# Sequential Bifurcations `sb` implements the Sequential Bifurcations screening method (Bettonvil and Kleijnen 1996). ```r sb(p, sign = rep("+", p), interaction = FALSE) ## S3 method for class 'sb' ask(x, i = NULL, ...) ## S3 method for class 'sb' tell(x, y, ...) ## S3 method for class 'sb' print(x, ...) ## S3 method for class 'sb' plot(x, ...) ``` ## Arguments - `p`: number of factors. - `sign`: a vector fo length `p` filled with `"+"` and `"-"`, giving the (assumed) signs of the factors effects. - `interaction`: a boolean, `TRUE` if the model is supposed to be with interactions, `FALSE` otherwise. - `x`: a list of class `"sb"` storing the state of the screening study at the current iteration. - `y`: a vector of model responses. - `i`: an integer, used to force a wanted bifurcation instead of that proposed by the algorithm. - ``...``: not used. ## Details The model without interaction is $$ Y=\beta_0 + \sum_{i=1}^p \beta_i X_iY = beta_0 + sum_{i=1}^p beta_i X_i $$ while the model with interactions is $$ Y=\beta_0 + \sum_{i=1}^p \beta_i X_i + \sum_{1 \leq i < j \leqp} \gamma_{ij} X_i X_jY = beta_0 + sum_{i=1}^p beta_i X_i + sum_{1 <= i < j <= p} gamma_{ij} X_i X_j $$ In both cases, the factors are assumed to be uniformly distributed on $[-1,1]$. This is a difference with Bettonvil et al. where the factors vary across $[0,1]$ in the former case, while $[-1,1]$ in the latter. Another difference with Bettonvil et al. is that in the current implementation, the groups are splitted right in the middle. ## Returns `sb` returns a list of class `"sb"`, containing all the input arguments detailed before, plus the following components: - **i**: the vector of bifurcations. - **y**: the vector of observations. - **ym**: the vector of mirror observations (model with interactions only). The groups effects can be displayed with the `print` method. ## References B. Bettonvil and J. P. C. Kleijnen, 1996, **Searching for important factors in simulation models with many factors: sequential bifurcations**, European Journal of Operational Research, 96, 180--194. ## Author(s) Gilles Pujol ## Examples ```r # a model with interactions p <- 50 beta <- numeric(length = p) beta[1:5] <- runif(n = 5, min = 10, max = 50) beta[6:p] <- runif(n = p - 5, min = 0, max = 0.3) beta <- sample(beta) gamma <- matrix(data = runif(n = p^2, min = 0, max = 0.1), nrow = p, ncol = p) gamma[lower.tri(gamma, diag = TRUE)] <- 0 gamma[1,2] <- 5 gamma[5,9] <- 12 f <- function(x) { return(sum(x * beta) + (x %*% gamma %*% x))} # 10 iterations of SB sa <- sb(p, interaction = TRUE) for (i in 1 : 10) { x <- ask(sa) y <- list() for (i in names(x)) { y[[i]] <- f(x[[i]]) } tell(sa, y) } print(sa) plot(sa) ```

sb function