ModProb: Logarithm of unnormalized probability of a given model

Description

This function calculates the logarithm of unnormalized probability of a given set of covariates for both survival and binary response data. It uses the inverse moment nonlocal prior (iMOM) for non zero coefficients and beta binomial prior for the model space.

Usage

ModProb(
  X,
  resp,
  mod_cols,
  nlptype = "piMOM",
  tau,
  r,
  a,
  b,
  family = c("logistic", "survival")
)

Arguments

The design matrix. It is assumed that the design matrix has standardized columns. It is recommended that to use the output of PreProcess function of the package.

resp

For logistic regression models, this variable is the binary response vector. For Cox proportional hazard models this is a two column matrix where the first column contains the survival time vector and the second column is the censoring status for each observation.

mod_cols

A vector of column indices of the design matrix, representing the model.

nlptype

Determines the type of nonlocal prior that is used in the analyses. It can be "piMOM" for product inverse moment prior, or "pMOM" for product moment prior. The default is set to piMOM prior.

tau

Hyperparameter tau of the iMOM prior.

Hyperparameter r of the iMOM prior.

First parameter in the beta binomial prior.

Second parameter in the beta binomial prior.

family

Determines the type of data analysis. logistic is for binary outcome and logistic regression model whereas, survival represents survival outcomes and the Cox proportional hazard model.

Value

It returns the unnormalized probability for the selected model.

References

Nikooienejad, A., Wang, W., and Johnson, V. E. (2016). Bayesian variable selection for binary outcomes in high dimensional genomic studies using nonlocal priors. Bioinformatics, 32(9), 1338-1345. Nikooienejad, A., Wang, W., & Johnson, V. E. (2020). Bayesian variable selection for survival data using inverse moment priors. Annals of Applied Statistics, 14(2), 809-828.

Examples

Run this code

# NOT RUN {
### Simulating Logistic Regression Data
n <- 400
p <- 1000
set.seed(123)
Sigma <- diag(p)
full <- matrix(c(rep(0.5, p*p)), ncol=p)
Sigma <- full + 0.5*Sigma
cholS <- chol(Sigma)
Beta <- c(1,1.8,2.5)
X = matrix(rnorm(n*p), ncol=p)
X = X%*%cholS
beta <- numeric(p)
beta[c(1:length(Beta))] <- Beta
XB <- X%*%beta
probs <- as.vector(exp(XB)/(1+exp(XB)))
y <- rbinom(n,1,probs)

### Calling the function for a subset of the true model, with an arbitrary
### parameters for prior densities
mod <- c(1:3)
Mprob <- ModProb(X, y, mod, tau = 0.7, r = 1, a = 7, b = 993,
                 family = "logistic")

Mprob
# }