |
Utah |
a56 |
Wyoming |
a57 |
Pacific |
a58 |
Alaska |
a59 |
California |
a60 |
Hawaii |
a61 |
Oregon |
a62 |
Washington |
a63 |
American Samoa |
a64 |
C.N.M.I. |
a65 |
Guam |
a66 |
Peurto Rico |
a67 |
U.S. Virgin Islands |
C.N.M.I.: Commonwealth of Northern Mariana Islands.
CDC Morbidity and Mortality Weekly Report (http://www.cdc.gov/MMWR/).
data(syph) plot(ts(syph$a33), ylab = "Count", main = "Maryland", las = 1)data(syph) plot(ts(syph$a33), ylab = "Count", main = "Maryland", las = 1)
zim is used to fit zero-inflated models.
zim(formula, data, subset, na.action, weights = 1, offset = 0, control = zim.control(...), ...)zim(formula, data, subset, na.action, weights = 1, offset = 0, control = zim.control(...), ...)
formula |
an objective of class " |
data |
an optional dataframe, list or environment containing the variables in the model. |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
na.action |
a function which indicates what should happen when the data contain |
weights |
an optional vector of 'prior weights' to be used in the fitting process. |
offset |
this can be used to specify a priori known component to be included in the linear predictor during fitting. |
control |
control arguments. |
... |
additional arguments. |
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.
Auxiliary function for zim fitting. Typically only used internally by
zim.fit, but may be used to construct a control argument for either function.
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)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)
dist |
count model family. |
method |
algorithm for parameter estimation. |
type |
type of matrix inverse. |
robust |
logical; if TRUE, robust standard errors will be calculated. |
trace |
logical; if TRUE, display iteration history. |
start |
initial parameter values. |
minit |
minimum number of iterations. |
maxit |
maximum number of iterations. |
epsilon |
positive convergence tolerance. |
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.
zim.fit(y, X, Z, weights = rep(1, nobs), offset = rep(0, nobs), control = zim.control(...), ...)zim.fit(y, X, Z, weights = rep(1, nobs), offset = rep(0, nobs), control = zim.control(...), ...)
y |
response variable. |
X |
design matrix for log-linear part. |
Z |
design matrix for logistic part. |
weights |
an optional vector of 'prior weights' to be used in the fitting process. |
offset |
offset variable |
control |
control arguments from |
... |
additional argumetns. |
Density, distribution function, quantile function and random generation for the zero-inflated
negative binomial (ZINB) distribution with parameters k, lambda, and omega.
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)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)
x, q
|
vector of quantiles. |
p |
vector of probabilities. |
n |
number of random values to return. |
k |
dispersion parameter. |
lambda |
vector of (non-negative) means. |
omega |
zero-inflation parameter. |
log, log.p
|
logical; if TRUE, probabilities |
lower.tail |
logical; if TRUE (default), probabilities are |
dzinb gives the density, pzinb gives the distribution function,
qzinb gives the quantile function, and rzinb generates random deviates.
dzip, pzip, qzip, and rzip
for the zero-inflated Poisson (ZIP) distribution.
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)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)
Density, distribution function, quantile function and random generation for the
zero-inflated Poisson (ZIP) distribution with parameters lambda and omega.
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)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)
x, q
|
vector of quantiles. |
p |
vector of probabilities. |
n |
number of random values to return. |
lambda |
vector of (non-negative) means. |
omega |
zero-inflation parameter. |
log, log.p
|
logical; if TRUE, probabilities |
lower.tail |
logical; if TRUE (default), probabilities are |
dzip gives the density, pzip gives the distribution function,
qzip gives the quantile function, and rzip generates random deviates.
dzinb, pzinb, qzinb, and rzinb
for the zero-inflated negative binomial (ZINB) distribution.
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)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)