Estimating regression models with unknown break-points

Statistics in Medicine

Volumn 22, Issue 19, 2003, Pages 3055-3071

  Muggeo, Vito M R ^a  

^a UNIVERSITY OF PALERMO   (Italy)

Author keywords

Break point; Non linear model; Segmented regression; Taylor expansion; Threshold value

Indexed keywords

ANALYSIS OF VARIANCE; ANALYTIC METHOD; ARTICLE; CHRONIC BRONCHITIS; COMPUTER PROGRAM; HEART TRANSPLANTATION; LINEAR REGRESSION ANALYSIS; LOGISTIC REGRESSION ANALYSIS; MATHEMATICAL MODEL; PREDICTION; SIMULATION; SURVIVAL;

BRONCHITIS; CHRONIC DISEASE; DUST; HEART TRANSPLANTATION; HUMANS; MODELS, STATISTICAL; REGRESSION ANALYSIS; SURVIVAL ANALYSIS;

EID: 0141704311     PISSN: 02776715     EISSN: None     Source Type: Journal    
DOI: 10.1002/sim.1545     Document Type: Article

References (28)

1. Stasinopoulos DM, Rigby RA. Detecting break points in generalised linear models. Computational Statistics and Data Analysis 1992; 13:461-471.
2. Seber GAF, Wild CJ. Nonlinear Regression. Wiley: New York, 1989.
3. Molinari N, Daurès J, Durand J. Regression splines for threshold selection in survival data analysis. Statistics in Medicine 2001; 20(5):237-247.
4. Ulm K. A statistical methods for assessing a threshold in epidemiological studies. Statistics in Medicine 1991; 10:341-349.
5. Cox C. Threshold dose-response models in toxicology. Biometrics 1987; 43:511-523.
6. Schwartz PF, Gennings C, Chinchilli VM. Threshold models for combination data from reproductive and developmental experiments. Journal of the American Statistical Association 1995; 90:862-870.
7. Pires AM, Branco JA, Picado A, Mendonça E. Models for the estimation of a 'no effect concentration'. Environmetrics 2002; 13:15-27.
8. Feder PI. The log likelihood ratio in segmented regression. Annals of Statistics 1975; 3:84-97.
9. Beckman RJ, Cook RD. Testing for two-phase regressions. Technometrics 1979; 21:65-69.
10. Ertel JE, Fowlkes EB. Some algorithms for linear spline and piecewise multiple linear regression. Journal of the American Statistical Association 1976: 71:640-648.
11. Tishler A, Zang I. A maximum likelihood method for piecewise regression models with a continuous dependent variable. Applied Statistics 1981; 30:116-124.
12. Hastie TJ, Tibshirani RJ. Generalized Additive Models. Chapman & Hall: London, 1990.
13. Kunst AE, Looman CWN, Mackenbach JP. Outdoor air temperature and mortality in the Netherlands: a time series analysis. American Journal of Epidemiology 1993; 137:331-341.
14. Gössl C, Küchenhoff H. Bayesian analysis of logistic regression with an unknown change point and covariate measurement error. Statistics in Medicine 2001; 20:3109-3121.
15. Küchenhoff HK, Carrol RJ. Segmented regression with errors in predictors: semi-parametric and parametric methods. Statistics in Medicine 1997; 16:169-188.
16. Rigby RA, Stasinopoulos DM. Detecting break points in the hazard function in survival analysis. Statistical Modelling 1992; 303-311.
17. Küchenhoff H, Ulm K. Comparison of statistical methods for assessing threshold limiting values in occupational epidemiology. Computational Statistics 1997; 12:249-264.
18. Vermont J, Bosson JL. François P, Rueff RC, Demongeot JA. Strategies for graphical threshold determination. Computer Methods and Programs in Biomedicine 1991: 35:141-150.
19. Küchenhoff H. An exact algorithm for estimating breakpoints in segmented generalized linear models. Computational Statistics 1997; 12:235-247.
20. Hawkins DM. Point estimation of the parameters of piecewise regression models. Applied Statistics 1976; 25:51-57.
21. Bacon DW, Watts DG. Estimating the transition between two intersecting straight lines. Biometrika 1971; 58:525-534.
22. Griffiths DA, Miller AJ. Hyperbolic regression - a model based on two-phase piecewise linear regression with a smooth transition between regimens. Communications in Statistics 1973; 2:561-569.
23. Tishler A, Zang I. A new maximum likelihood algorithm for piecewise regression. Applied Statistics 1981; 76:980-987.
24. Pastor R, Guallar E. Use of two-segmented logistic regression to estimate change-points in epidemiologic studies. American Journal of Epidemiology 1998; 148:631-642.
25. Box GEP, Tidwell PW. Transformation of the independent variables. Technometrics 1962; 4:531-550.
26. McCullagh P, Nelder JA. Generalized Linear Models. 2nd edn. Chapman & Hall: London, 1989.
27. Neyman J. Contribution to discussion of the symposium on interval estimation. Journal of the Royal Statistical Society, Series B 1954; 16:216-218.
28. Julious SA. Inference and estimation in a changepoint regression problem. Statistician 2001; 50:51-61.