{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,19]],"date-time":"2026-05-19T21:13:02Z","timestamp":1779225182328,"version":"3.51.4"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1011515","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T00:00:00Z","timestamp":1696982400000}}],"reference-count":89,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T00:00:00Z","timestamp":1695945600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP200100177"],"award-info":[{"award-number":["DP200100177"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Developing mechanistic insight by combining mathematical models and experimental data is especially critical in mathematical biology as new data and new types of data are collected and reported. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally-efficient workflow we call<jats:italic>Profile-Wise Analysis<\/jats:italic>(PWA) that addresses all three steps in a unified way. Recently-developed methods for constructing \u2018profile-wise\u2019 prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters. We then demonstrate how to combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. Our three case studies illustrate practical aspects of the workflow, focusing on ordinary differential equation (ODE) mechanistic models with both Gaussian and non-Gaussian noise models. While the case studies focus on ODE-based models, the workflow applies to other classes of mathematical models, including partial differential equations and simulation-based stochastic models. Open-source software on GitHub can be used to replicate the case studies.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011515","type":"journal-article","created":{"date-parts":[[2023,9,29]],"date-time":"2023-09-29T17:31:58Z","timestamp":1696008718000},"page":"e1011515","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":42,"title":["Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models"],"prefix":"10.1371","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6254-313X","authenticated-orcid":true,"given":"Matthew J.","family":"Simpson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oliver J.","family":"Maclaren","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2023,9,29]]},"reference":[{"key":"pcbi.1011515.ref001","doi-asserted-by":"crossref","first-page":"100367","DOI":"10.1016\/j.epidem.2019.100367","article-title":"Contemporary statistical inference for infectious disease models using Stan","volume":"29","author":"A Chatzilena","year":"2019","journal-title":"Epidemics"},{"issue":"2","key":"pcbi.1011515.ref002","article-title":"Visualization in Bayesian workflow","volume":"182","author":"J Gabry","year":"2019","journal-title":"Journal of the Royal Statistical Society: Series A (Statistics in Society)"},{"key":"pcbi.1011515.ref003","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1198\/106186004X11435","article-title":"Exploratory data analysis for complex models","volume":"13","author":"A Gelman","year":"2004","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"pcbi.1011515.ref004","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","volume-title":"Bayesian data analysis","author":"A Gelman","year":"2013","edition":"3"},{"key":"pcbi.1011515.ref005","unstructured":"Gelman A, Vehtari A, Simpson D, Margossian CC, Carpenter B, Yao Y, Kennedy L, Gabry J, B\u00fcrkner PC, Modr\u00e1k M. 2020. 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(arxiv.org\/abs\/2011.01808)."},{"issue":"27","key":"pcbi.1011515.ref006","doi-asserted-by":"crossref","first-page":"6209","DOI":"10.1002\/sim.9164","article-title":"Bayesian workflow for disease transmission modeling in Stan","volume":"40","author":"L Grinsztajn","year":"2021","journal-title":"Statistics in medicine"},{"key":"pcbi.1011515.ref007","doi-asserted-by":"crossref","first-page":"e1002803","DOI":"10.1371\/journal.pcbi.1002803","article-title":"Approximate Bayesian Computation","volume":"9","author":"M Sunn\u00e5ker","year":"2013","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1011515.ref008","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-21736-9","volume-title":"All of statistics: a concise course in statistical inference","author":"L Wasserman","year":"2004"},{"key":"pcbi.1011515.ref009","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511813559","volume-title":"Principles