RII {RII}R Documentation

Relative Index of Inequality Estimation

Description

Estimates the relative index of inequality (Sergeant and Firth, 2004) for data consisting of the amount of exposure and observed numbers of outcomes in a set of ordered (socio-economic) classes, possibly cross-classified by some standardizing variable such as age. The (continuous) incidence rate is modelled by fitting smoothing splines by maximum penalized likelihood, with smoothing parameter selection by cross validation.

Usage

RII(count, pop, loglambda = NULL, grid = NULL, se = FALSE, B = NULL, alpha = 0.025, returnboot = FALSE)

Arguments

count A matrix of outcome counts with number of rows equal to the number of classes and number of columns equal to the number of standardizing groups. The outcome might be death, or disease incidence, for example.
pop A matrix of amounts of exposure, with dimension the same as that of count. The amount of exposure could be, for example, the number of person-years at risk, the mid-study period population or the number of individuals at risk at the start of the study period.
loglambda Optional value of the smoothing parameter (on log scale)
grid A vector of values (on log scale) on which to search for a starting value for use in the optimization of the smoothing parameter
se Should a bootstrap standard error be computed?
B The number of bootstrap samples to use if computing a standard error
alpha
returnboot

{ If a standard error is computed, should the bootstrap datasets and their respective RII estimates and values of loglambda be returned?}

Details

If loglambda is supplied then this value of the smoothing parameter is used in all calculations and grid is redundant. For no smoothing, specify loglambda = -Inf. Specifying loglambda = Inf will induce a linear fit.

If loglambda is not supplied then grid is required. The element of grid which yields the smallest value of the cross validation score is taken to be the starting value in a minimization of the score over the smoothing parameter. If this element is equal to min(grid), the optimum loglambda is taken to be -Inf. If this element is equal to max(grid), the optimum loglambda is taken to be Inf. If bootstrapping is performed, grid is used for each bootstrap dataset.

For a given value of the smoothing parameter, the penalized Poisson log likelihood is maximized.

Value

An object of class RII, with some of the components

count count
pop pop
loglambda The value of the smoothing parameter (on log scale) used to estimate the RII
par The optimum spline coefficients. When loglambda = Inf these are the intercept and gradient of the linear fit.
group.effects Standardizing group effects
maxval Maximum value of the penalized log likelihood
expected The fitted outcome counts
residuals Deviance residuals
var Delta method approximation of var(RII)
var.log Delta method approximation of var(log(RII))
RII The estimated RII
se Bootstrap standard error for log(RII)
alpha alpha
ci Approximate 1-2*alpha empirical percentile interval for the RII
boot.data The B bootstrap datasets
boot.rep The estimated RIIs for the bootstrap datasets
boot.lambda The values of loglambda used to estimate the RIIs for the bootstrap datasets

Note

Methods available for objects of class RII are

Author(s)

Jamie Sergeant, jamie.sergeant@nuffield.oxford.ac.uk

References

Sergeant, J. C. and Firth D. (2004) Relative index of inequality: definition, estimation and inference. In preparation.

See Also

plot.RII, RII.CVplot.

Examples

## Estimate the RII for the LSDeaths data,
## using a smoothing parameter of 1
data(LSDeaths)
LSdead <- xtabs(Deaths ~ class + age, data = LSDeaths)
LSatrisk <- xtabs(AtRisk ~ class + age, data = LSDeaths)
LSRII <- RII(LSdead, LSatrisk, loglambda = 0)

[Package RII version 0.4-1 Index]