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Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models

Analysis of instrumental variables is an effective approach to dealing with endogenous variables and unmeasured confounding issue in causal inference. We propose using the piecewise linear model to fit the relationship between the continuous instrumental variable and the continuous explanatory varia...

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Autores principales: Liu, Shuo Shuo, Zhu, Yeying
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9497487/
https://www.ncbi.nlm.nih.gov/pubmed/36141121
http://dx.doi.org/10.3390/e24091235
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author Liu, Shuo Shuo
Zhu, Yeying
author_facet Liu, Shuo Shuo
Zhu, Yeying
author_sort Liu, Shuo Shuo
collection PubMed
description Analysis of instrumental variables is an effective approach to dealing with endogenous variables and unmeasured confounding issue in causal inference. We propose using the piecewise linear model to fit the relationship between the continuous instrumental variable and the continuous explanatory variable, as well as the relationship between the continuous explanatory variable and the outcome variable, which generalizes the traditional linear instrumental variable models. The two-stage least square and limited information maximum likelihood methods are used for the simultaneous estimation of the regression coefficients and the threshold parameters. Furthermore, we study the limiting distribution of the estimators in the correctly specified and misspecified models and provide a robust estimation of the variance-covariance matrix. We illustrate the finite sample properties of the estimation in terms of the Monte Carlo biases, standard errors, and coverage probabilities via the simulated data. Our proposed model is applied to an education-salary data, which investigates the causal effect of children’s years of schooling on estimated hourly wage with father’s years of schooling as the instrumental variable.
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spelling pubmed-94974872022-09-23 Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models Liu, Shuo Shuo Zhu, Yeying Entropy (Basel) Article Analysis of instrumental variables is an effective approach to dealing with endogenous variables and unmeasured confounding issue in causal inference. We propose using the piecewise linear model to fit the relationship between the continuous instrumental variable and the continuous explanatory variable, as well as the relationship between the continuous explanatory variable and the outcome variable, which generalizes the traditional linear instrumental variable models. The two-stage least square and limited information maximum likelihood methods are used for the simultaneous estimation of the regression coefficients and the threshold parameters. Furthermore, we study the limiting distribution of the estimators in the correctly specified and misspecified models and provide a robust estimation of the variance-covariance matrix. We illustrate the finite sample properties of the estimation in terms of the Monte Carlo biases, standard errors, and coverage probabilities via the simulated data. Our proposed model is applied to an education-salary data, which investigates the causal effect of children’s years of schooling on estimated hourly wage with father’s years of schooling as the instrumental variable. MDPI 2022-09-02 /pmc/articles/PMC9497487/ /pubmed/36141121 http://dx.doi.org/10.3390/e24091235 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Liu, Shuo Shuo
Zhu, Yeying
Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models
title Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models
title_full Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models
title_fullStr Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models
title_full_unstemmed Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models
title_short Simultaneous Maximum Likelihood Estimation for Piecewise Linear Instrumental Variable Models
title_sort simultaneous maximum likelihood estimation for piecewise linear instrumental variable models
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9497487/
https://www.ncbi.nlm.nih.gov/pubmed/36141121
http://dx.doi.org/10.3390/e24091235
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