SDRepresentation {DescriptiveRepresentationCalculator}

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, 2023.

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

• John Gerring, Connor T. Jerzak, Erzen Oncel. (2023), The Composition of Descriptive Representation, American Political Science Review, p. 1-18. doi:10.1017/S0003055423000680

Examples

SDRep <- SDRepresentation(PopShares = c(1/3, 2/3, 1/3),
                                BodyN = 50)

print( SDRep )