# sm.monotonicity: A test of monotonicity in a regression curve. In sm: Smoothing Methods for Nonparametric Regression and Density Estimation

## Description

This function uses the idea of a ‘critical bandwidth’ to assess the evidence that a regression curve is non-monotonic. A hypothesis test is carried out by bootstrap methods and the empirical p-value is reported. Response variables on a continuous scale or with binomial variation can be handled.

## Usage

 `1` ```sm.monotonicity(x, y, N = rep(1, length(y)), h, type = "continuous", ...) ```

## Arguments

 `x` a vector of covariate values. `y` a vector of responses observed at the covariate locations. `N` a vector of sample sizes at the covariate locations, when the responses have a binomial error structure. `h` a smoothing parameter to be used in the construction of the nonparametric regression estimates. A normal kernel function is used and `h` is its standard deviation(s). However, if this argument is omitted `h` will be selected automatically, using the `method` which is currently active. See `sm.options` and `h.select` for details. `type` an indicator of whether the response variable is on a `"continuous"` or `"binomial"` scale. `...` other optional parameters are passed to the `sm.options` function, through a mechanism which limits their effect only to this call of the function; some of those relevant for this function are `add`, `ngrid`, `xlab`, `ylab`, `xlim`, `ylim`, `lty`, `col`; see the documentation of `sm.options` for their description.

## Details

The first reference below describes the statistical methods used in the function. The test is an extension of one by Silverman (1986) for density estimation.

## Value

a list containing the following items

 `p` the p-value for the test of the null hypothesis that the true curve is monotonic. `hcrit` the ‘critical’ smoothing parameter. This is the smallest value which, when applied to the observed data, makes the curve monotonic. `h` the smoothing parameter used for double-smoothing (see the reference below).

## Side Effects

a plot of the curves generated by the bootstrap procedure is produced, unless the option `display="none"` is set. Those curves which are non-monotonic, and therefore contribute to the empirical p-value, are drawn in red.

## References

Bowman, A.W., Jones, M.C. and Gijbels, I. (1998). Testing monotonicity of regression. J.Comp.Graph.Stat. 7, 489-500.

## See Also

`sm.regression`, `sm.options`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ``` ## Not run: # Radiocarbon dating data with(radioc, { ind <- (Cal.age>5000 & Cal.age<6000) cal.age <- Cal.age[ind] rc.age <- Rc.age[ind] sm.monotonicity(cal.age, rc.age, method = "aicc", nboot = 200) }) # Hosmer & Lemeshow birth data with(birth, { sm.monotonicity(Lwt[Smoke == "N"], Low[Smoke == "N"], type = "binomial") }) ## End(Not run) ```

sm documentation built on May 1, 2019, 8:06 p.m.