R: A test of monotonicity in a regression curve.

sm.monotonicity {sm} | R Documentation

## A test of monotonicity in a regression curve.

### 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

    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

    	## 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)

[Package sm version 2.2-5.4 Index]