| Title: | Hot Spots |
|---|---|
| Description: | The hotspots package is designed to look within a set of measured values of a variable and identify values that are disproportionately high based on both the deviance of any given value from a statistical distribution and its similarity to other values. Because this relative magnitude of each value is taken into account, a value that is a statistical outlier may not always be a hot spot if other values are similarly large. |
| Authors: | Anthony Darrouzet-Nardi |
| Maintainer: | Anthony Darrouzet-Nardi <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0.3 |
| Built: | 2024-11-25 03:22:33 UTC |
| Source: | https://github.com/cran/hotspots |
Calculates the magnitude of disproportionality for values within a dataset.
disprop(z)disprop(z)
z |
|
Calculates the magnitude of disproportionality for each value within the data by dividing
the difference between each value and the median by the difference between the hot spot cutoff,
(Ch, as calculated by the function hotspots), and the median:
disproportionality = (x - med(x)) / (Ch - med(x))
Using this equation, all hot spots have a magnitude of disproportionality of > 1. Increasingly skewed distributions (for example, lognormal distributions with higher standard deviation) will have higher magnitudes of disproportionality for some of their values.
A list containing the objects positive, negative, or both, depending on the which tails were
calculated in the hotspots object. These objects are numeric vectors of the magnitudes of disproportionality.
NA values are preserved.
Anthony Darrouzet-Nardi
rln30 <- sort(c(rlnorm(15),rlnorm(15)*-1,NA), na.last = TRUE) rln30 disprop(hotspots(rln30, tail = "both")) #higher levels of disproportionality rln30sd2 <- sort(c(rlnorm(15,sd = 3),rlnorm(15,sd = 3)*-1,NA), na.last = TRUE) rln30sd2 disprop(hotspots(rln30sd2, tail = "both"))rln30 <- sort(c(rlnorm(15),rlnorm(15)*-1,NA), na.last = TRUE) rln30 disprop(hotspots(rln30, tail = "both")) #higher levels of disproportionality rln30sd2 <- sort(c(rlnorm(15,sd = 3),rlnorm(15,sd = 3)*-1,NA), na.last = TRUE) rln30sd2 disprop(hotspots(rln30sd2, tail = "both"))
Calculates a hot spot or outlier cutoff for a statistical population based on deviance from the normal or t distribution. In the case of the hot spot cutoff, the relative magnitude of the values is also taken into account to determine if values are disproportionately large relative to other values. Thus, a value that is a statistical outlier may not always be a hot spot if other values are similarly large.
hotspots(x, p = 0.99, tail = "positive", distribution = "t", var.est = "mad") outliers(x, p = 0.99, tail = "positive", distribution = "t", var.est = "mad", center.est = "mean")hotspots(x, p = 0.99, tail = "positive", distribution = "t", var.est = "mad") outliers(x, p = 0.99, tail = "positive", distribution = "t", var.est = "mad", center.est = "mean")
x |
a numeric vector |
p |
probability level of chosen distribution used for calculation of cutoff (between 0 and 1) |
tail |
determines whether cutoffs are calculated for positive numbers within |
distribution |
statistical distribution used to calculate the hot spot or outlier cutoff. Defaults to |
var.est |
character vector indicating the function to be used to estimate the level of variation within the data.
Defaults to the robust measure |
center.est |
character vector indicating the function to be used to center the data for identification of outliers.
Defaults to |
This function first scales the data by dividing them by a
robust version of the root mean square. The robust
root mean square (rrms) is calculated as:
rrms = sqrt(med(x)^2 + var.est(x)^2)
where var.est is the user-specified function for estimating the level of variation within the data.
This scaling of the data allows for the comparison of scaled values with a statistical distribution,
which in turn allows discrimination between outliers that do not substantially influence the data
from those that do. For the outlier function, the data are scaled after centering the
data using the user-specified center.est function, which defaults to the mean.
The hotspot or outlier cutoff (for positive values, negative values, or both) is then calculated as:
cutoff = (med(x/rrms) + F^-1(p))*rrms
where F is a cumulative distribution function for the t or normal distribution
(its inverse F^-1 being a quantile function; e.g., qt),
and p is a user-defined parameter indicating the probability of F^-1 beyond which we wish
to define the cutoff.
