maximize_spline_metric {cutpointr}

Optimize a metric function in binary classification after spline smoothing

Description

Given a function for computing a metric in metric_func, this function smoothes the function of metric value per cutpoint using smoothing splines. Then it optimizes the metric by selecting an optimal cutpoint. For further details on the smoothing spline see ?stats::smooth.spline. The metric function should accept the following inputs:

• tp: vector of number of true positives

• fp: vector of number of false positives

• tn: vector of number of true negatives

• fn: vector of number of false negatives

Usage

maximize_spline_metric(
  data,
  x,
  class,
  metric_func = youden,
  pos_class = NULL,
  neg_class = NULL,
  direction,
  w = NULL,
  df = NULL,
  spar = 1,
  nknots = cutpoint_knots,
  df_offset = NULL,
  penalty = 1,
  control_spar = list(),
  tol_metric,
  use_midpoints,
  ...
)

minimize_spline_metric(
  data,
  x,
  class,
  metric_func = youden,
  pos_class = NULL,
  neg_class = NULL,
  direction,
  w = NULL,
  df = NULL,
  spar = 1,
  nknots = cutpoint_knots,
  df_offset = NULL,
  penalty = 1,
  control_spar = list(),
  tol_metric,
  use_midpoints,
  ...
)

Arguments

data

A data frame or tibble in which the columns that are given in x and class can be found.

x

(character) The variable name to be used for classification, e.g. predictions or test values.

class

(character) The variable name indicating class membership.

metric_func

(function) A function that computes a metric to be optimized. See description.

pos_class

The value of class that indicates the positive class.

neg_class

The value of class that indicates the negative class.

direction

(character) Use ">=" or "<=" to select whether an x value >= or <= the cutoff predicts the positive class.

w

Optional vector of weights of the same length as x; defaults to all 1.

df

The desired equivalent number of degrees of freedom (trace of the smoother matrix). Must be in (1,nx], nx the number of unique x values.

spar

Smoothing parameter, typically (but not necessarily) in (0,1]. When spar is specified, the coefficient lambda of the integral of the squared second derivative in the fit (penalized log likelihood) criterion is a monotone function of spar.

nknots

Integer or function giving the number of knots. The function should accept data and x (the name of the predictor variable) as inputs. By default nknots = 0.1 * log(n_dat / n_cut) * n_cut where n_dat is the number of observations and n_cut the number of unique predictor values.

df_offset

Allows the degrees of freedom to be increased by df_offset in the GCV criterion.

penalty

The coefficient of the penalty for degrees of freedom in the GCV criterion.

control_spar

Optional list with named components controlling the root finding when the smoothing parameter spar is computed, i.e., NULL. See help("smooth.spline") for further information.

tol_metric

All cutpoints will be returned that lead to a metric value in the interval [m_max - tol_metric, m_max + tol_metric] where m_max is the maximum achievable metric value. This can be used to return multiple decent cutpoints and to avoid floating-point problems.

use_midpoints

(logical) If TRUE (default FALSE) the returned optimal cutpoint will be the mean of the optimal cutpoint and the next highest observation (for direction = ">") or the next lowest observation (for direction = "<") which avoids biasing the optimal cutpoint.

...

Further arguments that will be passed to metric_func.

Details

The above inputs are arrived at by using all unique values in x, Inf, and -Inf as possible cutpoints for classifying the variable in class.

Value

A tibble with the columns optimal_cutpoint, the corresponding metric value and roc_curve, a nested tibble that includes all possible cutoffs and the corresponding numbers of true and false positives / negatives and all corresponding metric values.

See Also

Other method functions: maximize_boot_metric(), maximize_gam_metric(), maximize_loess_metric(), maximize_metric(), oc_manual(), oc_mean(), oc_median(), oc_youden_kernel(), oc_youden_normal()

Examples

oc <- cutpointr(suicide, dsi, suicide, gender, method = maximize_spline_metric,
df = 5, metric = accuracy)
plot_metric(oc)