fbase1.geometric.logit {RegressionFactory}

Single-Parameter Base Log-likelihood Function for Exponential GLM

Description

Vectorized, single-parameter base log-likelihood functions for geometric GLM using logit link function. The base function(s) can be supplied to the expander function regfac.expand.1par in order to obtain the full, high-dimensional log-likleihood and its derivatives.

Usage

fbase1.geometric.logit(u, y, fgh=2)

Arguments

u

Varying parameter of the base log-likelihood function. This parameter is intended to be projected onto a high-dimensional space using the familiar regression transformation of u <- X%*%beta. In the typical use-case where the caller is regfac.expand.1par, a vector of values are supplied, and return objects will have the same length as u.

y

Fixed slot of the base distribution, corresponding to the response variable in the regression model. For Geometric family, it must be a vector of non-negative integers.

fgh

Integer with possible values 0,1,2. If fgh=0, the function only calculates and returns the log-likelihood vector and no derivatives. If fgh=1, it returns the log-likelihood and its first derivative in a list. If fgh=2, it returns the log-likelihood, as well as its first and second derivatives in a list.

Value

If fgh==0, the function returns -(y*u+(1+y)*log(1+exp(-u))) for log. If fgh==1, a list is returned with elements f and g, where the latter is a vector of length length(u), with each element being the first derivative of the above expressions. If fgh==2, the list will include an element named h, consisting of the second derivatives of f with respect to u.

Note

The logit function must be applied to the probability parameter to give X%*%beta, which is in turn the inverse of the mean of the geometric distribution. For brevity, we still call the link function 'logit'.

Author(s)

Alireza S. Mahani, Mansour T.A. Sharabiani

See Also

regfac.expand.1par

Examples

## Not run: 
library(sns)
library(MfUSampler)

# using the expander framework and base distributions to define
# log-likelihood function for geometric regression
loglike.geometric <- function(beta, X, y, fgh) {
  regfac.expand.1par(beta, X, y, fbase1.geometric.logit, fgh)
}

# generate data for geometric regression
N <- 1000
K <- 5
X <- matrix(runif(N*K, min=-0.5, max=+0.5), ncol=K)
beta <- runif(K, min=-0.5, max=+0.5)
y <- rgeom(N, prob = 1/(1+exp(-X%*%beta)))

# mcmc sampling of log-likelihood
nsmp <- 100

# Slice Sampler
beta.smp <- array(NA, dim=c(nsmp,K)) 
beta.tmp <- rep(0,K)
for (n in 1:nsmp) {
  beta.tmp <- MfU.Sample(beta.tmp
    , f=loglike.geometric, X=X, y=y, fgh=0)
  beta.smp[n,] <- beta.tmp
}
beta.slice <- colMeans(beta.smp[(nsmp/2+1):nsmp,])

# Adaptive Rejection Sampler
beta.smp <- array(NA, dim=c(nsmp,K)) 
beta.tmp <- rep(0,K)
for (n in 1:nsmp) {
  beta.tmp <- MfU.Sample(beta.tmp, uni.sampler="ars"
   , f=function(beta, X, y, grad) {
     if (grad)
       loglike.geometric(beta, X, y, fgh=1)$g
     else
       loglike.geometric(beta, X, y, fgh=0)
   }
   , X=X, y=y)
  beta.smp[n,] <- beta.tmp
}
beta.ars <- colMeans(beta.smp[(nsmp/2+1):nsmp,])

# SNS (Stochastic Newton Sampler)
beta.smp <- array(NA, dim=c(nsmp,K)) 
beta.tmp <- rep(0,K)
for (n in 1:nsmp) {
  beta.tmp <- sns(beta.tmp, fghEval=loglike.geometric, X=X, y=y, fgh=2, rnd = n>nsmp/4)
  beta.smp[n,] <- beta.tmp
}
beta.sns <- colMeans(beta.smp[(nsmp/2+1):nsmp,])

# compare sample averages with actual values
cbind(beta, beta.sns, beta.slice, beta.ars)

## End(Not run)