segmented (version 0.5-3.0)

pscore.test: Testing for existence of one breakpoint

Description

Given a (generalized) linear model, the (pseudo) Score statistic tests for the existence of one breakpoint.

Usage

pscore.test(obj, seg.Z, k = 10, alternative = c("two.sided", "less", "greater"), 
    values=NULL, dispersion=NULL, df.t=NULL, more.break=FALSE)

Arguments

obj

a fitted model typically returned by glm or lm. Even an object returned by segmented can be set. Offset and weights are allowed.

seg.Z

a formula with no response variable, such as seg.Z=~x1, indicating the (continuous) segmented variable being tested. Only a single variable may be tested and an error is printed when seg.Z includes two or more terms. seg.Z can be omitted if i)obj is a segmented fit with a single segmented covariate (and that variable is taken), or ii)if it is a "lm" or "glm" fit with a single covariate (and that variable is taken).

k

optional. Number of points used to compute the pseudo Score statistic. See Details.

alternative

a character string specifying the alternative hypothesis.

values

optional. The evaluation points where the Score test is computed. See Details for default values.

dispersion

optional. the dispersion parameter for the family to be used to compute the test statistic. When NULL (the default), it is inferred from obj. Namely it is taken as 1 for the Binomial and Poisson families, and otherwise estimated by the residual Chi-squared statistic in the model obj (calculated from cases with non-zero weights divided by the residual degrees of freedom).

df.t

optional. The degress-of-freedom used to compute the p-value. When NULL, the df extracted from obj are used.

more.break

optional logical. If obj is a segmented fit, more.break=FALSE tests for the actual breakpoint in obj, while more.break=TRUE tests for an additional breakpoint. Ignored when obj is not a segmented fit.

Value

A list with class 'htest' containing the following components:

method

title (character)

data.name

the regression model and the segmented variable being tested

statistic

the point within the range of the covariate in seg.Z at which the maximum (or the minimum if alternative="less") occurs

parameter

number of evaluation points

p.value

the p-value

process

the alternative hypothesis set

Details

pscore.test tests for a non-zero difference-in-slope parameter of a segmented relationship. Namely, the null hypothesis is \(H_0:\beta=0\), where \(\beta\) is the difference-in-slopes, i.e. the coefficient of the segmented function \(\beta(x-\psi)_+\). The hypothesis of interest \(\beta=0\) means no breakpoint. Simulation studies have shown that such Score test is more powerful than the Davies test (see reference) when the alternative hypothesis is `one changepoint'.

The dispersion value, if unspecified, is taken from obj. If obj represents the fit under the null hypothesis (no changepoint), the dispersion parameter estimate will be usually larger, leading to a (potentially severe) loss of power.

The k evaluation points are k equally spaced values in the range of the segmented covariate. k should not be small. Specific values can be set via values. However I have found no important difference due to number and location of the evaluation points, thus default is k=10 equally-spaced points.

References

Muggeo, V.M.R. (2016) Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling. J of Statistical Computation and Simulation, 86, 3059--3067.

See Also

See also davies.test.

Examples

# NOT RUN {
set.seed(20)
z<-runif(100)
x<-rnorm(100,2)
y<-2+10*pmax(z-.5,0)+rnorm(100,0,3)

o<-lm(y~z+x)

#testing for one changepoint
#use the simple null fit
pscore.test(o,~z) #compare with davies.test(o,~z)..

#use the segmented fit
os<-segmented(o, ~z)
pscore.test(os,~z) #smaller p-value, as it uses the dispersion under the alternative (from 'os') 

#test for the 2nd breakpoint in the variable z
pscore.test(os,~z, more.break=TRUE) 

  
# }