Transformations {coin} | R Documentation

## Functions for Data Transformation

### Description

Transformations for factors and numeric variables.

### Usage

    id_trafo(x)
    rank_trafo(x, ties.method = c("mid-ranks", "random"))
    normal_trafo(x, ties.method = c("mid-ranks", "average-scores"))
    median_trafo(x, mid.score = c("0", "0.5", "1"))
    savage_trafo(x, ties.method = c("mid-ranks", "average-scores"))
    consal_trafo(x, ties.method = c("mid-ranks", "average-scores"), a = 5)
    koziol_trafo(x, ties.method = c("mid-ranks", "average-scores"), j = 1)
    klotz_trafo(x, ties.method = c("mid-ranks", "average-scores"))
    mood_trafo(x, ties.method = c("mid-ranks", "average-scores"))
    ansari_trafo(x, ties.method = c("mid-ranks", "average-scores"))
    fligner_trafo(x, ties.method = c("mid-ranks", "average-scores"))
    logrank_trafo(x, ties.method = c("mid-ranks", "Hothorn-Lausen",
                                     "average-scores"),
                  weight = logrank_weight, ...)
    logrank_weight(time, n.risk, n.event,
                   type = c("logrank", "Gehan-Breslow", "Tarone-Ware", "Prentice",
                            "Prentice-Marek", "Andersen-Borgan-Gill-Keiding",
                            "Fleming-Harrington", "Gaugler-Kim-Liao", "Self"),
                   rho = NULL, gamma = NULL)
    f_trafo(x)
    of_trafo(x, scores = NULL)
    zheng_trafo(x, increment = 0.1)
    maxstat_trafo(x, minprob = 0.1, maxprob = 1 - minprob)
    fmaxstat_trafo(x, minprob = 0.1, maxprob = 1 - minprob)
    ofmaxstat_trafo(x, minprob = 0.1, maxprob = 1 - minprob)
    trafo(data, numeric_trafo = id_trafo, factor_trafo = f_trafo,
          ordered_trafo = of_trafo, surv_trafo = logrank_trafo,
          var_trafo = NULL, block = NULL)
    mcp_trafo(...)

### Arguments

`x` | an object of class `"numeric"`, `"factor"`, `"ordered"` or `"Surv"`.

`ties.method`

a character, the method used to handle ties. The score generating function either uses the mid-ranks (`"mid-ranks"`, default) or, in the case of `rank_trafo`, randomly broken ties (`"random"`). Alternatively, the average of the scores resulting from applying the score generating function to randomly broken ties are used (`"average-scores"`). See `logrank_test` for a detailed description of the methods used in `logrank_trafo`.

`mid.score` | a character, the score assigned to observations exactly equal to the median: either 0 (`"0"`, default), 0.5 (`"0.5"`) or 1 (`"1"`); see `median_test`.
`a` | a numeric vector, the values taken as the constant a in the Conover-Salsburg scores. Defaults to `5`.
`j` | a numeric, the value taken as the constant j in the Koziol-Nemec scores. Defaults to `1`.
`weight` | a function where the first three arguments must correspond to `time`, `n.risk`, and `n.event` given below. Defaults to `logrank_weight`.
`time` | a numeric vector, the ordered distinct time points.
`n.risk` | a numeric vector, the number of subjects at risk at each time point specified in `time`.
`n.event` | a numeric vector, the number of events at each time point specified in `time`.
`type` | a character, one of `"logrank"` (default), `"Gehan-Breslow"`, `"Tarone-Ware"`, `"Prentice"`, `"Prentice-Marek"`, `"Andersen-Borgan-Gill-Keiding"`, `"Fleming-Harrington"` or `"Self"`; see `logrank_test`.
`rho` | a numeric vector, the ρ constant when `type` is `"Tarone-Ware"`, `"Fleming-Harrington"` or `"Self"`; see `logrank_test`. Defaults to `NULL`, implying `0.5` for `type = "Tarone-Ware"` and `0` otherwise.
`gamma` | a numeric vector, the γ constant when `type` is `"Fleming-Harrington"` or `"Self"`; see `logrank_test`. Defaults to `NULL`, implying `0`.
`scores` | a numeric vector or list, the scores corresponding to each level of an ordered factor. Defaults to `NULL`, implying `1:nlevels(x)`.
`increment` | a numeric, the score increment between the order-restricted sets of scores. A fraction greater than 0, but smaller than or equal to 1. Defaults to `0.1`.
`minprob` | a numeric, a fraction between 0 and 0.5; see `maxstat_test`. Defaults to `0.1`.
`maxprob` | a numeric, a fraction between 0.5 and 1; see `maxstat_test`. Defaults to `1 - minprob`.
`data` | an object of class `"data.frame"`.
`numeric_trafo` | a function to be applied to elements of class `"numeric"` in `data`, returning a matrix with `nrow(data)` rows and an arbitrary number of columns. Defaults to `id_trafo`.
`factor_trafo` | a function to be applied to elements of class `"factor"` in `data`, returning a matrix with `nrow(data)` rows and an arbitrary number of columns. Defaults to `f_trafo`.
`ordered_trafo` | a function to be applied to elements of class `"ordered"` in `data`, returning a matrix with `nrow(data)` rows and an arbitrary number of columns. Defaults to `of_trafo`.
`surv_trafo` | a function to be applied to elements of class `"Surv"` in `data`, returning a matrix with `nrow(data)` rows and an arbitrary number of columns. Defaults to `logrank_trafo`.
`var_trafo` | an optional named list of functions to be applied to the corresponding variables in `data`. Defaults to `NULL`.
`block` | an optional factor whose levels are interpreted as blocks. `trafo` is applied to each level of `block` separately. Defaults to `NULL`.
`...` | `logrank_trafo()`: further arguments to be passed to `weight`. `mcp_trafo()`: factor name and contrast matrix (as matrix or character) in a tag = value format for multiple comparisons based on a single unordered factor; see `mcp` in package multcomp.

