zic.reg {bizicount}

Univariate zero-inflated Poisson and negative binomial regression models

Description

This function from the bizicount package estimates univariate zero-inflated Poisson and negative binomial regression models via maximum likelihood using either the nlm or optim optimization functions. It's class has associated simulate methods for post-estimation diagnostics using the DHARMa package, as well as an extract method for printing professional tables using texreg. Visit the 'See Also' section for links to these methods for zicreg objects.

Usage

zic.reg(
  fmla = NULL,
  data,
  dist = "pois",
  link.ct = "log",
  link.zi = "logit",
  optimizer = "nlm",
  starts = NULL,
  subset,
  na.action,
  weights = rep(1, length(y)),
  X = NULL,
  z = NULL,
  y = NULL,
  offset.ct = NULL,
  offset.zi = NULL,
  warn.parent = T,
  keep = F,
  ...
)

Arguments

fmla

A formula of the form ⁠y ~ x_1 + x_2 + ... + x_n + offset(count_var) | z_1 + ... z_n + offset(zi_var)⁠, where the x values are covariates in the count portion of the model, and z are in the zero-inflation portion. The z and x variables can be the same. If NULL, design matrices, the response vector, and offsets can be entered directly; see X, z, y, offset.ct, and offset.zi below.

data

A data.frame containing all variables appearing in fmla, including offsets. If not specified, variables are searched for in parent environment.

dist

The distribution used for the count portion of the zero-inflated mixture. One of c("pois", "nbinom"), partial matching supported.

link.ct

String specifying the link function used for the count portion of the mixture distribution. One of c("log", "identity", "sqrt"). See family.

link.zi

Character string specifying the link function used for the zero-inflation portion of the mixture distribution. One of c("logit", "probit", "cauchit", "log", "cloglog"). See family.

optimizer

String specifying the optimizer to be used for fitting, one of c("nlm", "optim"). If "optim", defaults to method="BFGS".

starts

Optional vector of starting values used for the numerical optimization procedure. Should have count parameters first (with intercept first, if applicable), followed by zero-inflated parameters (with intercept first, if applicable), and the inverse dispersion parameter last (if applicable).

subset

Vector indicating the subset of observations on which to estimate the model

na.action

A function which indicates what should happen when the data contain NAs. Default is na.omit.

weights

An optional numeric vector of weights for each observation.

X, z

If fmla = NULL, these are the design matrices of covariates for the count and zero-inflation portions, respectively. Both require no missingness. Similar in spirit to glm.fit in that it can be faster for larger datasets because it bypasses model matrix creation.

y

If fmla = NULL, a vector containing the response variable.

offset.ct, offset.zi

If fmla = NULL, vectors containing the (constant) offset for the count and zero-inflated portions, respectively. Must be equal in length to y, and row-dim of X, z. If left NULL, defaults to rep(0, length(y)).

warn.parent

Logical indicating whether to warn about data not being supplied.

keep

Logical indicating whether to keep the model matrices in the returned model object. Must be TRUE to use DHARMa and texreg with the model object, e.g., via simulate.zicreg and extract.zicreg, as well as base generics like fitted and predict.

...

Additional arguments to pass on to the chosen optimizer, either nlm or optim. See 'Examples'.

Value

An S3 zicreg-class object, which is a list containing:

• call – The original function call

• obj – The class of the object

• coef – Vector of coefficients, with count, then zi, then dispersion.

• se – Vector of asymptotic standard errors

• grad – Gradient vector at convergence

• link.ct – Name of link used for count portion

• link.zi – Name of link used for zero-inflated portion

• dist – Name of distribution used for count portion

• optimizer – Name of optimization package used in fitting

• coefmat.ct – Coefficient matrix for count portion

• coefmat.zi – Coefficient matrix for zero-inflated portion

• convergence – Convergence code from optimization routine.

• coefmat.all – Coefficient matrix for both parts of the model

• theta – Coefficient matrix for dispersion, if applicable.

• covmat – Asymptotic covariance matrix

• nobs – Number of observations

• aic – Akaike information

• bic – Bayes information

• loglik – Log-likelihood at convergence

• model – List containing model matrices if keep = TRUE

Author(s)

John Niehaus

References

Lambert, Diane. "Zero-inflated Poisson regression, with an application to defects in manufacturing." Technometrics 34.1 (1992): 1-14.

See Also

simulate.zicreg, extract.zicreg

Examples

## ZIP example
# Simulate some zip data
n=1000
x = cbind(1, rnorm(n))
z = cbind(1, rbeta(n, 4, 8))
b = c(1, 2.2)
g = c(-1, 1.7)
lam = exp(x %*% b)
psi = plogis(z %*% g)

y = bizicount::rzip(n, lambda = lam, psi=psi)
dat = cbind.data.frame(x = x[,-1], z = z[,-1], y = y)

# estimate zip model using NLM, no data.frame

mod = zic.reg(y ~ x[,-1] | z[,-1])

# same model, with dataframe

mod = zic.reg(y ~ x | z, data = dat)


# estimate zip using NLM, adjust stepmax via ... param

mod = zic.reg(y ~ x[,-1] | z[,-1], stepmax = .5)


# estimate zip using optim

mod = zic.reg(y ~ x[,-1] | z[,-1], optimizer = "optim")


# pass different method, reltol to optim using ... param

mod = zic.reg(y ~ x[,-1] | z[,-1],
        optimizer = "optim",
        method = "Nelder-Mead",
        control = list(reltol = 1e-10)
        )

# No formula, specify design matrices and offsets.
zic.reg(y=y, X=x, z=z)



## ZINB example
# simulate zinb data

disp = .5
y = bizicount::rzinb(n, psi = psi, size = disp, mu=lam)


# zinb model, use keep = TRUE for post-estimation methods

mod = zic.reg(y ~ x[,-1] | z[,-1], dist = "n", keep = TRUE)

print(mod)
summary(mod)