Title: Characterizing Observed and Expected Representation
Version: 1.1.0
Description: A system for analyzing descriptive representation, especially for comparing the composition of a political body to the population it represents. Users can compute the expected degree of representation for a body under a random sampling model, the expected degree of representation variability, as well as representation scores from observed political bodies. The package is based on Gerring, Jerzak, and Oncel (2024) <doi:10.1017/S0003055423000680>.
URL: https://github.com/cjerzak/DescriptiveRepresentationCalculator-software/
BugReports: https://github.com/cjerzak/DescriptiveRepresentationCalculator-software/issues
Depends: R (≥ 3.3.3)
License: GPL-3
Encoding: UTF-8
Imports: stats
Suggests: knitr
VignetteBuilder: knitr
RoxygenNote: 7.3.2
NeedsCompilation: no
Packaged: 2025-01-14 22:22:29 UTC; cjerzak
Author: Connor Jerzak ORCID iD [aut, cre], John Gerring ORCID iD [aut], Erzen Oncel ORCID iD [aut]
Maintainer: Connor Jerzak <connor.jerzak@gmail.com>
Repository: CRAN
Date/Publication: 2025-01-14 22:40:06 UTC

Compute the expected degree of representation for any group in a political body

Description

Finds the degree of expected representation for any group in a political body under a random sampling model as described in Gerring, Jerzak and Oncel (2024).

Usage

ExpectedRepresentation(PopShares, BodyN, a = -0.5, b = 1)

Arguments

PopShares

A numeric vector containing the group-level population proportions.

BodyN

A positive integer denoting the size of the political body in question.

a, b

The a and b parameters control the affine transformation for how the representation measure is summarized. That is, a and b control how the expected L1 deviation of the population shares from the body shares is re-weighted. The expected L1 deviation is the average value of the absolute deviation of the population from body shares under a random sampling model. This expected L1 deviation is multiplied by a; b is as an additive re-scaling term: a*E[L1]+b. By default, a=-0.5 and b=1 so that the expected Rose Index of Proportionality is returned.

Value

The expected degree of representation (a scalar).

References

See Also

Examples


ExpectedRep <- ExpectedRepresentation(PopShares = c(1/4, 2/4, 1/4),
                                      BodyN = 50)

print( ExpectedRep )

Compute the observed degree of representation for any group in a political body

Description

Finds the degree of observed representation for any group in a political body.

Usage

ObservedRepresentation(BodyMemberCharacteristics, PopShares, BodyShares, a = -0.5, b = 1)

Arguments

BodyMemberCharacteristics

A vector specifying the characteristics for members of a political body.

PopShares

A numeric vector specifying population shares of identities specified in the body-member characteristics input. The names of the entries in PopShares should correspond to identities in that body-member characteristics input (see Example).

BodyShares

(optional) A numeric vector with same structure as PopShares specifying group population shares of a given body. If specified, used by default instead of BodyMemberCharacteristics.

a, b

Parameters controlling the affine transformation for how the representation measure is summarized. That is, a and b control how the L1 deviation of the population shares from the body shares is re-weighted. This expected L1 deviation is multiplied by a; b is as an additive re-scaling term: a*L1+b. By default, a=-0.5 and b=1 so that the Rose Index of Proportionality is returned.

Value

The observed degree of representation (a scalar). By default, this quantity is the Rose Index of Proportionality.

See Also

Examples


ObsRep <- ObservedRepresentation(
                        BodyMemberCharacteristics = c("A","A","C","A","C","A"),
                        PopShares = c("A"=1/4,"B"=2/4, "C"=1/4))

print( ObsRep )

Compute the amount of representation left unexplained by a random sampling model.

Description

Finds the residual standard deviation when using the expected representation for any group in a political body to predict observed representation as described in Gerring, Jerzak and Oncel (2024).

Usage

SDRepresentation(PopShares, BodyN, a = -0.5, b = 1, nMonte = 10000)

Arguments

PopShares

A numeric vector containing the group-level population proportions.

BodyN

A positive integer denoting the size of the political body in question.

a, b

Parameters controlling the affine transformation for how the representation measure is summarized. That is, a and b control how the expected L1 deviation of the population shares from the body shares is re-weighted. The expected L1 deviation is the average value of the absolute deviation of the population from body shares under a random sampling model. This expected L1 deviation is multiplied by a; b is as an additive re-scaling term: a*E[L1]+b. By default, a=-0.5 and b=1 so that the expected Rose Index of Proportionality is used in the calculation.

nMonte

A positive integer denoting number of Monte Carlo iterations used to approximate the variance of representation under a random sampling model.

Value

A scalar summary of the amount of representation not explained by a random sampling model. More precisely, this function returns the the residual standard deviation when using the expected degree of representation to predict observed representation under a random sampling model.

References

See Also

Examples


SDRep <- SDRepresentation(PopShares = c(1/4, 2/4, 1/4),
                                BodyN = 50)

print( SDRep )