distribution_metrics: Distribution Metrics

In certe-medical-epidemiology/certestats: A Certe R Package for Statistical Modelling

Distribution Metrics

Description

These are simple distribution metric functions.

Usage

se(x, na.rm = getOption("na.rm", FALSE))

ci(x, level = 0.95, na.rm = getOption("na.rm", FALSE))

sum_of_squares(x, correct_mean = TRUE, na.rm = getOption("na.rm", FALSE))

cv(x, na.rm = getOption("na.rm", FALSE))

cqv(x, na.rm = getOption("na.rm", FALSE))

mse(actual, predicted, na.rm = getOption("na.rm", FALSE))

mape(actual, predicted, na.rm = getOption("na.rm", FALSE))

rmse(actual, predicted, na.rm = getOption("na.rm", FALSE))

mae(actual, predicted, na.rm = getOption("na.rm", FALSE))

z_score(x, na.rm = getOption("na.rm", FALSE))

midhinge(x, na.rm = getOption("na.rm", FALSE))

ewma(x, lambda, na.rm = getOption("na.rm", FALSE))

rr_ewma(x, lambda, na.rm = getOption("na.rm", FALSE))

normalise(n, n_ref, per = 1000)

normalize(n, n_ref, per = 1000)

scale_sd(x)

centre_mean(x)

percentiles(x, na.rm = getOption("na.rm", FALSE))

deciles(x, na.rm = getOption("na.rm", FALSE))

Arguments

x	values
na.rm	a logical to indicate whether empty must be removed from x
level	alpha level, defaults to 95%
correct_mean	with TRUE (the default) correct for the mean will be applied, by summing each square of x after the mean of x has been subtracted, so that this says something about x. With FALSE, all x^2 are simply added together, so this says something about x's location in the data.
actual	Vector of actual values
predicted	Vector of predicted values
lambda	smoothing parameter, a value between 0 and 1. A value of 0 is equal to x, a value of 1 equal to the mean of x. The EWMA looks back and has a delay - the rrEWMA takes the mean of a 'forward' and 'backward' EWMA.
n	number to be normalised
n_ref	reference to use for normalisation
per	normalisation factor

Details

These are the explanations of the functions:

• se() calculates the standard error: sd / square root of length

• ci() calculates the confidence intervals for a mean (defaults at 95%), which returns length 2

• sum_of_squares() calculates the sum of (x - mean(x)) ^ 2

• cv() calculates the coefficient of variation: standard deviation / mean

• cqv() calculates the coefficient of quartile variation: (Q3 - Q1) / (Q3 + Q1)

• mse() calculates the mean squared error

• mape() calculates the mean absolute percentage error

• rmse() calculates the root mean squared error

• mae() calculates the mean absolute error

• z_score() calculates the number of standard deviations from the mean: (x - mean) / sd

• midhinge() calculates the mean of interquartile range: (Q1 + Q3) / 2

• ewma() calculates the EWMA (exponentially weighted moving average)

• rr_ewma() calculates the rrEWMA (reversed-recombined exponentially weighted moving average)

• normalise() normalises the data based on a reference: (n / reference) * unit

• scale_sd() normalises the data to have a standard deviation of 1, while retaining the mean

• centre_mean() normalises the data to have a mean of 0, while retaining the standard deviation

• percentiles() and deciles() take a numeric vector as input, and return the lowest percentiles or deciles for each value

Default values of na.rm

This 'certestats' package supports a global default setting for na.rm in many mathematical functions. This can be set with options(na.rm = TRUE) or options(na.rm = FALSE).

For normality(), quantile() and IQR(), this also applies to the type argument. The default, type = 7, is the default of base R. Use type = 6 to comply with SPSS.

See Also

For the sum of squares: https://www.thoughtco.com/sum-of-squares-formula-shortcut-3126266

Examples

x <- c(0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 6)
percentiles(x)
deciles(x)

percentiles(rnorm(10))

library(dplyr, warn.conflicts = FALSE)
tib <- as_tibble(matrix(as.integer(runif(40, min = 1, max = 7)), ncol = 4),
                 .name_repair = function(...) LETTERS[1:4])
tib

# percentiles per column
tib |> mutate_all(percentiles)

certe-medical-epidemiology/certestats documentation built on Nov. 9, 2024, 8:15 p.m.