of statistical inference","author":"DR Cox","year":"2006"},{"key":"pcbi.1011515.ref010","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF00485695","article-title":"Frequentist probability and frequentist statistics","author":"J Neyman","year":"1977","journal-title":"Synthese"},{"key":"pcbi.1011515.ref011","volume-title":"Bayesian theory","author":"JM Bernardo","year":"2009"},{"key":"pcbi.1011515.ref012","volume-title":"Information theory, inference and learning algorithms","author":"DJ MacKay","year":"2003"},{"key":"pcbi.1011515.ref013","doi-asserted-by":"crossref","first-page":"20200055","DOI":"10.1098\/rsif.2020.0055","article-title":"Parameter identifiability analysis for spatiotemporal models of cell invasion","volume":"17","author":"MJ Simpson","year":"2020","journal-title":"Journal of the Royal Society Interface"},{"issue":"4","key":"pcbi.1011515.ref014","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1214\/aos\/1176344723","article-title":"Predictive likelihood","volume":"7","author":"D Hinkley","year":"1979","journal-title":"The Annals of Statistics"},{"key":"pcbi.1011515.ref015","article-title":"Assessment of prediction uncertainty quantification methods in systems biology","author":"AF Villaverde","year":"2022","journal-title":"IEEE\/ACM Transactions on Computational Biology and Bioinformatics"},{"issue":"1","key":"pcbi.1011515.ref016","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1196\/annals.1407.003","article-title":"Extracting falsifiable predictions from sloppy models","volume":"1115","author":"RN Gutenkunst","year":"2007","journal-title":"Annals of the New York Academy of Sciences"},{"key":"pcbi.1011515.ref017","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1093\/bioinformatics\/btv743","article-title":"Fast integration-based prediction bands for ordinary differential equation models","volume":"32","author":"H Hass","year":"2016","journal-title":"Bioinformatics"},{"key":"pcbi.1011515.ref018","doi-asserted-by":"crossref","first-page":"2564","DOI":"10.1111\/febs.12276","article-title":"Profile likelihood in systems biology","volume":"280","author":"C Kreutz","year":"2013","journal-title":"The FEBS Journal"},{"key":"pcbi.1011515.ref019","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1186\/1752-0509-6-120","article-title":"Likelihood based observability analysis and confidence intervals for predictions of dynamics models","volume":"6","author":"C Kreutz","year":"2013","journal-title":"BMC Systems Biology"},{"key":"pcbi.1011515.ref020","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.cmpb.2015.02.001","article-title":"A consensus approach for estimating the predictive accuracy of dynamic models in biology","volume":"119","author":"AF Villaverde","year":"2015","journal-title":"Computer Methods and Programs in Biomedicine"},{"key":"pcbi.1011515.ref021","unstructured":"Oliver D, He N, Reynolds AC (1996) Conditioning permeability fields to pressure data. In Proc. 5th Eur. Conf. Mathematics of Oil Recovery, Sept."},{"key":"pcbi.1011515.ref022","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.idm.2023.01.007","article-title":"Likelihood-based estimation and prediction for a measles outbreak in Samoa","volume":"8","author":"D Wu","year":"2023","journal-title":"Infectious Disease Modelling"},{"key":"pcbi.1011515.ref023","doi-asserted-by":"crossref","first-page":"20220560","DOI":"10.1098\/rsif.2022.0560","article-title":"Computationally efficient framework for diagnosing, understanding, and predicting biphasic population growth","volume":"19","author":"RJ Murphy","year":"2022","journal-title":"Journal of the Royal Society Interface"},{"key":"pcbi.1011515.ref024","doi-asserted-by":"crossref","first-page":"108950","DOI":"10.1016\/j.mbs.2022.108950","article-title":"Profile likelihood-based parameter and predictive interval analysis guides model choice for ecological population dynamics","volume":"355","author":"MJ Simpson","year":"2023","journal-title":"Mathematical Biosciences"},{"key":"pcbi.1011515.ref025","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1038\/s41567-020-01121-y","article-title":"Fixed-time descriptive statistics underestimate extremes of epidemic curve ensembles","volume":"17","author":"JL Juul","year":"2021","journal-title":"Nature Physics"},{"key":"pcbi.1011515.ref026","unstructured":"Maclaren OJ, Nicholson R. 2019. What can be estimated? Identifiability, estimability, causal inference and ill-posed inverse problems. arXiv. https:\/\/arxiv.org\/abs\/1904.02826."