Last data update: 2014.03.03

R: Significance Level for Changepoint
 sl R Documentation

## 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" )
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
```

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