R: Ordinal Superiority Measures

ordsup {VGAM} | R Documentation

## Ordinal Superiority Measures

### Description

Ordinal superiority measures for the linear model and cumulative link models: the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model.

### Usage

    ordsup(object, ...)
    ordsup.vglm(object, all.vars = FALSE, confint = FALSE, ...)

### Arguments

`object` | A `vglm` fit. Currently it must be one of: `cumulative`, `uninormal`. The links for `cumulative` must be `logitlink` or `probitlink`, and `parallel = TRUE` is also needed. For `uninormal` the mean must use `identitylink` and model the `sd` as intercept-only.
`all.vars` | Logical. The default is to use explanatory variables which are binary, but all variables are used (except the intercept) if set to `TRUE`.
`confint` | Logical. If `TRUE` then `confintvglm` is called to return confidence intervals for gamma and Delta. By default, Wald intervals are produced, but they can be replaced by profile intervals by setting `method = "profile"`.
`...` | Parameters that can be fed into `confintvglm`, e.g., `level = 0.95` and `method = c("wald", "profile")`.

### Details

Details are given in Agresti and Kateri (2017) and this help file draws directly from this. This function returns two quantities for comparing two groups on an ordinal categorical response variable, while adjusting for other explanatory variables. They are called “ordinal superiority” measures, and the two groups can be compared without supplementary explanatory variables. Let Y1 and Y2 be independent random variables from groups A and B, say, for a quantitative ordinal categorical scale. Then Delta = P(Y1 > Y2) - P(Y2 > Y1) summarizes their relative size. A second quantity is gamma = P(Y1 > Y2) - 0.5 * P(Y2 = Y1). Then Delta=2 * gamma -1. whereas gamma=(Delta + 1)/2. The range of gamma is [0, 1], while the range of Delta is [-1, 1]. The examples below are based on that paper. This function is currently implemented for a very limited number of specific models.

### Value

By default, a list with components `gamma` and `Delta`, where each is a vector with elements corresponding to binary explanatory variables (i.e., 0 or 1), and if no explanatory variables are binary then a `NULL` is returned. If `confint = TRUE` then the list contains 4 more components: `lower.gamma`, `upper.gamma`, `Lower.Delta`, `Upper.Delta`.

### Author(s)

Thomas W. Yee

### References

Agresti, A. and Kateri, M. (2017). Ordinal probability effect measures for group comparisons in multinomial cumulative link models. Biometrics, 73, 214–219.

### See Also

`cumulative`, `propodds`, `uninormal`.

### Examples

    ## Not run:
    Mental <- read.table("http://www.stat.ufl.edu/~aa/glm/data/Mental.dat",
                         header = TRUE)  # Make take a while to load in
    Mental$impair <- ordered(Mental$impair)
    pfit3 <- vglm(impair ~ ses + life, data = Mental,
             cumulative(link = "probitlink", reverse = FALSE, parallel = TRUE))
    coef(pfit3, matrix = TRUE)
    ordsup(pfit3)  # The 'ses' variable is binary

    # Fit a crude LM
    fit7 <- vglm(as.numeric(impair) ~ ses + life, uninormal, data = Mental)
    coef(fit7, matrix = TRUE)  # 'sd' is estimated by MLE
    ordsup(fit7)
    ordsup(fit7, all.vars = TRUE)  # Some output may not be meaningful
    ordsup(fit7, confint = TRUE, method = "profile")

    ## End(Not run)

[Package VGAM version 1.1-3 Index]