# Bootstrap for msel function Function `bootstrap_msel` provides bootstrap estimates of the parameters of the model estimated via the `msel` function. Function `bootstrap_combine_msel` allows to combine several objects of class `'bootstrap_msel'`. ```r bootstrap_msel( object, iter = 100, opt_type = "optim", opt_args = NULL, is_ind = FALSE, n_sim = 1000, n_cores = 1 ) bootstrap_combine_msel(...) ``` ## Arguments - `object`: an object of class 'msel'. - `iter`: the number of bootstrap iterations. - `opt_type`: the same as `opt_type` argument of the `msel` function. - `opt_args`: the same as `opt_args` argument of the `msel` functions. - `is_ind`: logical; if `TRUE` then the function also returns a numeric matrix of indexes of observations used in the bootstrap samples. - `n_sim`: the same as `n_sim` argument of the `msel` function. - `n_cores`: the same as `n_cores` argument of the `msel` function. - `...`: objects returned by function `bootstrap_msel` to be combined into a single object. ## Returns Function `bootstrap_msel` returns an object of class `"bootstrap_msel"`. This object is a list which may contain the following elements: * `par` - a numeric matrix such that `par[b, ]` is a vector of the estimates of the parameters of the model estimated via `msel` function on the `b`-th bootstrap sample. * `iter` - the number of the bootstrap iterations. * `cov` - bootstrap estimate of the covariance matrix which equals to `cov(par)`. * `ind` - a numeric matrix such that `ind[, b]` stores the indexes of the observations from `object$data` included into the `b`-th bootstrap sample. Function `bootstrap_combine_msel` returns the object which combines several objects returned by the `bootstrap_msel` function into a single object. ## Details The function generates `iter` bootstrap samples and estimates the parameters $\theta$ of the model by using each of these samples. Estimate $\hat{\theta}^{(b)}$ from the $b$-th of these samples is stored as the `b`-th row of the numeric matrix `par` which is an element of the returned object. Use `update_msel` function to transfer the bootstrap estimates to the object of class `'msel'`. ## Examples ```r # ------------------------------- # Bootstrap for the probit model # ------------------------------- # --- # Step 1 # Simulation of data # --- # Load required package library("mnorm") # Set seed for reproducibility set.seed(123) # The number of observations n <- 100 # Regressors (covariates) w1 <- runif(n = n, min = -1, max = 1) w2 <- runif(n = n, min = -1, max = 1) # Random errors u <- rnorm(n = n, mean = 0, sd = 1) # Coefficients gamma <- c(-1, 2) # Linear index li <- gamma[1] * w1 + gamma[2] * w2 # Latent variable z_star <- li + u # Cuts cuts <- c(-1, 0.5, 2) # Observable ordered outcome z <- rep(0, n) z[(z_star > cuts[1]) & (z_star <= cuts[2])] <- 1 z[(z_star > cuts[2]) & (z_star <= cuts[3])] <- 2 z[z_star > cuts[3]] <- 3 table(z) # Data data <- data.frame(w1 = w1, w2 = w2, z = z) # --- # Step 2 # Estimation of the parameters # --- # Estimation model <- msel(formula = z ~ w1 + w2, data = data) summary(model) # --- # Step 3 # Bootstrap # --- # Perform bootstrap bootstrap <- bootstrap_msel(model) # Test the hypothesis that H0: gamma[2] = -2gamma[1] # by using the t-test and with bootstrap p-values fn_test <- function(object) { gamma <- coef(object, eq = 1) return(gamma[2] + 2 * gamma[1]) } b <- test_msel(object = model, fn = fn_test, test = "t", method = "bootstrap", ci = "percentile", se_type = "bootstrap", bootstrap = bootstrap) summary(b) # Replicate the analysis with the additional 20 bootstrap iterations bootstrap2 <- bootstrap_msel(model, iter = 20) bootstrap_new <- bootstrap_combine_msel(bootstrap, bootstrap2) b2 <- test_msel(object = model, fn = fn_test, test = "t", method = "bootstrap", ci = "percentile", se_type = "bootstrap", bootstrap = bootstrap) summary(b2) ```

bootstrap function