Estimating the number of changepoints in segmented regression models: comparative study and application
Estimating the number of changepoints in segmented regression models
Keywords:
Information criteria, Hypothesis testing, Segmented regression, Changepoints, Higher education
Abstract
This paper deals with the problem of selecting the number of changepoints in segmented regression models. The aim is to review selection criteria, namely information criteria and hypothesis testing, and to propose a novel application in the context of students' careers in higher education. The performance of the selection criteria is assessed through simulation studies. Furthermore, we investigate the relationship between University students' performance and one of its main determinants, finding out that this relationship is actually broken-line.
References
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title={ANALISI DELLE CARRIERE UNIVERSITARIE NELLE LAUREE SCIENTIFICHE DI BASE IN ITALIA NELL’ULTIMO DECENNIO},
author={Attanasio, Massimo and Enea, Marco and Albano, Alessandro and Priulla, Andrea},
year={2018}
}
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number={3},
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publisher={Springer}
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year={1977},
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}
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}
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}
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publisher={Wiley Online Library}
}
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}
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author={Muggeo, Vito MR},
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number={15},
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publisher={Taylor \& Francis}
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number={1},
pages={9--16},
year={2002},
publisher={Elsevier}
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publisher={Taylor \& Francis Group}
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title={A new look at the statistical model identification},
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year={1974},
publisher={Ieee}
}
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title={Estimating the number of change-points via Schwarz'criterion},
author={Yao, Yi-Ching},
journal={Statistics \& Probability Letters},
volume={6},
number={3},
pages={181--189},
year={1988},
publisher={Elsevier}
}
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pages={497--525},
year={1997},
publisher={JSTOR}
}
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title={Estimating and testing linear models with multiple structural changes},
author={Bai, Jushan and Perron, Pierre},
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pages={47--78},
year={1998},
publisher={JSTOR}
}
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title={Computation and analysis of multiple structural change models},
author={Bai, Jushan and Perron, Pierre},
journal={Journal of applied econometrics},
volume={18},
number={1},
pages={1--22},
year={2003},
publisher={Wiley Online Library}
}
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title={A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data},
author={Zhang, Nancy R and Siegmund, David O},
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volume={63},
number={1},
pages={22--32},
year={2007},
publisher={Wiley Online Library}
}
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publisher={Wiley Online Library}
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journal={The annals of statistics},
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publisher={Institute of Mathematical Statistics}
}
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title={Asymptotic theory for bent-cable regression—the basic case},
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number={1-2},
pages={143--156},
year={2005},
publisher={Elsevier}
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volume={1},
number={3},
pages={161--175},
year={2001},
publisher={Sage Publications Sage CA: Thousand Oaks, CA}
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title={Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity},
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number={3},
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publisher={Wiley Online Library}
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journal={Journal of the Royal Statistical Society: Series C (Applied Statistics)},
volume={54},
number={5},
pages={919--939},
year={2005},
publisher={Wiley Online Library}
}
title={ANALISI DELLE CARRIERE UNIVERSITARIE NELLE LAUREE SCIENTIFICHE DI BASE IN ITALIA NELL’ULTIMO DECENNIO},
author={Attanasio, Massimo and Enea, Marco and Albano, Alessandro and Priulla, Andrea},
year={2018}
}
@article{chen2011comparison,
title={A comparison of estimators for regression models with change points},
