AMAZonn: A Multicollinearity-adjusted Adaptive LASSO for Zero-inflated...

In himelmallick/AMAZonn: A Multicollinearity-adjusted Adaptive LASSO for Zero-inflated Count Regression

Description

A Multicollinearity-adjusted Adaptive LASSO for Zero-inflated Count Regression fits zero-inflated regression models for count data via penalized maximum likelihood.

Usage

AMAZonn(formula, data, weights, subset = NULL, na.action = na.omit,
  offset = NULL, standardize = TRUE, family = c("poisson", "negbin",
  "geometric"), link = c("logit", "probit", "cloglog", "cauchit", "log"),
  control = zeroinfl.control(...), penalty = c("enet", "mnet", "snet"),
  start = NULL, model = TRUE, y = TRUE, x = FALSE, nlambda = 100,
  lambda.count = NULL, lambda.zero = NULL, penalty.factor.count = NULL,
  penalty.factor.zero = NULL, lambda.count.min.ratio = 1e-04,
  lambda.zero.min.ratio = 0.1, alpha.count = 1, alpha.zero = alpha.count,
  gamma.count = 3, gamma.zero = gamma.count, rescale = FALSE, init.theta,
  theta.fixed = FALSE, EM = TRUE, maxit.em = 200, convtype = c("count",
  "both"), maxit = 1000, maxit.theta = 1, reltol = 1e-05,
  eps.bino = 1e-05, shortlist = FALSE, trace = FALSE)

Arguments

formula	symbolic description of the model, see details.
data, subset, na.action	arguments controlling formula processing via model.frame.
weights	optional numeric vector of weights.
offset	optional numeric vector with an a priori known component to be included in the linear predictor of the count model. See below for more information on offsets.
standardize	Logical flag for x variable standardization, prior to fitting the model sequence. The coefficients are always returned on the original scale. Default is standardize=TRUE.
family	character specification of count model family (a log link is always used).
link	character specification of link function in the binary zero-inflation model (a binomial family is always used).
control	a list of control arguments specified via zeroinfl.control.
penalty	penalty considered as one of enet, mnet, snet.
start	starting values for the parameters in the linear predictor.
model, y, x	logicals. If TRUE the corresponding components of the fit (model frame, response, model matrix) are returned.
nlambda	number of lambda value, default value is 100. The sequence may be truncated before nlambda is reached if a close to saturated model for the zero component is fitted.
lambda.count	A user supplied lambda.count sequence. Typical usage is to have the program compute its own lambda.count and lambda.zero sequence based on nlambda and lambda.min.ratio.
lambda.zero	A user supplied lambda.zero sequence.
penalty.factor.count, penalty.factor.zero	These are numeric vectors with the same length as predictor variables. that multiply lambda.count,lambda.zero, respectively, to allow differential shrinkage of coefficients. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in the model. Default is same shrinkage for all variables.
lambda.count.min.ratio, lambda.zero.min.ratio	Smallest value for lambda.count and lambda.zero, respectively, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero except the intercepts). Note, there is a closed formula for lambda.max for penalty="enet". If rescale=TRUE, lambda.max is the same for penalty="mnet" or "snet". Otherwise, some modifications are required. In the current implementation, for small gamma value, the square root of the computed lambda.zero[1] is used when penalty="mnet" or "snet".
alpha.count	The elastic net mixing parameter for the count part of model.
alpha.zero	The elastic net mixing parameter for the zero part of model.
gamma.count	The tuning parameter of the snet or mnet penalty for the count part of model.
gamma.zero	The tuning parameter of the snet or mnet penalty for the zero part of model.
rescale	logical value, if TRUE, adaptive rescaling
init.theta	The initial value of theta for family="negbin".
theta.fixed	Logical value only used for family="negbin". If TRUE, theta is not updated.
EM	Using EM algorithm. Not implemented otherwise
maxit.em	Maximum number of EM algorithm
convtype	convergency type, default is for count component only for speedy computation
maxit	Maximum number of coordinate descent algorithm
maxit.theta	Maximum number of iterations for estimating theta scaling parameter if family=" negbin". Default value maxit.theta may be increased, yet may slow the algorithm
reltol	Convergence criteria, default value 1e-5 may be reduced to make more accurate yet slow
eps.bino	a lower bound of probabilities to be claimed as zero, for computing weights and related values when family="binomial".
shortlist	logical value, if TRUE, limited results return
trace	If TRUE, progress of algorithm is reported

Details

The algorithm fits penalized zero-inflated count data regression models using the coordinate descent algorithm within the EM algorithm. The returned fitted model object is of class "AMAZonn" and is similar to fitted "glm" and "zeroinfl" objects. For elements such as "coefficients" a list is returned with elements for the zero and count component, respectively.

Value

The function AMAZonn returns a list of following components

coefficients	a list with elements "count" and "zero" containing the coefficients from the respective models,
residuals	a vector of raw residuals (observed - fitted),
fitted.values	a vector of fitted means,
weights	the case weights used,
terms	a list with elements "count", "zero" and "full" containing the terms objects for the respective models,
theta	estimate of the additional θ parameter of the negative binomial model (if a negative binomial regression is used),
loglik	log-likelihood of the fitted model,
family	character string describing the count distribution used,
link	character string describing the link of the zero-inflation model,
linkinv	the inverse link function corresponding to link,
converged	logical value, TRUE indicating successful convergence of AMAZonn, FALSE indicating otherwise
call	the original function call
formula	the original formula
levels	levels of the categorical regressors
contrasts	a list with elements "count" and "zero" containing the contrasts corresponding to levels from the respective models,
model	the full model frame (if model = TRUE),
y	the response count vector (if y = TRUE),
x	a list with elements "count" and "zero" containing the model matrices fromthe respective models (if x = TRUE),

Examples

data("docvisits", package = "zic")
## with simple inflation (no regressors for zero component)
Zonn_zip <- AMAZonn(docvisits ~ . | ., data = docvisits, family = "poisson", nlambda = 10)
summary(Zonn_zip)
Zonn_zinb <- AMAZonn(docvisits ~ . | ., data = docvisits, family = "negbin", nlambda=10)
summary(Zonn_zinb)

himelmallick/AMAZonn documentation built on July 24, 2019, 2:39 a.m.