# Two-Lines Test of U-Shapes Implements the two-lines test for U-shaped (or inverted U-shaped) relationships introduced by Simonsohn (2018). ```r twolines( f, graph = 1, link = "gaussian", data = NULL, pngfile = "", quiet = FALSE ) ``` ## Arguments - `f`: A formula object specifying the model (e.g., y ~ x1 + x2 + x3). The first predictor is the one tested for a u-shaped relationship. - `graph`: Integer. If 1 (default), produces a plot. If 0, no plot is generated. - `link`: Character string specifying the link function for the GAM model. Default is "gaussian". - `data`: An optional data frame containing the variables in the formula. If not provided, variables are evaluated from the calling environment. - `pngfile`: Optional character string. If provided, saves the plot to a PNG file with the specified filename. - `quiet`: Logical. If TRUE, suppresses the Robin Hood details messages. Default is FALSE. ## Returns A list containing: * All elements from `reg2()`: `b1`, `b2`, `p1`, `p2`, `z1`, `z2`, `u.sig`, `xc`, `glm1`, `glm2`, `rob1`, `rob2`, `msg`, `yhat.smooth` * `yobs`: Observed y values (adjusted for covariates if present) * `y.hat`: Fitted values from GAM * `y.ub`, `y.lb`: Upper and lower bounds for fitted values * `y.most`: Most extreme fitted value * `x.most`: x-value associated with most extreme fitted value * `f`: Formula as character string * `bx1`, `bx2`: Linear and quadratic coefficients from preliminary quadratic regression * `minx`: Minimum x value * `midflat`: Median of flat region * `midz1`, `midz2`: Z-statistics at midpoint ## Details Reference: Simonsohn, Uri (2018) "Two lines: A valid alternative to the invalid testing of U-shaped relationships with quadratic regressions." AMPPS, 538-555. tools:::Rd_expr_doi("10.1177/2515245918805755") The test beings fitting a GAM model, predicting y with a smooth of x, and optionally with covariates. It identifies the interior most extreme value of fitted y, and adjusts from the matching x-value to set the breakpoint relying on the Robin Hood procedure introduced also by Simonsohn (2018). It then estimates the (once) interrupted regression using that breakpoint, and reports the slope and significance of the average slopes at either side of it. A U-shape is significant if the slopes are of opposite sign and are both individually significant. ## Examples ```r # Simple example with simulated data set.seed(123) x <- rnorm(100) y <- -x^2 + rnorm(100) data <- data.frame(x = x, y = y) result <- twolines(y ~ x, data = data) # With covariates z <- rnorm(100) y <- -x^2 + 0.5*z + rnorm(100) data <- data.frame(x = x, y = y, z = z) result <- twolines(y ~ x + z, data = data) # Without data argument (variables evaluated from environment) x <- rnorm(100) y <- -x^2 + rnorm(100) result <- twolines(y ~ x) ```

twolines function