chngpt.test: Threshold Model Hypothesis Testing

In chngpt: Estimation and Hypothesis Testing for Threshold Regression

Threshold Model Hypothesis Testing

Description

Hypothesis testing for threshold models. Only linear models and logistic models are supported at this point.

Usage

chngpt.test (formula.null, formula.chngpt, family=c("binomial","gaussian"), data, 
    type=c("step","hinge","segmented","stegmented"),
    test.statistic=c("lr","score"), # support for score is gradually descreasing
    chngpts=NULL, lb.quantile=.1, ub.quantile=.9, 
    chngpts.cnt=50, #this is set to 25 if int is weighted.two.sided or weighted.one.sided
    prec.weights=NULL,
    p.val.method=c("MC","param.boot"), 
    mc.n=5e4, # 1e3 won't cut it, the p values estimated could be smaller than nominal
    boot.B=1e4,
    robust=FALSE,
    keep.fits=FALSE, verbose=FALSE
) 


antoch.test (formula, data, chngpt.var, plot.=FALSE)

## S3 method for class 'chngpt.test'
plot(x, by.percentile=TRUE, both=FALSE, main=NULL, ...) 

Arguments

formula.null	formula for the null model.
formula.chngpt	formula for the change point model. For example, suppose formula.null=y~z and we want to test whether I(x>cutff) is a significant predictor, formula.chngpt=~x If instead we are interested in testing the null that neither I(x>cutff) nor z*I(x>cutff) is a significant predictor, formula.chngpt=~x*z
data	data frame.
family	Currently only linear and logistic regression are supported.
type	step: flat before and after change point; hinge: flat before and slope after change point; segmented: slope before and after change point
test.statistic	method for testing main effects of some threshold model.
chngpts	A grid of potential change points to maximize over. If not supplied, they will be set to a vector of length chngpt.cnt equally spaced between lb.quantile and ub.quantile.
robust	Boolean.
lb.quantile	number. The lower bound in the search for change point in the unit of quantile.
ub.quantile	number. The upper bound in the search for change point in the unit of quantile.
chngpts.cnt	integer. Number of potential change points to maximize over.
mc.n	integer. Number of multivariate normal samples to generate in the Monte Carlo procedure to evaluate p-value.
verbose	Boolean.
chngpt.var	string. Name of the predictor to detect change point
plot.	Boolean. Whether to make a plot.
formula	formula.
x	An object of type chngpt.test.
...	arguments passed to or from methods
by.percentile
both
main
prec.weights
p.val.method
boot.B
keep.fits

Details

The model under the altnerative is the model under the null plus terms involving the threshold. For example, when the type is segmented and formula.null=~z, formula.chngpt=~x, the model under the null is ~z+x and the model under the alternative is ~z+x+(x-e)_+.

If there are missing values in the chngpt formula, those rows will be removed from the whole dataset, including null model and chngpt model.

antoch.test is only implemented for main effect only and is based on Antoch et al. (2004). Also see Fong et al. (2014).

Value

A list of class htest and chngpt.test

p.value	P-value
family	Family from input
method	Method from input

References

Fong, Y., Huang, Y., Gilbert, P., Permar S. (2017) chngpt: threshold regression model estimation and inference, BMC Bioinformatics, 18(1):454.

Fong Y, Di C, and Permar S. (2015) Change-Point Testing in Logistic Regression Models with Interaction Term. Statistics in Medicine. 34:1483–1494

Pastor-Barriuso, R. and Guallar, E. and Coresh, J. (2003) Transition models for change-point estimation in logistic regression. Statistics in Medicine. 22:13141

Antoch, J. and Gregoire, G. and Jaruskova, D. (2004) Detection of structural changes in generalized linear models. Statistics and probability letters. 69:315

Examples

dat=sim.chngpt("thresholded", "step", n=200, seed=1, beta=1, alpha=-1, x.distr="norm", e.=4, 
    family="binomial")
test=chngpt.test(formula.null=y~z, formula.chngpt=~x, dat, type="step", family="binomial",
    mc.n=10)
test
plot(test)

dat=sim.chngpt("thresholded", "segmented", n=200, seed=1, beta=1, alpha=-1, x.distr="norm", e.=4,
    family="binomial")
test=chngpt.test(formula.null=y~z, formula.chngpt=~x, dat, type="segmented", family="binomial",
    mc.n=10)
test
plot(test)

test = chngpt.test (formula.null=Volume~1, formula.chngpt=~Girth, family="gaussian", data=trees, 
    type="segmented", mc.n=1e4, verbose=FALSE, chngpts.cnt=100, test.statistic="lr")
test
plot(test)


## Not run: 
# not run because otherwise the examples take >5s and that is a problem for R CMD check

# has interaction
test = chngpt.test(formula.null=y~z, formula.chngpt=~x*z, dat, type="step", family="binomial")
test
plot(test)


## End(Not run)

chngpt documentation built on Feb. 16, 2023, 10:38 p.m.