Description Usage Arguments Details Value Note Examples

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

1 2 3 4 |

`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. |

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.

'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".

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.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
# 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
``` |

```
Loading required package: Rcpp
lm.br version 2.9.3, '?lm.br' starts help
SL= 0.291069 for theta0 = 6.1 by method CLR int.er.< 8.63628e-12
MC evaluation of conditional likelihood-ratio SL
for theta0= 6.1, target accuracy = 0.001:
iteration est. SL est. acc.
1000000 0.290158 0.00090767
SL= 0.290158 for theta0 = 6.1 by method CLR-MC
MC evaluation of conditional likelihood-ratio SL
for theta0= 6.1, target accuracy = 1e-05:
iteration est. SL est. acc.
2000000 0.28954 0.000641415
4000000 0.290008 0.000453766
6000000 0.289915 0.000370463
8000000 0.289843 0.000320807
10000000 0.289997 0.000286984
SL= 0.289997 for theta0 = 6.1 by method CLR-MC
SL= 0.195294 for (th0,a0)= ( 6.1, 88.2 ) by method CLR int.er.< 0.000422366
SL= 0.189867 for (th0,a0)= ( 6.1, 88.2 ) by method AF
MC evaluation of conditional likelihood-ratio SL
for (th0,a0)= (6.1,88.2), target accuracy = 0.001:
iteration est. SL est. acc.
1000000 0.194994 0.000315389
SL= 0.194994 for (th0,a0)= ( 6.1, 88.2 ) by method CLR-MC
[1] 0.1949942
```

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