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| #' Use a Lagrange multiplier (score) test to compare nested GEE models. | ||
| #' | ||
| #' @name scoreTestGEE | ||
| #' @author Jack R. Leary | ||
| #' @description Performs a basic Lagrange multiplier test to determine whether an alternate model is significantly better than a nested null model. This is the GEE equivalent (kind of) of \code{\link{modelLRT}}. Be careful with small sample sizes. | ||
| #' @importFrom stats model.matrix predict pchisq | ||
| #' @param mod.1 The model under the alternative hypothesis. Must be of class \code{geem}. Defaults to NULL. | ||
| #' @param mod.0 The model under the null hypothesis. Must be of class \code{geem}. Defaults to NULL. | ||
| #' @param alt.df The dataframe used to fit the alternative model. Defaults to NULL. | ||
| #' @param null.df The dataframe used to fit the null model. Defaults to NULL. | ||
| #' @param sandwich.var Boolean specifying whether the sandwich variance-covariance matrix should be used. Defaults to FALSE. | ||
| #' @return A list containing the Score test statistic, a \emph{p}-value, and the degrees of freedom used in the test. | ||
| #' @details | ||
| #' \itemize{ | ||
| #' \item Calculating the test statistic involves taking the inverse of the variance-covariance matrix of the coefficients. Ideally this would be done using the "true" inverse with something like \code{\link{solve}}, \code{\link{qr.solve}}, or \code{\link{chol2inv}}, but in practice this can cause issues when the variance-covariance matrix is near-singular. With this in mind, we use the Moore-Penrose pseudoinverse as implemented in \code{\link[MASS]{ginv}} instead, which leads to more stable results. | ||
| #' \item The \emph{p}-value is calculated using an asymptotic \eqn{\Chi^2} distribution, with the degrees of freedom equal to the number of non-intercept coefficients in the alternative model. | ||
| #' } | ||
| #' @seealso \code{\link[geeM]{geem}} | ||
| #' @seealso \code{\link{waldTestGEE}} | ||
| #' @seealso \code{\link{modelLRT}} | ||
|
|
||
| scoreTestGEE <- function(mod.1 = NULL, | ||
| mod.0 = NULL, | ||
| alt.df = NULL, | ||
| null.df = NULL, | ||
| sandwich.var = FALSE) { | ||
| # check inputs | ||
| if (is.null(mod.1) || is.null(mod.0) || is.null(alt.df) || is.null(null.df)) { stop("Please provide all inputs to scoreTestGEE().") } | ||
| if (inherits(mod.1, "try-error") || inherits(mod.0, "try-error")) { | ||
| res <- list(Score_Stat = NA_real_, | ||
| DF = NA_real_, | ||
| P_Val = NA_real_, | ||
| Notes = "No test performed due to model failure.") | ||
| return(res) | ||
| } | ||
| mod.1 <- mod.1$final_mod | ||
| if (!(inherits(mod.1, "geem") && inherits(mod.0, "geem"))) { stop("You must provide two geeM models to scoreTestGee().") } | ||
| if (length(coef(mod.0)) != 1) { stop("Null GEE model must be intercept-only.") } | ||
| if (length(coef(mod.1)) <= length(coef(mod.0))) { | ||
| # can't calculate Score statistic if both models are intercept-only | ||
| res <- list(Score_Stat = 0, | ||
| DF = 0, | ||
| P_Val = 1, | ||
| Notes = NA_character_) | ||
| } else { | ||
| X_null <- stats::model.matrix(mod.0, data = null.df) | ||
| X_alt <- stats::model.matrix(mod.1, data = alt.df) | ||
| residuals_null <- null.df$Y - exp(stats::predict(mod.0)) | ||
| if (sandwich.var) { | ||
| V_null <- as.matrix(mod.0$var) | ||
| } else { | ||
| V_null <- as.matrix(mod.0$naiv.var) | ||
| } | ||
| X_alt_t <- t(X_alt) | ||
| U <- X_alt_t %*% residuals_null | ||
| V_U <- (X_alt_t * as.numeric(V_null)) %*% X_alt | ||
| V_U_inv <- try({ eigenMapMatrixInvert(V_U) }, silent = TRUE) | ||
| if (inherits(V_U_inv, "try-error")) { | ||
| V_U_inv <- eigenMapPseudoInverse(V_U) | ||
| } | ||
| test_stat <- as.numeric(t(U) %*% V_U_inv %*% U) | ||
| df1 <- ncol(X_alt) - ncol(X_null) | ||
| p_value <- 1 - stats::pchisq(test_stat, df = df1) | ||
| res <- list(Score_Stat = test_stat, | ||
| DF = df1, | ||
| P_Val = p_value, | ||
| Notes = NA_character_) | ||
| } | ||
| return(res) | ||
| } |
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