Package 'abnormality'

Title: Measure a Subject's Abnormality with Respect to a Reference Population
Description: Contains the functions to implement the methodology and considerations laid out by Marks et al. in the manuscript Measuring Abnormality in High Dimensional Spaces: Applications in Biomechanical Gait Analysis. As of 2/27/2018 this paper has been submitted and is under scientific review. Using high-dimensional datasets to measure a subject’s overall level of abnormality as compared to a reference population is often needed in outcomes research. Utilizing applications in instrumented gait analysis, that article demonstrates how using data that is inherently non-independent to measure overall abnormality may bias results. A methodology is introduced to address this bias to accurately measure overall abnormality in high dimensional spaces. While this methodology is in line with previous literature, it differs in two major ways. Advantageously, it can be applied to datasets in which the number of observations is less than the number of features/variables, and it can be abstracted to practically any number of domains or dimensions. After applying the proposed methodology to the original data, the researcher is left with a set of uncorrelated variables (i.e. principal components) with which overall abnormality can be measured without bias. Different considerations are discussed in that article in deciding the appropriate number of principal components to keep and the aggregate distance measure to utilize.
Authors: Michael Marks [aut, cre]
Maintainer: Michael Marks <[email protected]>
License: MIT + file LICENSE
Version: 0.1.0
Built: 2025-03-05 03:00:38 UTC
Source: https://github.com/mmarks13/abnormality

Help Index

Generate a matrix of correlated variables

Description

Generate a matrix of correlated variables

Usage

generate_correlated_matrix(n, p, corr, constant_cov_matrix = T, mean = 0)

Arguments

n

number of observations
p

number of features/variables
corr

the correlation coefficient (-1 < r < 1)
constant_cov_matrix

should the value of corr be constant in the covariance matrix, or should corr be the average value in the covariance matrix.
mean

the mean value of the generated variables.

Value

an n x p matrix

Examples

Subject <- generate_correlated_matrix(1, 100, corr = .75,constant_cov_matrix = TRUE)
Reference_Population <- generate_correlated_matrix(100, 100, corr = .75,constant_cov_matrix = TRUE)

Measure a Subject's Abnormality with Respect to a Reference Population

Description

Measure a Subject's Abnormality with Respect to a Reference Population

Usage

overall_abnormality(Subj, Ref, stopping_rule = "Kaiser-Guttman",
  dist_measure = "MAD", TVE = 1, k = 2)

Arguments

Subj

a vector of length n
Ref

an n x p matrix containing the reference population.
stopping_rule

the stopping rule to use when deciding the number of principal components to retain. Options include: c("Kaiser-Guttman", "brStick","TVE").
dist_measure

the aggregate distance measure to use. Options include: c("MAD", "Euclidean", Manhattan","RMSE", "Lk-Norm")
TVE

a numeric value between 0 and 1. The minimum total variance explained for the retained principal components. This will only be used if "TVE" is chosen as the stopping_rule.
k

the value of k if Lk-Norm is chosen as a distance measure

Value

An unbiased measure of overall abnormality of the subject as compared to the reference population based on the parameters supplied.

Examples

p = 100
Subj <- rep(1, p)
Reference_Population <- generate_correlated_matrix(100, p, corr = 0.75,constant_cov_matrix = TRUE)
overall_abnormality(Subj,Reference_Population)
overall_abnormality(Subj,Reference_Population,dist_measure = "Euclidean")
overall_abnormality(Subj,Reference_Population,stopping_rule = "TVE", TVE = .90)
overall_abnormality(Subj,Reference_Population,dist_measure = "Lk-Norm",k=.5,stopping_rule="brStick")