},{"key":"pcbi.1011515.ref027","unstructured":"Maclaren, OJ, Nicholson, R. 2021. Models, identifiability, and estimability in causal inference. In 38th International Conference on Machine Learning. Workshop on the Neglected Assumptions in Causal Inference. ICML."},{"key":"pcbi.1011515.ref028","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198507659.001.0001","volume-title":"In all likelihood: statistical modelling and inference using likelihood","author":"Y Pawitan","year":"2001"},{"key":"pcbi.1011515.ref029","volume-title":"Statistical inference in science","author":"DA Sprott","year":"2008"},{"issue":"48","key":"pcbi.1011515.ref030","doi-asserted-by":"crossref","first-page":"30055","DOI":"10.1073\/pnas.1912789117","article-title":"The frontier of simulation-based inference","volume":"117","author":"K Cranmer","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"pcbi.1011515.ref031","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1111\/j.2517-6161.1984.tb01290.x","article-title":"Monte Carlo methods of inference for implicit statistical models","volume":"46","author":"PJ. Diggle","year":"1984","journal-title":"Journal of the Royal Statistical Society: Series B (Methodological)"},{"issue":"1","key":"pcbi.1011515.ref032","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1214\/14-STS498","article-title":"Bayesian indirect inference using a parametric auxiliary model","volume":"30","author":"CC Drovandi","year":"2015","journal-title":"Statistical Science"},{"key":"pcbi.1011515.ref033","first-page":"96","article-title":"A comparison of inferential methods for highly nonlinear state space models in ecology and epidemiology","author":"M Fasiolo","year":"2016","journal-title":"Statistical Science"},{"key":"pcbi.1011515.ref034","doi-asserted-by":"crossref","first-page":"1102","DOI":"10.1038\/nature09319","article-title":"Statistical inference for noisy nonlinear ecological dynamic systems","volume":"466","author":"SN Wood","year":"2010","journal-title":"Nature"},{"key":"pcbi.1011515.ref035","doi-asserted-by":"crossref","first-page":"111201","DOI":"10.1016\/j.jtbi.2022.111201","article-title":"Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models","volume":"549","author":"MJ Simpson","year":"2022","journal-title":"Journal of Theoretical Biology"},{"key":"pcbi.1011515.ref036","doi-asserted-by":"crossref","first-page":"20210214","DOI":"10.1098\/rspa.2021.0214","article-title":"Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media","volume":"477","author":"MJ Simpson","year":"2021","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"issue":"2","key":"pcbi.1011515.ref037","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1111\/j.1369-7412.2003.05341.x","article-title":"Estimating functions in indirect inference","volume":"66","author":"K Heggland","year":"2004","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"pcbi.1011515.ref038","doi-asserted-by":"crossref","first-page":"S85","DOI":"10.1002\/jae.3950080507","article-title":"Indirect inference","volume":"8","author":"C Gourieroux","year":"1993","journal-title":"Journal of Applied Econometrics"},{"key":"pcbi.1011515.ref039","doi-asserted-by":"crossref","first-page":"110998","DOI":"10.1016\/j.jtbi.2021.110998","article-title":"Parameter identifiability and model selection for sigmoid population growth models","volume":"535","author":"MJ Simpson","year":"2022","journal-title":"Journal of Theoretical Biology"},{"key":"pcbi.1011515.ref040","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.csda.2018.07.008","article-title":"Likelihood-free inference in high dimensions with synthetic likelihood","volume":"128","author":"VMH Ong","year":"2018","journal-title":"Computational Statistics & Data 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estimate","volume":"246","author":"DA Campbell","year":"2013","journal-title":"Mathematical Biosciences"},{"key":"pcbi.1011515.ref045","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.mbs.2016.10.009","article-title":"On the relationship between sloppiness and identifiability","volume":"282","author":"O