# Coefficient estimation for a specific set of covariates This function estimates coefficient vector for a given set of covariates in a logistic regression and Cox proportional hazard models. It uses the inverse moment nonlocal prior (iMOM) for non zero coefficients. ```r CoefEst( X, resp, mod_cols, nlptype = "piMOM", tau, r, family = c("logistic", "survival") ) ``` ## Arguments - `X`: The design matrix. It is assumed that the preprocessing steps have been done on this matrix. It is recommended that to use the output of `PreProcess` function of the package. Also note that the `X` should NOT have a vector of $1$'s as the first column. If the coefficients of a selected model by `bvs` is to be estimated, it is highly recommended that the design matrix that is one of the outputs of the `bvs` function and is reported as `des_mat` to be used here. - `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 selected 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. - `r`: Hyperparameter `r` of the iMOM 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. ## Returns It returns the vector of coefficients for the given model. ## Examples ```r ### Simulating Survival Data n <- 400 p <- 1000 lambda <- 0.8 cens_rate <- 0.27 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(-1.8, 1.2, -1.7, 1.4, -1.4, 1.3) X = matrix(rnorm(n*p), ncol=p) X = X%*%cholS X <- scale(X) beta <- numeric(p) beta[c(1:length(Beta))] <- Beta XB <- X%*%beta uvector <- -log(runif(n)); times <- uvector/(lambda*exp(XB)) cens_time <- quantile(times,1-cens_rate) status <- as.numeric(times < cens_time) TS <- cbind(times,status) ### Estimating coeffcients of the true model and an arbitrary hyper ### parameter for the iMOM prior density mod <- c(1:6) coef <- CoefEst(X, TS, mod, tau = 1.8, r = 2, family = "survival") coef ``` ## References Nikooienejad, A., Wang, W., and Johnson, V. E. (2016). Bayesian variable selection for binary outcomes in high dimensional genomic studies using non-local 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. ## See Also `ModProb` ## Author(s) Amir Nikooienejad

CoefEst function