### Details

The utility functions documented here are used to define specialized test procedures.

`id_trafo` is the identity transformation.

`rank_trafo`, `normal_trafo`, `median_trafo`, `savage_trafo`, `consal_trafo` and `koziol_trafo` compute rank scores, normal scores, median scores, Savage scores, Conover-Salsburg scores (see `neuropathy`) and Koziol-Nemec scores, respectively, for location problems.

`klotz_trafo`, `mood_trafo`, `ansari_trafo` and `fligner_trafo` compute Klotz scores, Mood scores, Ansari-Bradley scores and Fligner-Killeen scores, respectively, for scale problems.

`logrank_trafo` computes weighted logrank scores for right-censored data, allowing for a user-defined weight function through the `weight` argument (see `GTSG`).

`f_trafo` computes dummy matrices for factors and `of_trafo` assigns scores to ordered factors. For ordered factors with two levels, the scores are normalized to the [0, 1] range. `zheng_trafo` computes a finite collection of order-restricted scores for ordered factors (see `jobsatisfaction`, `malformations` and `vision`).

`maxstat_trafo`, `fmaxstat_trafo` and `ofmaxstat_trafo` compute scores for cutpoint problems (see `maxstat_test`).

`trafo` applies its arguments to the elements of `data` according to the classes of the elements. A `trafo` function with modified default arguments is usually supplied to `independence_test` via the `xtrafo` or `ytrafo` arguments. Fine tuning, i.e., different transformations for different variables, is possible by supplying a named list of functions to the `var_trafo` argument.

`mcp_trafo` computes contrast matrices for factors.

### Value

A numeric vector or matrix with `nrow(x)` rows and an arbitrary number of columns. For `trafo`, a named matrix with `nrow(data)` rows and an arbitrary number of columns.

### Note

Starting with coin version 1.1-0, all transformation functions are now passing through missing values (i.e., `NA`s). Furthermore, `median_trafo` and `logrank_trafo` are now increasing functions (in conformity with most other transformations in this package).

### Examples

    ## Dummy matrix, two-sample problem (only one column)
    f_trafo(gl(2, 3))

    ## Dummy matrix, K-sample problem (K columns)
    x <- gl(3, 2)
    f_trafo(x)

    ## Score matrix
    ox <- as.ordered(x)
    of_trafo(ox)
    of_trafo(ox, scores = c(1, 3:4))
    of_trafo(ox, scores = list(s1 = 1:3, s2 = c(1, 3:4)))
    zheng_trafo(ox, increment = 1/3)

    ## Normal scores
    y <- runif(6)
    normal_trafo(y)

    ## All together now
    trafo(data.frame(x = x, ox = ox, y = y), numeric_trafo = normal_trafo)

    ## The same, but allows for fine-tuning
    trafo(data.frame(x = x, ox = ox, y = y), var_trafo = list(y = normal_trafo))

    ## Transformations for maximally selected statistics
    maxstat_trafo(y)
    fmaxstat_trafo(x)
    ofmaxstat_trafo(ox)

    ## Apply transformation blockwise (as in the Friedman test)
    trafo(data.frame(y = 1:20), numeric_trafo = rank_trafo, block = gl(4, 5))

    ## Multiple comparisons
    dta <- data.frame(x)
    mcp_trafo(x = "Tukey")(dta)

    ## The same, but useful when specific contrasts are desired
    K <- rbind("2 - 1" = c(-1,  1, 0),
               "3 - 1" = c(-1,  0, 1),
               "3 - 2" = c( 0, -1, 1))
    mcp_trafo(x = K)(dta)

[Package coin version 1.3-0 Index]