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Two-stage sampling in the estimation of growth parameters and percentile norms: sample weights versus auxiliary variable estimation

Vamvakas, G; Norbury, C; Pickles, A; (2021) Two-stage sampling in the estimation of growth parameters and percentile norms: sample weights versus auxiliary variable estimation. BMC Medical Research Methodology , 21 , Article 173. 10.1186/s12874-021-01353-3. Green open access

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Abstract

BACKGROUND: The use of auxiliary variables with maximum likelihood parameter estimation for surveys that miss data by design is not a widespread approach, despite its documented improved efficiency over traditional approaches that deploy sampling weights. Although efficiency gains from the use of Normally distributed auxiliary variables in a model have been recorded in the literature, little is known about the effects of non-Normal auxiliary variables in the parameter estimation. METHODS: We simulate growth data to mimic SCALES, a two-stage survey of language development with a screening phase (stage one) for which data are observed for the whole sample and an intensive assessments phase (stage two), for which data are observed for a sub-sample, selected using stratified random sampling. In the simulation, we allow a fully observed Poisson distributed stratification criterion to be correlated with the partially observed model responses and develop five generalised structural equation growth models that host the auxiliary information from this criterion. We compare these models with each other and with a weighted growth model in terms of bias, efficiency, and coverage. We finally apply our best performing model to SCALES data and show how to obtain growth parameters and population norms. RESULTS: Parameter estimation from a model that incorporates a non-Normal auxiliary variable is unbiased and more efficient than its weighted counterpart. The auxiliary variable method is capable of producing efficient population percentile norms and velocities. CONCLUSIONS: The deployment of a fully observed variable that dominates the selection of the sample and correlates strongly with the incomplete variable of interest appears beneficial for the estimation process.

Type: Article
Title: Two-stage sampling in the estimation of growth parameters and percentile norms: sample weights versus auxiliary variable estimation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1186/s12874-021-01353-3
Publisher version: https://doi.org/10.1186/s12874-021-01353-3
Language: English
Additional information: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
Keywords: Auxiliary variable, Weights, Two-stage design, Missing data, Population norms
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > Div of Psychology and Lang Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > Div of Psychology and Lang Sciences > Language and Cognition
URI: https://discovery.ucl.ac.uk/id/eprint/10133792
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