BayesCslogistic: Perform a Bayesian Analysis of a conditionally specified logistic regression model

Description

This function generates a posterior density sample from a conditionally specified logistic regression model for multivariate binary data using a random walk Metropolis algorithm. The user supplies data and priors, and a sample from the posterior density is returned as a object, which can be subsequently analyzed with functions provided in the coda package.

Usage

BayesCslogistic(formula, type = TRUE, intercept = TRUE, 
           burnin = 1000, mcmc = 10000, thin=1, 
           tune=1.1, beta.start = NA, b0 = 0, B0 = 0, ...)

Arguments

formula

Model formula.

type

logical variable indicating if covariates have the same effect 'TRUE' or different effect 'FALSE' for each variable.

intercept

logical variable indicating if only the intercept 'TRUE' or all the covariates have different effect 'FALSE' for each variable. The option 'type' must be 'FALSE'.

burnin

The number of burn-in iterations for the sampler.

mcmc

The number of Metropolis iterations for the sampler.

thin

The thinning interval used in the simulation. The number of mcmc iterations must be divisible by this value.

tune

Metropolis tuning parameter. Make sure that the acceptance rate is satisfactory (typically between 0.20 and 0.5) before using the posterior density sample for inference.

beta.start

The starting value for the $\beta$ vector. This can either be a scalar or a column vector with dimension equal to the number of betas. If this takes a scalar value, then that value will serve as the starting value for all of the betas. The

The prior mean of $\beta$. This can either be a scalar or a column vector with dimension equal to the number of betas. If this takes a scalar value, then that value will serve as the prior mean for all of the betas.

The prior precision of $\beta$. This can either be a scalar or a square matrix with dimensions equal to the number of betas. If this takes a scalar value, then that value times an identity matrix serves as the prior precision of $\beta$.

...

further arguments to be passed.

Value

An mcmc object that contains the posterior density sample. This object can be summarized by functions provided by the coda package.

References

Garcia-Zattera, M. J., Jara, A., Lesaffre, E. and Declerck, D. (2007). Conditional independence of multivariate binary data with an application in caries research. Computational Statistics and Data Analysis, 51(6): 3223-3232.

Joe, H. and Liu, Y. (1996). A model for multivariate response with covariates based on compatible conditionally specified logistic regressions. Satistics & Probability Letters 31: 113-120.

Examples

Run this code

# simulated data set

  library(mvtnorm)

  n <- 400
  mu1 <- c(-1.5,-0.5)
  Sigma1 <- matrix(c(1, -0.175,-0.175,1),ncol=2)
  agev <- as.vector(sample(seq(5,6,0.1),n,replace=TRUE))
  beta1 <- 0.2

  z <- rmvnorm(n,mu1,Sigma1)
  zz <- cbind(z[,1]+beta1*agev,z[,2]+beta1*agev)
  dat <- cbind(zz[,1]>0,zz[,2]>0,agev)
  colnames(dat) <- c("y1","y2","age")
  data0 <- data.frame(dat)
  attach(data0)

# equal effect of age for all the covariates

  y <- cbind(y1,y2)

  fit0 <- BayesCslogistic(y~age)
  fit0
  summary(fit0)
  plot(fit0)

# different effects: only intercept

  fit1 <- BayesCslogistic(y~age,type=FALSE)
  fit1
  summary(fit1)
  plot(fit1)

# different effects: all the covariates 

  fit2 <- BayesCslogistic(y~age,type=FALSE,intercept=FALSE)
  fit2
  summary(fit2)
  plot(fit2)