author={Chen, Cathy WS and Chan, Jennifer SK and Gerlach, Richard and Hsieh, William YL},
journal={Statistics and Computing},
volume={21},
number={3},
pages={395--414},
year={2011},
publisher={Springer}
}
@article{davies1977hypothesis,
title={Hypothesis testing when a nuisance parameter is present only under the alternative},
author={Davies, Robert B},
journal={Biometrika},
volume={64},
number={2},
pages={247--254},
year={1977},
publisher={Oxford University Press}
}
@article{zhang2007modified,
title={A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data},
author={Zhang, Nancy R and Siegmund, David O},
journal={Biometrics},
volume={63},
number={1},
pages={22--32},
year={2007},
publisher={Wiley Online Library}
}
@article{shao1997asymptotic,
title={An asymptotic theory for linear model selection},
author={Shao, Jun},
journal={Statistica sinica},
pages={221--242},
year={1997},
publisher={JSTOR}
}
@article{giada2014new,
title={A new indicator for higher education student performance},
author={Adelfio, Giada and Boscaino, Giovanni and Capursi, Vincenza},
journal={Higher Education},
volume={68},
number={5},
pages={653--668},
year={2014},
publisher={Springer}
}
@article{ulm1991statistical,
title={A statistical method for assessing a threshold in epidemiological studies},
author={Ulm, Kurt},
journal={Statistics in medicine},
volume={10},
number={3},
pages={341--349},
year={1991},
publisher={Wiley Online Library}
}
@article{attanasio2014association,
title={An association model for bivariate data with application to the anlysis of university students' success.},
author={Attanasio, M and Enea, M},
year={2014},
publisher={Taylor \& Francis Group}
}
@article{muggeo2016testing,
title={Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling},
author={Muggeo, Vito MR},
journal={Journal of Statistical Computation and Simulation},
volume={86},
number={15},
pages={3059--3067},
year={2016},
publisher={Taylor \& Francis}
}
@article{betts2007thresholds,
title={Thresholds in songbird occurrence in relation to landscape structure},
author={Betts, Matthew G and Forbes, Graham J and Diamond, Antony W},
journal={Conservation Biology},
volume={21},
number={4},
pages={1046--1058},
year={2007},
publisher={Wiley Online Library}
}
@incollection{attanasio2013can,
title={Can the Students’ Career be Helpful in Predicting an Increase in Universities Income?},
author={Attanasio, Massimo and Boscaino, Giovanni and Capursi, Vincenza and Plaia, Antonella},
booktitle={Statistical Models for Data Analysis},
pages={9--16},
year={2013},
publisher={Springer}
}
@article{birch2006student,
title={Student outcomes at university in Australia: A quantile regression approach},
author={Birch, Elisa Rose and Miller, Paul W},
journal={Australian Economic Papers},
volume={45},
number={1},
pages={1--17},
year={2006},
publisher={Wiley Online Library}
}
@article{cheesman2006determinants,
title={Determinants of student performance at university: Reflections from the Caribbean},
author={Cheesman, Jennifer and Simpson, Natalee and Wint, Alvin G},
journal={Unpublished Manuscript},
year={2006}
}
@article{grilli2013predicting,
title={Predicting students’ academic performance: a challenging issue in statistical modelling},
author={Grilli, Leonardo and Rampichini, Carla and Varriale, Roberta},
journal={CLEUP: Cladag 2013 Book of abstracts},
year={2013},
publisher={Citeseer}
}
@article{horn2011factors,
title={Factors Explaining The Academic Success Of Second-Year Economics Students: An Exploratory Analysis},
author={Horn, Petronella and Jansen, Ada and Yu, Derek},
journal={South African Journal of Economics},
volume={79},
number={2},
pages={202--210},
year={2011},
publisher={Wiley Online Library}
}
@article{tattersall2006case,
title={A case study in the measurement of educational efficiency in open and distance learning},
author={Tattersall, Colin and Waterink, Wim and H{\"o}ppener, Pierre and Koper, Rob},
journal={Distance Education},
volume={27},
number={3},
pages={391--404},
year={2006},
publisher={Taylor \& Francis}
}
@article{van2011looking,
title={Looking for students’ personal characteristics predicting study outcome},
author={Van Bragt, Cyrille AC and Bakx, Anouke WEA and Bergen, Theo CM and Croon, Marcel A},
journal={Higher Education},
volume={61},
number={1},
pages={59--75},
year={2011},
publisher={Springer}
}
@article{shi2002regression,
title={Regression model selection—a residual likelihood approach},
author={Shi, Peide and Tsai, Chih-Ling},
journal={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
volume={64},
number={2},
pages={237--252},
year={2002},
publisher={Wiley Online Library}
}
@book{priestley1981spectral,
title={Spectral analysis and time series: probability and mathematical statistics},
author={Priestley, Maurice Bertram},
number={04; QA280, P7.},
year={1981}
}
@Manual{R,
title = {R: A Language and Environment for Statistical Computing},
author = {{R Core Team}},
organization = {R Foundation for Statistical Computing},
address = {Vienna, Austria},
year = {2019},
url = {https://www.R-project.org/},
}
