R/difference-smooths.R

In gratia: Graceful 'ggplot'-Based Graphics and Other Functions for GAMs Fitted Using 'mgcv'

#' Differences of factor smooth interactions
#'
#' Estimates pairwise differences (comparisons) between factor smooth
#' interactions (smooths with a factor `by` argument) for pairs of groups
#' defined by the factor. The group means can be optionally included in the
#' difference.
#'
#' @param model A fitted model.
#' @param smooth character; which smooth to compute differences for.
#' @param n numeric; the number of points at which to evaluate the difference
#'   between pairs of smooths.
#' @param ci_level numeric between 0 and 1; the coverage of credible interval.
#' @param data data frame of locations at which to evaluate the difference
#'   between smooths.
#' @param group_means logical; should the group means be included in the
#'   difference?
#' @param partial_match logical; should `smooth` match partially against
#'   `smooths`? If `partial_match = TRUE`, `smooth` must only be a single
#'   string, a character vector of length 1. Unlike similar functions, the
#'   default here is `TRUE` because the intention is that users will be matching
#'   against factor-by smooth labels.
#' @param unconditional logical; account for smoothness selection in the model?
#' @param frequentist logical; use the frequentist covariance matrix?
#' @param ... arguments passed to other methods. Not currently used.
#'
#' @export
#' @examples
#'
#' load_mgcv()
#' \dontshow{
#' op <- options(pillar.sigfig = 3, cli.unicode = FALSE)
#' }
#' df <- data_sim("eg4", seed = 42)
#' m <- gam(y ~ fac + s(x2, by = fac) + s(x0), data = df, method = "REML")
#'
#' sm_dif <- difference_smooths(m, smooth = "s(x2)")
#' sm_dif
#'
#' draw(sm_dif)
#'
#' # include the groups means for `fac` in the difference
#' sm_dif2 <- difference_smooths(m, smooth = "s(x2)", group_means = TRUE)
#' draw(sm_dif2)
#' \dontshow{options(op)}
`difference_smooths` <- function(model, ...) {
    UseMethod("difference_smooths")
}

#' @export
#'
#' @importFrom purrr pmap
#' @importFrom dplyr bind_rows
#' @importFrom tibble add_column as_tibble
#' @importFrom stats qnorm coef
#' @importFrom utils combn
#'
#' @rdname difference_smooths
`difference_smooths.gam` <- function(model,
                                     smooth,
                                     n = 100,
                                     ci_level = 0.95,
                                     data = NULL,
                                     group_means = FALSE,
                                     partial_match = TRUE,
                                     unconditional = FALSE,
                                     frequentist = FALSE,
                                     ...) {
    if (missing(smooth)) {
        stop("Must specify a smooth to difference via 'smooth'.")
    }

    # smooths in model
    S <- smooths(model) # vector of smooth labels - "s(x)"
    # select smooths
    select <-
        check_user_select_smooths(smooths = S, select = smooth,
                                  partial_match = partial_match,
                                  model_name = expr_label(substitute(object)))
    sm_ids <- which(select)
    smooths <- get_smooths_by_id(model, sm_ids)
    if (is.null(data)) {
        sm_data <- map(sm_ids, smooth_data,
                       model = model, n = n, include_all = TRUE)
        data <- bind_rows(sm_data)
    } else {
        data <- as_tibble(data)
    }
    by_var <- by_variable(smooths[[1L]])
    smooth_var <- smooth_variable(smooths[[1L]])
    pairs <- as_tibble(as.data.frame(t(combn(levels(data[[by_var]]), 2)),
                                     stringsAsFactor = FALSE))
    names(pairs) <- paste0("f", 1:2)

    Xp <- predict(model, newdata = data, type = "lpmatrix")
    V <- get_vcov(model, unconditional = unconditional,
                  frequentist = frequentist)
    coefs <- coef(model)

    out <- pmap(pairs, calc_difference, smooth = smooth, by_var = by_var,
                smooth_var = smooth_var, data = data, Xp = Xp, V = V,
                coefs = coefs, group_means = group_means)
    out <- bind_rows(out)
    crit <- coverage_normal(ci_level)
    out <- add_column(out,
                      lower = out$diff - (crit * out$se),
                      upper = out$diff + (crit * out$se),
                      .after = 6L)
    out
}

#' @export
`difference_smooths.bam` <- function(model, ...) {
    NextMethod()
}

#' @export
`difference_smooths.gamm` <- function(model, ...) {
    difference_smooths(model[["gam"]], ...)
}

#' @export
`difference_smooths.list` <- function(model, ...) {
    if (! is_gamm4(model)) {
        stop("'object' is not a `gamm4()` fit. Can't handle general lists.")
    }
    difference_smooths(model$gam, ...)
}

#' @importFrom tibble new_tibble
#' @importFrom dplyr bind_cols
`calc_difference` <- function(f1, f2, smooth, by_var, smooth_var, data, Xp, V,
                              coefs, group_means = FALSE) {
    ## make sure f1 and f2 are characters
    f1 <-  as.character(f1)
    f2 <-  as.character(f2)
    cnames <- colnames(Xp)

    # what are we keeping?
    keep <- if (isTRUE(group_means)) {
        # columns of Xp associated with pair of smooths, including parametric
        # terms for the group means
        c1 <- grepl(paste0(by_var, f1), cnames, fixed = TRUE)
        c2 <- grepl(paste0(by_var, f2), cnames, fixed = TRUE)
        # set the intercept to be included
        c0 <- grepl("(Intercept)", cnames, fixed = TRUE)
        (c0 | c1 | c2)
    } else {
        # columns of Xp associated with pair of smooths, but not
        c1 <- grepl(mgcv_by_smooth_labels(smooth, by_var, f1), cnames,
                    fixed = TRUE)
        c2 <- grepl(mgcv_by_smooth_labels(smooth, by_var, f2), cnames,
            fixed = TRUE)
        (c1 | c2)
    }

    ## rows of Xp associated with pair of smooths
    r1 <- data[[by_var]] == f1
    r2 <- data[[by_var]] == f2

    ## difference rows of Xp for pair of smooths
    X <- Xp[r1, ] - Xp[r2, ]

    ## zero the cols related to other splines and covariates
    X[, ! keep] <- 0

    ## compute difference
    sm_diff <- drop(X %*% coefs)
    se <- sqrt(rowSums((X %*% V) * X))
    nr <- NROW(X)
    out <- list(smooth = rep(smooth, nr), by = rep(by_var, nr),
                level_1 = rep(f1, nr),
                level_2 = rep(f2, nr),
                diff = sm_diff, se = se)
    out <- new_tibble(out, nrow = NROW(X), class = "difference_smooth")
    ## Only need rows associated with one of the levels
    out <- bind_cols(out, data[r1, smooth_var])

    out
}