# B.Iso: Defining Smooths in logbin.smooth Formulae In logbin: Relative Risk Regression Using the Log-Binomial Model

## Description

Function used in the definition of smooth terms within `logbin.smooth` model formulae. The function does not evaluate a smooth — it exists purely to help set up a model using smooths.

## Usage

 ```1 2 3``` ```B(..., knots = NULL, knot.range = 0:5) Iso(...) ```

## Arguments

 `...` variable that this smooth is a function of. Note that unlike `gam`, smooths that are functions of more than one variable are not supported. `knots` unique positions of interior knots of a B-spline basis. Boundary knots are created automatically. `knot.range` if `knots` is not specified, a vector containing a series of non-negative integers denoting the number of interior knots for which the model will be fit. These are placed at evenly-spaced quantiles of the observed covariate values. At least one of `knots` or `knot.range` must be non-missing.

## Details

The function does not evaluate the variable arguments; the output from this function is used when producing the model matrix, at which point the actual basis functions are constructed.

`B` is used to specify an order-3 B-spline basis (which can be restricted to be monotonically non-decreasing via the `mono` argument in `logbin.smooth`). If `length(knot.range) > 1`, models with each of the specified number of interior knots will be fit, and the model with the best (smallest) `aic.c` will be returned.

`Iso` is used to specify an isotonic basis, designed such that the resulting function has non-negative increments at each observed covariate value. When `Iso` is used, the resulting function will always be monotonically non-decreasing, regardless of the value of `mono`.

## Value

An object of class `"B.smooth"` (for `B`) or `"Iso.smooth"` (for `Iso`), which is a list with the following elements:

 `term` name of the term provided in the `...` argument. `termlabel` label for the term in the model; e.g. for term `"x"` it will be `"B(x)"` or `"Iso(x)"`. `knots` vector of interior knots (if specified). `NA` for `Iso`. `knot.range` vector of number of interior knots. `NA` for `Iso`.

## Author(s)

Mark W. Donoghoe markdonoghoe@gmail.com

`logbin.smooth`
`s` performs a similar function in the `mgcv` package.
 ```1 2``` ```## See example(logbin.smooth) for an example of specifying smooths in model ## formulae. ```