# Fitting Binary Regression with a Skew-Probit Link Function This function fits a binary regression with a skew-probit link function. Naive MLE, Jeffrey's prior and Cauchy prior type of penalization are implemented to find estimates. ```r skewProbit(formula, data = list(), penalty = "Jeffrey", initial = NULL, cvtCov = TRUE, delta0 = 3, level = 0.95) ``` ## Arguments - `formula`: an object of class "formula" as in `lm`, `glm` - `data`: an optional data frame, list or environment containing the variables in the model as in `lm`, `glm` - `penalty`: type of penalty function. Default option is "Jeffrey". "Cauchy" will give estimates with Cauchy prior penaly function. "Naive" will give ML estimates. - `initial`: a logical value. If specified, it will be used for the initial value of numerical optimization. - `cvtCov`: a logical value. If it is true, then all numerical values will be standardized to have mean zero and unit standard deviation. - `delta0`: an initial guess of skewness parameter. - `level`: a confidence level. Default value is 0.95. ## Details This function uses `ucminf` package for optimization. Also package `sn` is necessary. A detailed disscussion can be found in the reference below. ## Returns An object of class `skewProbit` is returned with - **coefficients**: A named vector of coefficients - **stderr**: Standard errors of coefficients - **zscore**: Z-scores of coefficients - **pval**: p-values of coefficients - **lower**: Lower limits of confidence intervals - **upper**: Upper limits of confidence intervals ## References Identifiability and bias reduction in the skew-probit model for a binary response. **To appear in Journal of Statistical Computation and Simulation**. ## Author(s) DongHyuk Lee, Samiran Sinha ## Examples ```r library(sn) library(ucminf) n <- 500 b0 <- 0.34 delta <- 4 b1 <- 1 b2 <- -0.7 set.seed(1234) x1 <- runif(n, -2, 2) x2 <- rnorm(n, sd = sqrt(4/3)) eta <- as.numeric(b0 + b1*x1 + b2*x2) p <- psn(eta, alpha = delta) y <- rbinom(n, 1, p) ## Not run: dat <- data.frame(y, x1 = x1, x2 = x2) mod1 <- skewProbit(y ~ x1 + x2, data = dat, penalty = "Jeffrey", cvtCov = FALSE, level = 0.95) mod2 <- skewProbit(y ~ x1 + x2, data = dat, penalty = "Naive", cvtCov = FALSE, level = 0.95) mod3 <- skewProbit(y ~ x1 + x2, data = dat, penalty = "Cauchy", cvtCov = FALSE, level = 0.95) summary(mod1) summary(mod2) summary(mod3) ## End(Not run) ```

skewProbit function