# Bootstraps the Stepwise Algorithm of stepAIC() for Choosing a Model by AIC Implements a Bootstrap procedure to investigate the variability of model selection under the stepAIC() stepwise algorithm of package MASS. ```r boot.stepAIC(object, data, B = 100, alpha = 0.05, direction = "backward", k = 2, verbose = FALSE, seed = 1L, ...) ``` ## Arguments - `object`: an object representing a model of an appropriate class; currently, `"lm"`, `"aov"`, `"glm"`, `"negbin"`, `"polr"`, `"survreg"`, and `"coxph"` objects are supported. - `data`: a `data.frame` or a `matrix` that contains the response variable and covariates. - `B`: the number of Bootstrap samples. - `alpha`: the significance level. - `direction`: the `direction` argument of `stepAIC()`. - `k`: the `k` argument of `stepAIC()`. - `verbose`: logical; if `TRUE` information about the evolution of the procedure is printed in the screen. - `seed`: numeric scalar denoting the seed used to create the Bootstrap samples. - ``...``: extra arguments to `stepAIC()`, e.g., `scope`. ## Details The following procedure is replicated `B` times: - **Step 1:**: Simulate a new data-set taking a sample with replacement from the rows of `data`. - **Step 2:**: Refit the model using the data-set from Step 1. - **Step 3:**: For the refitted model of Step 2 run the `stepAIC()` algorithm. Summarize the results by counting how many times (out of the `B` data-sets) each variable was selected, how many times the estimate of the regression coefficient of each variable (out of the times it was selected) it was statistically significant in significance level `alpha`, and how many times the estimate of the regression coefficient of each variable (out of the times it was selected) changed signs (see also Austin and Tu, 2004). ## Returns An object of class `BootStep` with components - **Covariates**: a numeric matrix containing the percentage of times each variable was selected. - **Sign**: a numeric matrix containing the percentage of times the regression coefficient of each variable had sign $+$ and $-$. - **Significance**: a numeric matrix containing the percentage of times the regression coefficient of each variable was significant under the `alpha` significance level. - **OrigModel**: a copy of `object`. - **OrigStepAIC**: the result of applying `stepAIC()` in `object`. - **direction**: a copy of the `direction` argument. - **k**: a copy of the `k` argument. - **BootStepAIC**: a list of length `B` containing the results of `stepAIC()` for each Bootstrap data-set. ## References Austin, P. and Tu, J. (2004). Bootstrap methods for developing predictive models, **The American Statistician**, 58 , 131--137. Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S, 4th ed. Springer, New York. ## Author(s) Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl ## See Also `stepAIC` in package MASS ## Examples ```r ## lm() Example ## n <- 350 x1 <- runif(n, -4, 4) x2 <- runif(n, -4, 4) x3 <- runif(n, -4, 4) x4 <- runif(n, -4, 4) x5 <- runif(n, -4, 4) x6 <- runif(n, -4, 4) x7 <- factor(sample(letters[1:3], n, rep = TRUE)) y <- 5 + 3 * x1 + 2 * x2 - 1.5 * x3 - 0.8 * x4 + rnorm(n, sd = 2.5) data <- data.frame(y, x1, x2, x3, x4, x5, x6, x7) rm(n, x1, x2, x3, x4, x5, x6, x7, y) lmFit <- lm(y ~ (. - x7) * x7, data = data) boot.stepAIC(lmFit, data) ##################################################################### ## glm() Example ## n <- 200 x1 <- runif(n, -3, 3) x2 <- runif(n, -3, 3) x3 <- runif(n, -3, 3) x4 <- runif(n, -3, 3) x5 <- factor(sample(letters[1:2], n, rep = TRUE)) eta <- 0.1 + 1.6 * x1 - 2.5 * as.numeric(as.character(x5) == levels(x5)[1]) y1 <- rbinom(n, 1, plogis(eta)) y2 <- rbinom(n, 1, 0.6) data <- data.frame(y1, y2, x1, x2, x3, x4, x5) rm(n, x1, x2, x3, x4, x5, eta, y1, y2) glmFit1 <- glm(y1 ~ x1 + x2 + x3 + x4 + x5, family = binomial(), data = data) glmFit2 <- glm(y2 ~ x1 + x2 + x3 + x4 + x5, family = binomial(), data = data) boot.stepAIC(glmFit1, data, B = 50) boot.stepAIC(glmFit2, data, B = 50) ```

boot.stepAIC function