# p-value computation for XWFs Randomization method to compute p-values for an optimized extrema-weighted features generalized additive model fit. ```r XWFpValues(GAMobject, xx, t, n.i, psi.list = NULL, F, z = NULL, w = function(t, i, b, left) ifelse(left, min(1, (1 - F(xx[[i]](t)))/(1 - b)), min(1, F(xx[[i]](t))/b)), n.boot = 100, progressbar = TRUE) ``` ## Arguments - `GAMobject`: The GAMobject returned by `xwfGridsearch` - `xx`: List of function for which to compute the XWFs - `t`: Matrix containing the times at which the functions xx were measured: Element (i,j) contains the time of the j-th measurement of the i-th function. - `n.i`: Vector containing the number of measurements for each function. The first n.i[i] elements of the i-th row of t should not be NA. - `psi.list`: List of predefined local features which are functions of a function (first argument) and a measurement time (second argument) - `F`: CDF of the values of the functions xx. Ignored if weighting function w is not the default. - `z`: Optional matrix with covariates to be included as linear predictors in the generalized additive model - `w`: Weighting function. The default is the one used in the original paper. See the default for what the roles of its 3 arguments are. - `n.boot`: Number for randomizations used to obtain the p-values. The resolution of the p-values is 1/n.boot - `progressbar`: Boolean specifying whether a progress bar indicating which randomizations have been completed should be displayed. ## Returns Named vector with p-values ## Examples ```r # Data simulation similar to Section 3.2 of the paper # Sample size n <- 100 # Length of trajectories n.i <- rep(5, n) max.n.i <- max(n.i) # Times t <- matrix(NA_integer_, nrow = n, ncol = max.n.i) for(i in 1:n) t[i, 1:n.i[i]] <- 1:n.i[i] # Sample periods phi <- runif(n = n, min = 1, max = 10) # Sample offsets m <- 10*runif(n = n) # Blood pressure measurements x <- t for(i in 1:n) x[i, 1:n.i[i]] <- sin(phi[i] * 2*pi/max.n.i * t[i, 1:n.i[i]]) + m[i] # Matrix with covariates z q <- 2 # Number of covariates z <- matrix(rnorm(n = n*q), nrow = n, ncol = q) # Generate outcomes temp <- phi*min(m, 7) temp <- 40*temp prob <- 1/(1+exp( 2*( median(temp)-temp ) )) y <- rbinom(n = n, size = 1, prob = prob) xx <- list() for(i in 1:n) xx[[i]] <- approxfun(x = t[i,1:n.i[i]], y = x[i,1:n.i[i]], rule = 2) # Estimate f weights <- matrix(1/n.i, ncol = max.n.i, nrow = n)[!is.na(t)] f <- density( x = t(sapply(X = 1:n, FUN = function(i) c(xx[[i]](t[i,1:n.i[i]]), rep(NA, max.n.i-n.i[i])))), weights = weights/sum(weights), na.rm = T ) # Define CDF of f, F CDF <- c(0) for(i in 2:length(f$x)) CDF[i] <- CDF[i-1]+(f$x[i]-f$x[i-1])*(f$y[i]+f$y[i-1])/2 F <- approxfun(x = f$x, y = CDF/max(CDF), yleft = 0, yright = 1) psi <- list( function(x, t) abs(x(t)-x(t-1)) ) XWFresult <- xwfGridsearch(y = y, xx = xx, t = t, n.i = n.i, psi.list = psi, F = F, z = z) XWFpValues( GAMobject = XWFresult$GAMobject, xx = xx, t = t, n.i = n.i, psi.list = psi, F = F, z = z, n.boot = 3 ) ```

XWFpValues function