Returns an object of class "hotspots". The functions summary and plot, can be used to
examine the properties of the cutoff. The function disprop can be used to calculate
the level of disproportionality for each value in the data. An object of class "hotspots"
is a list containing some or all of the following components:
x |
numeric input vector |
data |
vector with missing values ( |
distribution |
statistical distribution used to calculate the hot spot or outlier cutoff. |
var.est |
function used to estimate the level of variation within the data |
p |
probability level of chosen distribution used for calculation of cutoff |
tail |
tail(s) of data for which cutoffs were calculated |
dataset_name |
character vector with name of input data |
rrms |
robust root mean square |
positive.cut |
calculated hot spot or outlier cutoff for positive values |
negative.cut |
calculated hot spot or outlier cutoff for negative values |
center.est |
function to be used to center the data for identification of outliers (only for |
Anthony Darrouzet-Nardi
summary.hotspots, plot.hotspots, disprop
#basic operation on lognormal data rln100 <- hotspots(rlnorm(100)) summary(rln100) plot(rln100) #greater skew in data rln100sd2 <- hotspots(rlnorm(100,sd=2)) print(summary(rln100sd2),top = 5) plot(rln100sd2) #both tails on normally distributed data n100 <- hotspots(rnorm(100), tail = "both") summary(n100) plot(n100) #both tails on skewed data rln100pn <- hotspots(c(rlnorm(50),rlnorm(50)*-1),tail = "both") summary(rln100pn) plot(rln100pn) #importance of disproportionality on normally distributed data #contrast with n100 n100p3 <- hotspots(n100$x+3, tail = "both") summary(n100p3) plot(n100p3) #importance of disproportionality on skewed data #contrast with rln100 rln100p10 <- hotspots(rlnorm(100)+10) summary(rln100p10) plot(rln100p10) #outliers function ignores disproportionality rln100p10o <- outliers(rlnorm(100)+10) summary(rln100p10o) plot(rln100p10o) #some alternative parameters rln100a <- hotspots(rlnorm(100), p = 0.9, distribution = "normal", var.est = "sd") summary(rln100a) plot(rln100a)#basic operation on lognormal data rln100 <- hotspots(rlnorm(100)) summary(rln100) plot(rln100) #greater skew in data rln100sd2 <- hotspots(rlnorm(100,sd=2)) print(summary(rln100sd2),top = 5) plot(rln100sd2) #both tails on normally distributed data n100 <- hotspots(rnorm(100), tail = "both") summary(n100) plot(n100) #both tails on skewed data rln100pn <- hotspots(c(rlnorm(50),rlnorm(50)*-1),tail = "both") summary(rln100pn) plot(rln100pn) #importance of disproportionality on normally distributed data #contrast with n100 n100p3 <- hotspots(n100$x+3, tail = "both") summary(n100p3) plot(n100p3) #importance of disproportionality on skewed data #contrast with rln100 rln100p10 <- hotspots(rlnorm(100)+10) summary(rln100p10) plot(rln100p10) #outliers function ignores disproportionality rln100p10o <- outliers(rlnorm(100)+10) summary(rln100p10o) plot(rln100p10o) #some alternative parameters rln100a <- hotspots(rlnorm(100), p = 0.9, distribution = "normal", var.est = "sd") summary(rln100a) plot(rln100a)
Plot a Lorenz curve with a hot spot cutoff on it.
Lchs(x, ...)Lchs(x, ...)
x |
|
... |
further plotting parameters to pass to |
Uses the function plot.Lc from the ineq package to plot a Lorenz curve based on the data in a hotspots object. The location of the hot spot cutoff on the Lorenz curve is then drawn as a filled black circle.
Anthony Darrouzet-Nardi
Lchs(hotspots(rlnorm(100)))Lchs(hotspots(rlnorm(100)))
plot method for class "hotspots".
## S3 method for "hotspots" objects ## S3 method for class 'hotspots' plot(x, pch = par("pch"), ...)## S3 method for "hotspots" objects ## S3 method for class 'hotspots' plot(x, pch = par("pch"), ...)
x |
|
pch |
plotting character. See |
... |
further plotting parameters to pass to |
Uses the function densityplot from the lattice package to show the distribution of the data and the position
of the positive and/or negative hot spot or outlier cutoffs.
An object of class "trellis".
Anthony Darrouzet-Nardi
hotspots, summary.hotspots, densityplot
#both tails on skewed data rln100pn <- hotspots(c(rlnorm(50),rlnorm(50)*-1),tail = "both") plot(rln100pn) #modify graphical parameters plot(rln100pn, pch = 16, cex = 1.5)#both tails on skewed data rln100pn <- hotspots(c(rlnorm(50),rlnorm(50)*-1),tail = "both") plot(rln100pn) #modify graphical parameters plot(rln100pn, pch = 16, cex = 1.5)
summary method for class "hotspots".
## S3 method for "hotspots" objects ## S3 method for class 'hotspots' summary(object, ...) ## S3 method for "summary.hotspots" objects ## S3 method for class 'summary.hotspots' print(x, digits = max(3, getOption("digits") - 3), p_round = 1, top = 0, ...)## S3 method for "hotspots" objects ## S3 method for class 'hotspots' summary(object, ...) ## S3 method for "summary.hotspots" objects ## S3 method for class 'summary.hotspots' print(x, digits = max(3, getOption("digits") - 3), p_round = 1, top = 0, ...)
object |
|
x |
|
digits |
the number of significant digits to use when printing |
p_round |
the number of decimal places to print for percentages when printing |
top |
the number of the most disproportionate (highest or lowest) data values to print with their percent contributions to the total |
... |
further arguments passed to or from other methods |
The importance of hot spots within the data is evaluated by reporting the number of hot spots, the percentage of values that are hot spots, and the percent of the sum of values attributable to hot spots. The percent of the sum of values is likely only relevant if the data are either all positive or all negative. A warning is given if they are not.
A summary.hotspots object is a list containing all of the objects in a hotspots object as well as the following:
num_phs |
number of positive hot spots or outliers in data |
percent_phs |
percent of values identified as positive hot spots or outliers |
percent_phs_sum |
percent of the sum of the values attributable to positive hot spots or outliers |
num_nhs |
number of negative hot spots or outliers in data |
percent_nhs |
percent of values identified as negative hot spots or outliers |
percent_nhs_sum |
percent of the sum of the values attributable to negative hot spots or outliers |
m |
A list of summary statistics pertaining to the data (mean, median, min, max, scale
(determined by the argument ' |
)
disprop |
vector of levels of disproportionality as calculated by |
Anthony Darrouzet-Nardi
hotspots, plot.hotspots, disprop
rln100.sum <- summary(hotspots(rlnorm(101), tail = "both")) rln100.sum print(rln100.sum, top = 10, p_round = 0)rln100.sum <- summary(hotspots(rlnorm(101), tail = "both")) rln100.sum print(rln100.sum, top = 10, p_round = 0)