@article{chiu2002bent,
title={Bent-cable asymptotics when the bend is missing},
author={Chiu, Grace and Lockhart, Richard and Routledge, Richard},
journal={Statistics \& probability letters},
volume={59},
number={1},
pages={9--16},
year={2002},
publisher={Elsevier}
}
@article{hocking1976biometrics,
title={A Biometrics invited paper. The analysis and selection of variables in linear regression},
author={Hocking, Ronald R},
journal={Biometrics},
volume={32},
number={1},
pages={1--49},
year={1976},
publisher={JSTOR}
}
@article{mallows1973some,
title={Some comments on C p},
author={Mallows, Colin L},
journal={Technometrics},
volume={15},
number={4},
pages={661--675},
year={1973},
publisher={Taylor \& Francis Group}
}
@article{akaike1974new,
title={A new look at the statistical model identification},
author={Akaike, Hirotugu},
journal={IEEE transactions on automatic control},
volume={19},
number={6},
pages={716--723},
year={1974},
publisher={Ieee}
}
@article{yao1988estimating,
title={Estimating the number of change-points via Schwarz'criterion},
author={Yao, Yi-Ching},
journal={Statistics \& Probability Letters},
volume={6},
number={3},
pages={181--189},
year={1988},
publisher={Elsevier}
}
@article{liu1997segmented,
title={On segmented multivariate regression},
author={Liu, Jian and Wu, Shiying and Zidek, James V},
journal={Statistica Sinica},
pages={497--525},
year={1997},
publisher={JSTOR}
}
@article{bai1998estimating,
title={Estimating and testing linear models with multiple structural changes},
author={Bai, Jushan and Perron, Pierre},
journal={Econometrica},
pages={47--78},
year={1998},
publisher={JSTOR}
}
@article{bai2003computation,
title={Computation and analysis of multiple structural change models},
author={Bai, Jushan and Perron, Pierre},
journal={Journal of applied econometrics},
volume={18},
number={1},
pages={1--22},
year={2003},
publisher={Wiley Online Library}
}
@article{zhang2007modified,
title={A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data},
author={Zhang, Nancy R and Siegmund, David O},
journal={Biometrics},
volume={63},
number={1},
pages={22--32},
year={2007},
publisher={Wiley Online Library}
}
@article{tiwari2005bayesian,
title={Bayesian model selection for join point regression with application to age-adjusted cancer rates},
author={Tiwari, Ram C and Cronin, Kathleen A and Davis, William and Feuer, Eric J and Yu, Binbing and Chib, Siddhartha},
journal={Journal of the Royal Statistical Society: Series C (Applied Statistics)},
volume={54},
number={5},
pages={919--939},
year={2005},
publisher={Wiley Online Library}
}
@article{schwarz1978estimating,
title={Estimating the dimension of a model},
author={Schwarz, Gideon and others},
journal={The annals of statistics},
volume={6},
number={2},
pages={461--464},
year={1978},
publisher={Institute of Mathematical Statistics}
}
@article{chiu2005asymptotic,
title={Asymptotic theory for bent-cable regression—the basic case},
author={Chiu, Grace and Lockhart, Richard and Routledge, Richard},
journal={Journal of Statistical planning and inference},
volume={127},
number={1-2},
pages={143--156},
year={2005},
publisher={Elsevier}
}
@article{seber2003nonlinear,
title={Nonlinear Regression. Hoboken},
author={Seber, George AF and Wild, Christopher John},
journal={New Jersey: John Wiley \& Sons},
volume={62},
pages={63},
year={2003}
}
@article{smyth2001exact,
title={Exact and approximate REML for heteroscedastic regression},
author={Smyth, Gordon K and Huele, A Frederik and Verbyla, Ar{\=u}nas P},
journal={Statistical modelling},
volume={1},
number={3},
pages={161--175},
year={2001},
publisher={Sage Publications Sage CA: Thousand Oaks, CA}
}
@article{siino2017spatial,
title={Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity},
author={Siino, Marianna and Adelfio, Giada and Mateu, Jorge and Chiodi, Marcello and D’alessandro, Antonino},
journal={Stochastic Environmental Research and Risk Assessment},
volume={31},
number={7},
pages={1633--1648},
year={2017},
publisher={Springer}
}
@article{kass1995bayes,
title={Bayes factors},
author={Kass, Robert E and Raftery, Adrian E},
journal={Journal of the american statistical association},
volume={90},
number={430},
pages={773--795},
year={1995},
publisher={Taylor \& Francis}
}
@article{jeffreys1961theory,
title={Theory of probability, 3rd edn oxford: Oxford university press},
author={Jeffreys, H},
year={1961}
}
@article{kim2000permutation,
title={Permutation tests for joinpoint regression with applications to cancer rates},
author={Kim, Hyune-Ju and Fay, Michael P and Feuer, Eric J and Midthune, Douglas N},
journal={Statistics in medicine},
volume={19},
number={3},
pages={335--351},
year={2000},
publisher={Wiley Online Library}
}
@article{kim2009selecting,
title={Selecting the number of change-points in segmented line regression},
author={Kim, Hyune-Ju and Yu, Binbing and Feuer, Eric J},
journal={Statistica Sinica},
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Published
2020-10-24
Section
Statistics
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
