Design.trans {Design} | R Documentation

## Design Special Transformation Functions

### Description

This is a series of functions (`asis`, `pol`, `lsp`, `rcs`, `catg`, `scored`, `strat`, `matrx`, and `%ia%`) that set up special attributes (such as knots and nonlinear term indicators) that are carried through to fits (using for example `lrm`,`cph`, `ols`, `psm`). `anova.Design`, `summary.Design`, `plot.Design`, `survplot`, `fastbw`, `validate`, `specs`, `which.influence`, `nomogram.Design` and `latex.Design` use these attributes to automate certain analyses (e.g., automatic tests of linearity for each predictor are done by `anova.Design`). Many of the functions are called implicitly. Some S functions such as `ns` derive data-dependent transformations that are not "remembered" when predicted values are later computed, so the predictions will be incorrect. The functions listed here solve that problem.

`asis` is the identity transformation, `pol` is an ordinary (non-orthogonal) polynomial, `rcs` is a linear tail-restricted cubic spline function (natural spline, for which the `rcspline.eval` function generates the design matrix), `catg` is for a categorical variable, `scored` is for an ordered categorical variable, `strat` is for a stratification factor in a Cox model, `matrx` is for a matrix predictor, and `%ia%` represents restricted interactions in which products involving nonlinear effects on both variables are not included in the model. `asis, catg, scored, matrx` are seldom invoked explicitly by the user (only to specify `label` or `name`, usually).

In the list below, functions `asis` through `strat` can have arguments `x, parms, label, name` except that `parms` does not apply to `asis, matrx, strat`.

### Usage

    asis(x, parms, label, name)
    matrx(x, label, name)
    pol(x, parms, label, name)
    lsp(x, parms, label, name)
    rcs(x, parms, label, name)
    catg(x, parms, label, name)
    scored(x, parms, label, name)
    strat(x, label, name)
    %ia%(x1, x2)

### Arguments

`x` | a predictor variable (or a function of one). If you specify e.g. `pol(pmin(age,10),3)`, a cubic polynomial will be fitted in `pmin(age,10)` (`pmin` is the S vector element–by–element function). The predictor will be labeled `age` in the output, and plots with have `age` in its original units on the axes. If you use a function such as `pmin`, the predictor is taken as the first argument, and other arguments must be defined in the frame in effect when predicted values, etc., are computed.
`parms` | parameters of transformation (e.g. number or location of knots). For `pol` the argument is the order of the polynomial, e.g. `2` for quadratic (the usual default). For `lsp` it is a vector of knot locations (`lsp` will not estimate knot locations). For `rcs` it is the number of knots (if scalar), or vector of knot locations (if `>2` elements). The default number is the `nknots` system option if `parms` is not given. If the number of knots is given, locations are computed for that number of knots. For `catg`, `parms` is the category labels (not needed if variable is an S category or factor variable). If omitted, `catg` will use `unique(x)`, or `levels(x)` if `x` is a `category` or a `factor`. For `scored`, `parms` is a vector of unique values of variable (uses `unique(x)` by default). This is not needed if `x` is an S `ordered` variable. For `strat`, `parms` is the category labels (not needed if variable is an S category variable). If omitted, will use `unique(x)`, or `levels(x)` if `x` is `category` or `factor`. `parms` is not used for `matrix`.
`label` | label of predictor for plotting (default = `"label"` attribute or variable name)
`name` | Name to use for predictor in model. Default is name of argument to function
`x1` |
`x2` | two continuous variables for which to form a non-doubly-nonlinear interaction
`...` | a variety of things

### Author(s)

Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu

### See Also

`rcspline.eval`, `rcspline.restate`, `Design`, `cph`, `lrm`, `ols`, `datadist`

### Examples

    ## Not run:
    options(knots=4, poly.degree=2)
    country <- factor(country.codes)
    blood.pressure <- cbind(sbp=systolic.bp, dbp=diastolic.bp)
    fit <- lrm(Y ~ sqrt(x1)*rcs(x2) + rcs(x3,c(5,10,15)) +
           lsp(x4,c(10,20)) + country + blood.pressure + poly(age,2))
    # sqrt(x1) is an implicit asis variable, but limits of x1, not sqrt(x1)
    #       are used for later plotting and effect estimation
    # x2 fitted with restricted cubic spline with 4 default knots
    # x3 fitted with r.c.s. with 3 specified knots
    # x4 fitted with linear spline with 2 specified knots
    # country is an implied catg variable
    # blood.pressure is an implied matrx variable
    # since poly is not a Design function (pol is), it creates a
    #       matrx type variable with no automatic linearity testing
    #       or plotting
    f1 <- lrm(y ~ rcs(x1) + rcs(x2) + rcs(x1) %ia% rcs(x2))
    # %ia% restricts interactions. Here it removes terms nonlinear in
    # both x1 and x2
    f2 <- lrm(y ~ rcs(x1) + rcs(x2) + x1 %ia% rcs(x2))
    # interaction linear in x1
    f3 <- lrm(y ~ rcs(x1) + rcs(x2) + x1 %ia% x2)
    # simple product interaction (doubly linear)
    # Use x1 %ia% x2 instead of x1:x2 because x1 %ia% x2 triggers
    # anova to pool x1*x2 term into x1 terms to test total effect
    # of x1
    ## End(Not run)

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