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Likelihood‐Based Inference for the Finite Population Mean with Post‐Stratification Information Under Non‐Ignorable Non‐Response

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  • Sahar Z. Zangeneh
  • Roderick J. Little

Abstract

We describe models and likelihood‐based estimation of the finite population mean for a survey subject to unit non‐response, when post‐stratification information is available from external sources. A feature of the models is that they do not require the assumption that the data are missing at random (MAR). As a result, the proposed models provide estimates under weaker assumptions than those required in the absence of post‐stratification information, thus allowing more robust inferences. In particular, we describe models for estimation of the finite population mean of a survey outcome with categorical covariates and externally observed categorical post‐stratifiers. We compare inferences from the proposed method with existing design‐based estimators via simulations. We apply our methods to school‐level data from California Department of Education to estimate the mean academic performance index (API) score in years 1999 and 2000. We end with a discussion.

Suggested Citation

  • Sahar Z. Zangeneh & Roderick J. Little, 2022. "Likelihood‐Based Inference for the Finite Population Mean with Post‐Stratification Information Under Non‐Ignorable Non‐Response," International Statistical Review, International Statistical Institute, vol. 90(S1), pages 17-36, December.
    • Handle: RePEc:bla:istatr:v:90:y:2022:i:s1:p:s17-s36
    DOI: 10.1111/insr.12527
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    References listed on IDEAS

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    1. Kott, Phillip S. & Chang, Ted, 2010. "Using Calibration Weighting to Adjust for Nonignorable Unit Nonresponse," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1265-1275.
    2. Nilanjan Chatterjee & Yi-Hau Chen & Paige Maas & Raymond J. Carroll, 2016. "Constrained Maximum Likelihood Estimation for Model Calibration Using Summary-Level Information From External Big Data Sources," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 107-117, March.
    3. Little R.J., 2004. "To Model or Not To Model? Competing Modes of Inference for Finite Population Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 546-556, January.
    4. Roderick J. Little & Donald B. Rubin & Sahar Z. Zangeneh, 2017. "Conditions for Ignoring the Missing-Data Mechanism in Likelihood Inferences for Parameter Subsets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 314-320, January.
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