Chi\u015f","year":"2016","journal-title":"Mathematical Biosciences"},{"key":"pcbi.1011515.ref046","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.mbs.2014.08.008","article-title":"Determining identifiable parameter combinations using subset profiling","volume":"256","author":"MC Eisenberg","year":"2014","journal-title":"Mathematical Biosciences"},{"key":"pcbi.1011515.ref047","doi-asserted-by":"crossref","DOI":"10.1201\/9781315120003","volume-title":"Parameter redundancy and identifiability","author":"D Cole","year":"2020"},{"key":"pcbi.1011515.ref048","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1093\/bioinformatics\/btp358","article-title":"Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood","volume":"25","author":"A Raue","year":"2009","journal-title":"Bioinformatics"},{"key":"pcbi.1011515.ref049","doi-asserted-by":"crossref","first-page":"20110544","DOI":"10.1098\/rsta.2011.0544","article-title":"Joining forces of Bayesian and frequentist methodology: a study for inference in the presence of non-identifiability","volume":"371","author":"A Raue","year":"2013","journal-title":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"pcbi.1011515.ref050","doi-asserted-by":"crossref","first-page":"1440","DOI":"10.1093\/bioinformatics\/btu006","article-title":"Comparison of approaches for parameter identifiability analysis of biological systems","volume":"30","author":"A Raue","year":"2014","journal-title":"Bioinformatics"},{"key":"pcbi.1011515.ref051","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.coisb.2021.03.005","article-title":"On structural and practical identifiability","volume":"25","author":"F-G Wieland","year":"2021","journal-title":"Current Opinion in Systems Biology"},{"key":"pcbi.1011515.ref052","doi-asserted-by":"crossref","first-page":"e1010833","DOI":"10.1371\/journal.pcbi.1010833","article-title":"Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability","volume":"19","author":"RJ Murphy","year":"2023","journal-title":"PLOS Computational Biology"},{"key":"pcbi.1011515.ref053","doi-asserted-by":"crossref","first-page":"e1010734","DOI":"10.1371\/journal.pcbi.1010734","article-title":"Efficient inference and identifiability analysis for differential equation models with random parameters","volume":"18","author":"AP Browning","year":"2022","journal-title":"PLOS Computational Biology."},{"key":"pcbi.1011515.ref054","doi-asserted-by":"crossref","first-page":"2275","DOI":"10.1016\/j.bpj.2012.10.024","article-title":"MCMC can detect nonidentifiable models","volume":"103","author":"I Siekmann","year":"2012","journal-title":"Biophysical Journal"},{"key":"pcbi.1011515.ref055","doi-asserted-by":"crossref","first-page":"20160122","DOI":"10.1098\/rspa.2016.0122","article-title":"Modelling modal gating of ion channels with hierarchical Markov models","volume":"472","author":"I Siekmann","year":"2016","journal-title":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"pcbi.1011515.ref056","doi-asserted-by":"crossref","unstructured":"Fr\u00f6hlich F, Theis FJ, Hasenauer J. 2014. Uncertainty analysis for non-identifiable dynamical systems: Profile likelihoods, bootstrapping and more. International Conference on Computational Methods in Systems Biology. 61\u201372. 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analysis of nonlinear regression models","volume":"43","author":"H Sulieman","year":"2001","journal-title":"Technometrics"},{"issue":"4","key":"pcbi.1011515.ref064","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1016\/S0167-9473(03)00086-0","article-title":"A profile-based approach to parametric sensitivity in multiresponse regression models","volume":"45","author":"H Sulieman","year":"2004","journal-title":"Computational Statistics & Data Analysis"},{"key":"pcbi.1011515.ref065","doi-asserted-by":"crossref","first-page":"20200652","DOI":"10.1098\/rsif.2020.0652","article-title":"Identifiability analysis for stochastic differential equations models in systems biology","volume":"17","author":"AP Browning","year":"2020","journal-title":"Journal of the Royal Society Interface"},{"key":"pcbi.1011515.ref066","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8122-8","volume-title":"Simultaneous Statistical Inference","author":"RGJ Miller","year":"1981","edition":"2"},{"key":"pcbi.1011515.ref067","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1093\/biomet\/50.1-2.155","article-title":"Simultaneous tolerance intervals in regression","volume":"50","author":"GJ Lieberman","year":"1963","journal-title":"Biometrika"},{"key":"pcbi.1011515.ref068","volume-title":"Statistical Inference","author":"G Casella","year":"2001"},{"key":"pcbi.1011515.ref069","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1098\/rsif.2008.0172","article-title":"Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems","volume":"6","author":"T Toni","year":"2009","journal-title":"Journal of the Royal Society Interface"},{"key":"pcbi.1011515.ref070","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1098\/rsif.2009.0151","article-title":"Plug-and-play inference for disease dynamics: measles in large and small populations as a case study","volume":"7","author":"D He","year":"2010","journal-title":"Journal of the Royal Society Interface"},{"key":"pcbi.1011515.ref071","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1085\/jgp.201311116","article-title":"Determination of parameter identifiability in nonlinear biophysical models: A Bayesian approach","volume":"143","author":"KE Hines","year":"2014","journal-title":"Journal of General Physiology"},{"key":"pcbi.1011515.ref072","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0025-5564(02)00096-2","article-title":"Analysis of logistic growth models","volume":"179","author":"A Tsoularis","year":"2002","journal-title":"Mathematical Biosciences"},{"key":"pcbi.1011515.ref073","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1080\/00438243.1998.9980411","article-title":"Modelling paleoindian dispersals","volume":"30","author":"J Steele","year":"1998","journal-title":"World Archaeology"},{"key":"pcbi.1011515.ref074","doi-asserted-by":"crossref","first-page":"15","DOI":"10.5334\/jors.151","article-title":"DifferentialEquations.jl\u2014a performant and feature-rich ecosystem for solving differential equations in Julia","volume":"5","author":"C Rackauckas","year":"2017","journal-title":"Journal of Open Research Software"},{"key":"pcbi.1011515.ref075","unstructured":"Johnson SG. 2022. The NLopt module for Julia. Retrieved May 2023 NLopt."},{"key":"pcbi.1011515.ref076","unstructured":"Murphy RJ, Maclaren OJ, Simpson MJ. 2023. Implementing measurement error models for estimation and prediction in the life sciences. arXiv preprint."},{"key":"pcbi.1011515.ref077","doi-asserted-by":"crossref","first-page":"e01470","DOI":"10.1002\/ecm.1470","article-title":"A guide to state\u2013space modeling of ecological time series","volume":"91","author":"M Auger-M\u00e9th\u00e9","year":"2021","journal-title":"Ecological Monographs"},{"key":"pcbi.1011515.ref078","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/s12080-013-0195-3","article-title":"Statistical indicators and state\u2013space population models predict extinction in a population of bobwhite quail","volume":"6","author":"TJ Hefley","year":"2013","journal-title":"Theoretical Ecology"},{"key":"pcbi.1011515.ref079","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.ecolmodel.2013.05.003","article-title":"Fitting population growth models in the presence of measurement and detection error","volume":"263","author":"TJ Hefley","year":"2013","journal-title":"Ecological Modelling"},{"key":"pcbi.1011515.ref080","doi-asserted-by":"crossref","first-page":"1269","DOI":"10.1111\/j.1365-2656.2011.01868.x","article-title":"On observation distributions for state space models of population survey data","volume":"80","author":"J Knape","year":"2011","journal-title":"Journal of Animal Ecology"},{"key":"pcbi.1011515.ref081","article-title":"Modelling count data with partial differential equation models in biology","author":"MJ Simpson","year":"2023","journal-title":"bioRxiv"},{"key":"pcbi.1011515.ref082","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1214\/17-STS636","article-title":"Modeling and inference for infectious disease dynamics: a likelihood-based approach","volume":"33","author":"C Breto","year":"2018","journal-title":"Statistical Science"},{"key":"pcbi.1011515.ref083","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1080\/01621459.2019.1604367","article-title":"Panel data analysis 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