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Constrained Estimators and Consistency of a Regression Model on a Lexis Diagram

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  • Wenjiang Fu

Abstract

This article considers a regression model on a Lexis diagram of an a × p table with a single response in each cell following a distribution in the exponential family. A regression model on the fixed effects of a rows, p columns, and a + p − 1 diagonals induces a singular design matrix and yields multiple estimators, leading to parameter identifiability problem in age--period--cohort analysis in social sciences, demography, and epidemiology, where assessment of secular trend in age, period, and birth cohort of social events (e.g., violence) and diseases (e.g., cancer) is of interest. Similar problems also exist in other settings, such as in supersaturated designs. In this article, we study the finite sample properties of the multiple estimators, propose a penalized profile likelihood method to study the consistency and asymptotic bias, and demonstrate the results through simulations and data analysis. As a by-product, the identifiability problem is addressed with consistent estimation for model parameters and secular trend. We conclude that consistent estimation can be identified through estimable function and asymptotics studies in regressions with a singular design. Our method provides a novel approach to studying asymptotics of multiple estimators with a diverging number of nuisance parameters.

Suggested Citation

  • Wenjiang Fu, 2016. "Constrained Estimators and Consistency of a Regression Model on a Lexis Diagram," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 180-199, March.
  • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:180-199
    DOI: 10.1080/01621459.2014.998761
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    Cited by:

    1. Ahlfeldt, Gabriel M. & Maennig, Wolfgang & Mueller, Steffen Q., 2022. "The generation gap in direct democracy: Age vs. cohort effects," European Journal of Political Economy, Elsevier, vol. 72(C).
    2. Shih-Yung Su & Wen-Chung Lee, 2019. "Age-period-cohort analysis with a constant-relative-variation constraint for an apportionment of period and cohort slopes," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-21, December.
    3. Enrique Acosta & Stacey A. Hallman & Lisa Y. Dillon & Nadine Ouellette & Robert Bourbeau & D. Ann Herring & Kris Inwood & David J. D. Earn & Joaquin Madrenas & Matthew S. Miller & Alain Gagnon, 2019. "Determinants of Influenza Mortality Trends: Age-Period-Cohort Analysis of Influenza Mortality in the United States, 1959–2016," Demography, Springer;Population Association of America (PAA), vol. 56(5), pages 1723-1746, October.
    4. Zoë Fannon & Christiaan Monden & Bent Nielsen, 2021. "Modelling non‐linear age‐period‐cohort effects and covariates, with an application to English obesity 2001–2014," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 842-867, July.
    5. Zoë Fannon & B. Nielsen, 2018. "Age-period cohort models," Economics Papers 2018-W04, Economics Group, Nuffield College, University of Oxford.
    6. Gamba-Santamaria, Santiago & Melo-Velandia, Luis Fernando & Orozco-Vanegas, Camilo, 2024. "Decomposition of non-performing loans dynamics into a debt-servicing capacity and a risk taking indicators," The Quarterly Review of Economics and Finance, Elsevier, vol. 96(C).
    7. Zoë Fannon & Christiaan Monden & Bent Nielsen, 2018. "Age-period-cohort modelling and covariates, with an application to obesity in England 2001-2014," Economics Papers 2018-W05, Economics Group, Nuffield College, University of Oxford.
    8. Santiago Gamba-Santamaria & Luis Fernando Melo-Velandia & Camilo Orozco-Vanegas, 2021. "What can credit vintages tell us about non-performing loans?," Borradores de Economia 1154, Banco de la Republica de Colombia.
    9. Ethan Fosse & Christopher Winship, 2019. "Bounding Analyses of Age-Period-Cohort Effects," Demography, Springer;Population Association of America (PAA), vol. 56(5), pages 1975-2004, October.

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