# Spatial scale least angle regression (LARS) This function fits a spatial scale (SS) LARS model. ```r lars.ss(y, X, ss, a.lst, S.v, C.v, col.plot, verbose=TRUE, plot=TRUE) ``` ## Arguments - `y`: A numeric response vector - `X`: A data frame of numeric variables - `ss`: A vector of names to identify the different levels of covariates available as potential candidates for model input - `a.lst`: A list of identity matrices, where each column indicates a particular level or spatial scale for a specified covariate (e.g., ss1_x2) - `S.v`: A vector of positive integers, where each number denotes the number of spatial scales associated with a particular covariate - `C.v`: A vector, where all values are initialized to 0 - `col.plot`: A vector of colors (corresponding to each SS) used in the coefficient path plot - `verbose`: If TRUE, details are printed as the algorithm progresses - `plot`: If TRUE, a coefficient path plot is generated ## Details This function estimates coefficients using the SS LARS modeling approach. The function also provides summary details and plots a coefficient path plot. ## Returns A list with the following items: - **beta**: Regression coefficient estimates from all set of model solutions - **beta.aic**: Regression coefficient estimates from final model - **ind.v**: Vector of indices to denote the corresponding columns of X associated with each active predictor - **aic.v**: Vector of Akaike information criterion (AIC) values - **stack.ss**: Vector of indices to indicate the level at which each covariate enters the model ## References Grant LP, Gennings C, Wheeler, DC. (2015). Selecting spatial scale of covariates in regression models of environmental exposures. Cancer Informatics, 14(S2), 81-96. doi: 10.4137/CIN.S17302 ## Author(s) Lauren Grant, David Wheeler ## Examples ```r data(y) data(X) names.X <- colnames(X) ss <- c("ind", "ss1", "ss2") a.lst <- list(NULL) a.lst[[1]] <- 1 dim(a.lst[[1]]) <- c(1,1) dimnames(a.lst[[1]]) <- list(NULL, names.X[1]) a.lst[[2]] <- diag(2) dimnames(a.lst[[2]]) <- list(NULL, names.X[c(2,3)]) a.lst[[3]] <- diag(2) dimnames(a.lst[[3]]) <- list(NULL, names.X[c(4,5)]) S.v <- c(1,2,2) C.v <- rep(0,length(a.lst)) mod_LARS.ss <- lars.ss(y, X, ss, a.lst, S.v, C.v, c("black", "red", "green")) ```

lars.ss function