sl: Significance Level for Changepoint

In lm.br: Linear Model with Breakpoint

Significance Level for Changepoint

Description

Significance level of a postulate value for the changepoint's x- or (x,y)-coordinates.

Usage

## S4 method for signature 'Cpp_Clmbr'
sl( theta0,  method ="CLR", tolerance =0.001, output ="T" )
## S4 method for signature 'Cpp_Clmbr'
sl( theta0, alpha0,  method ="CLR", tolerance =0.001, output ="T" )

Arguments

theta0	postulate value for 'theta', the changepoint's x-coordinate.
alpha0	postulate value for 'alpha', the changepoint's y-coordinate.
method	"CLR", "MC" or "AF" which stand for conditional likelihood-ratio, conditional likelihood-ratio by Monte Carlo or approximate-F, details below.
tolerance	maximum absolute error in numerical integration for the "CLR" method or in Monte-Carlo evaluation for the "MC" method, not referenced for the "AF" method.
output	"T", "V" or "B" which stand for text, value or both.

Details

Knowles, Siegmund and Zhang (1991) reduced the conditional likelihood-ratio significance test to a probability expression based on a generic random variable.

The default method "CLR" evaluates this probability using a geometric-expectation formula that Knowles et al. also derived. This formula slightly over-estimates, but the error is negligible for significance levels below 0.20.

Method "MC" evaluates that probability expression directly by Monte Carlo simulation, which avoids the over-estimate of the "CLR" method.

Method "AF" estimates the distribution of the likelihood-ratio statistic by the related F-distribution (or chi-squared if variance is known) which would be exact for a linear model. This method is not exact, but it is common for non-linear regression.

Value

'sl' prints-out the result but does not return a value if 'output' is "T". 'sl' returns a numeric value if 'output' is "V" or "B".

Note

The 'tolerance' error-limit does not include the slight over-estimate that is inherent in the "CLR" method, nor the approximation inherent in the "AF" method.

Examples

#  Data for Patient B from Smith and Cook (1980)
y <- c(37.3, 47.1, 51.5, 67.6, 75.9, 73.3, 69.4, 61.5, 31.8, 19.4)
x <- 1:10
sc <- lm.br( y ~ x )

sc $ sl( 6.1 )
sc $ sl( 6.1, 'mc' )
sc $ sl( 6.1, 'mc', 0.00001 )
sc $ sl( 6.1, 88.2, 'clr' )
sc $ sl( 6.1, 88.2, 'af' )
tmp <- sc $ sl( 6.1, 88.2, 'mc', 0.001, "B" )
tmp

lm.br documentation built on March 19, 2024, 3:08 a.m.