ZIPExt {ZIPBayes}

Zero-inflated Poisson model under measurement error and external validation data are available

Description

The function implements the MCMC algorithm with data augmentation to estimate the parameters in the zero-inflated Poisson model while correcting for the measurement error arising from the responses. The function returns the trace of the sampled parameters in each interaction. To obtain the summary estimation, use summary().

Usage

ZIPExt (Ystar, Covarmainphi, Covarmainmu, Covarplus, Covarminus,
           Ystarval, Yval, Covarvalplus, Covarvalminus,
           betaphi, betamu, alphaplus, alphaminus,
           Uibound = c(7,11),
           priorgamma, priormu, priorSigma, 
           propsigmaphi,  propsigmamu = propsigmaphi, 
           propsigmaplus = propsigmaphi, propsigmaminus = propsigmaphi,
           seed = 1, nmcmc = 500)

Arguments

Ystar

a count vector of length n specifying the error-prone response in the zero-inflated Poisson model.

Covarmainphi

a n \times p_1 dimensional data.frame or matrix of the covariate data with respect to the probability component of the zero-inflated Poisson model

Covarmainmu

a n \times p_2 dimensional data.frame or matrix of the covariate data with respect to the mean component of the zero-inflated Poisson model

Covarplus

a n \times q_1 dimensional data.frame or matrix of the covariate data for the measurement error model of the add-in error process

Covarminus

a n \times q_2 dimensional data.frame or matrix of the covariate data for the measurement error model of the leave-out error process

Ystarval

a count vector of length m specifying the error-prone response in the validation data.

Yval

a count vector of length m specifying the precisely measured response in the validation data.

Covarvalplus

a m \times q_1 dimensional data.frame or matrix of the covariate for validation data of the add-in error process

Covarvalminus

a m \times q_2 dimensional data.frame or matrix of the covariate for validation data of the leave-out error process

betaphi

a vector of length p_1 specifying the initial values of the parameters in the probability component of the zero-inflated Poisson model

betamu

a vector of length p_2 specifying the initial values of the parameters in the probability component of the zero-inflated Poisson model

alphaplus

a vector of length q_1 specifying the initial values of the parameters for the measurement error model of the add-in error process

alphaminus

a vector of length q_2 specifying the initial values of the parameters in the probability component of the leave-out error process

Uibound

a vector of length 2 specifying the maximum number of the count in the inverse sampling method

priorgamma

a vector of length 2 specifying the two parameters of gamma prior

priormu

a vector of length q_2 specifying the mean vector of the normal prior for the measurement error model of the leave-out error process

priorSigma

a vector of length q_2 specifying the standard erros of the normal prior for the measurement error model of the leave-out error process

propsigmaphi

a vector of length p_1 specifying the standard error of the Gaussian proposal distribution for the parameters corresponds to the probability component.

propsigmamu

a vector of length p_2 specifying the standard error of the Gaussian proposal distribution for the parameters corresponds to the mean component.

propsigmaplus

a vector of length q_1 specifying the standard error of the Gaussian proposal distribution for the parameters corresponds to the add-in error process.

propsigmaminus

a vector of length q_1 specifying the standard error of the Gaussian proposal distribution for the parameters corresponds to the leave-out error process.

seed

a numeric value specifying the seed for random generator

nmcmc

a integer specify the number of the generation of MCMC algorithm

Details

Comparing to the ZIPMErr function, this function has an addition component – validation data. Here, the argument “Ystarval”, “Yval”, “Covarvalplus”, “Covarvalminus”, are new for the sceanrio with external validation.

Value

BayesResults

the list of trace of generated parameters for each component of the models. Data frame “betaphi_trace” corresponds to the probability component of ZIP response model; “betamu_trace” refers to the mean component of the ZIP response model. Data frames “alphaplus_trace” and “alphaminus_trace”, respectively, correspond to the add-in error and leave-out error process in the measruement error model.

Author(s)

Qihuang Zhang and Grace Y. Yi

References

Zhang, Qihuang. “Inference Methods for Noisy Correlated Responses with Measurement Error.” (2020).

See Also

glm

Examples

## load data
data(datasimExt)
set.seed(0)
example_ZIP_Ext <-  ZIPExt (Ystar = datasimExt$main$Ystar,
                            Covarmainphi = datasimExt$main[,c("intercept","X1")],
                            Covarmainmu = datasimExt$main[,c("intercept","X2")],
                            Covarplus = datasimExt$main[,c("intercept","Zplus")],
                            Covarminus = datasimExt$main[,c("intercept","Zminus")],
                            Ystarval = datasimExt$validation$Ystar, 
                            Yval = datasimExt$validation$Y,
                            Covarvalplus = datasimExt$validation[,3:4],
                            Covarvalminus = datasimExt$validation[,3:4],
                            betaphi = c(0.7,-0.7), betamu = c(1,-1.5), 
                            alphaplus = c(0,0), alphaminus=c(0,0),
                            priorgamma = c(0.001,0.001), priormu = c(0,0),
                            priorSigma = c(1,1), propsigmaphi = c(0.05,0.05), 
                            nmcmc = 10) 

summary(example_ZIP_Ext)