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Seek a Paradigm and Distrust It? Statistical Arguments and the Representation of Uncertainty

Published onSep 19, 2023
Seek a Paradigm and Distrust It? Statistical Arguments and the Representation of Uncertainty
key-enterThis Pub is a Commentary on

Bailey (2023a) does a very useful service to the polling and broader survey sampling communities by highlighting the insights that the Meng (2018) equation provides into current statistical practice in that area. Through the emphasis on the continuous nature of the independent and interactive effects of the data defect correlation (ρ) and population size on error (putting aside the ‘problem difficulty’), we see clearly how relying solely on expectations (in both the statistical and everyday senses) can lead us astray in real-world problems. While I fully endorse the general message of Bailey (2023a) that the clarity of the Meng identity forces analysts to take departures from random (or any probability) sampling more seriously, and provides a neat framework for understanding the logical unity of existing weighting-type methods (as elegantly explained by Meng, 2022a), I have two small comments regarding his proposed paradigm shift. The first relates to the seemingly quite strong dismissal of the existing methods within the missing at random (MAR) or conditional ignorability toolbox; the second builds on this to consider the wider problem of the full communication of the potential uncertainty associated with descriptive inferences from nonprobability samples.

From ‘Pollwashing’ to Poll Cleansing

The insights of Professors Bailey and Meng point toward greater acknowledgment of the potential effects of often dubious assumptions in survey sampling, wherever these may occur. Rather than this leading toward an automatic rejection or distrust of some methods, and an embracing of others, this seems to fall well within the tradition of a wholesome skepticism of all model-based results presented without adequate context and humility (e.g. Freedman, 2010; Greenland, 2021; Hodges, 1996; Mallows, 1998; Saltelli et al., 2020; Swanson, 2023; Thompson, 2022). Bailey (2023a) suggests that the concept of representativeness is essentially a ‘pollwashing’ technique, in that the claims of a reweighted, or otherwise adjusted, nonprobability sample to represent the population of interest can never be unambiguously evaluated. I struggle to see how this argument can be admitted as a fatal weakness of the MAR methods undergirt by this concept, while statistical modeling in general still breathes. We can no doubt agree that some claims of representativeness are better than others, but surely this depends on evaluation(s) of the arguments put forward by those doing the adjusting for any given purpose? Statistical models do not (or should not; Thompson, 2022) exist in a vacuum, and the presentation of population inferences resulting from reweighted samples are nowhere required to be foisted on a public without self-criticism. Auxiliary variables can be evaluated and justified by researchers just as well, or as poorly, as any assumption (by, for example, using theory and qualitative research, or extra-statistical logic such as causal graphs), and targeted sensitivity analyses performed where these are uncertain. If variables considered to be important for adjustment are unavailable, the usefulness of proxy variables can be discussed and investigated.

If the objection of Professor Bailey to representativeness is one of precise boundaries allowing the analyst to claim success in representation, then one immediately thinks of all the other arbitrary, and largely unhelpful, sharp boundaries in everyday use in statistical methods (null hypothesis significance testing, anyone?), and the extensively developed counterarguments for the importance of more nuanced continuous thinking (e.g. Greenland 2023b, 2023a). No doubt some assertions of representativeness by researchers are vague and meaningless, with little practical merit, but rejecting the concept as misleading or useless seems to brook no admittance of principled, well-theorized adjustments presented with appropriate sensitivity analyses or other caveats. The core concept of representativeness within the MAR framework, that is, whether or not adjusting for some variables that predict both survey response and outcome enables useful population inferences, seems little different in substance to the empirical reality of other key theoretical ideas in statistics, such as exchangeability (Draper et al., 1993). I suspect that none of this is in particular disagreement with Professor Bailey’s thoughts, I merely seek to emphasize the sliding scale of error highlighted by Meng (2018), and the checks and balances that might be associated with this, as a more inclusive broadening of the traditional paradigm than one that singles out the potential weaknesses of MAR assumptions only. Data analysts should by now appreciate that all models are wrong; the more important point is whether the missing parts of reality that stalk us are mice or tigers (Box, 1976; Stark 2022). The habit of shining a light on these, and naming them as well as we are able, may allow us to move from accusations of pollwashing to a regular practice of ‘poll cleansing.’

Field Guides to Mice and Tigers

Professor Bailey, both here and in his very readable and useful book (Bailey, 2023b), points to a number of ways in which this poll cleansing might be achieved, including his central points about investigating and attempting to minimize data missing not at random (MNAR) situations. As he recognizes more extensively in his book (Bailey, 2023b), other tools are available to ensure that we are not convicted of pollwashing, methods of better bounding our estimates with intervals that acknowledge potential biases and other sources of uncertainty, for example (he highlights Hartman & Huang, 2023, and Manski, 1990). Other techniques in this area have been suggested elsewhere, and these could be further explored by survey samplers (e.g. Coker et al., 2021; Meng, 2022b; Reichardt & Gollob, 1987). In a similar vein of exploring and exposing our assumptions to criticism, graphical plots of auxiliary variable balance before and after adjustment (e.g. Boyd et al., 2023; Makela et al., 2014), quantitative analogues of these in the form of R-indicators (Schouten et al., 2012), and transparent statements of the theory lying behind such adjustments in the form of causal graphs (Lee et al., 2023; Mohan & Pearl, 2021) or verbal models (Thompson, 2022), could also be included in reports. Potential indicators of nonignorable selection bias are also being rapidly developed (Andridge et al., 2019; Boonstra et al., 2021; Little et al., 2020). Perhaps more obviously, multiple model fits can also be presented: Little and Rubin (2020, pp. 402–403) describe such a case where both MAR and MNAR models were provided to a client. No doubt there is a rich vein of research here around how such model ‘multiverses’ (Steegen et al., 2016) can be most effectively communicated for different purposes (e.g. Liu et al., 2021).

The tradition of qualitative ‘risk of bias’ assessments for the internal validity of experiments and observational studies provides a further source of ideas in this area (Pescott et al., 2023), and I wonder whether reporting standards could be erected for assessments of polling sample external validity (i.e., generalizability) in the same way that is being attempted for descriptive inferences in other disciplines (Boyd et al., 2022; Simons et al., 2017)? The argument has been made by Sterba and colleagues (2011) that the clear presentation of information relating to nonprobability sampling is an ethical issue, and leading survey sampling statisticians have already called for such considerations to become standard (Lohr, 2022; Valliant, 2023). There seems to be a practical question here for the polling community (in its broadest sense) that I have not seen addressed: if polling samples are fully evaluated for their potential weaknesses, and broader estimates of uncertainty presented, will the resulting polling products be of practical use and interest? I assume that such information, being more realistic, would be useful for betting markets, but it seems likely that the media (and partisan funders?) would find it less attractive. It would certainly be interesting to learn Professor Bailey’s opinion on whether poll cleansing would be likely to survive and reproduce within the current environment.

Disclosure Statement

The author was supported by the NERC Exploring the Frontiers award number NE/X010384/1, “Biodiversity indicators from nonprobability samples: Interdisciplinary learning for science and society.”


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©2023 Oliver Pescott. This article is licensed under a Creative Commons Attribution (CC BY 4.0) International license, except where otherwise indicated with respect to particular material included in the article.

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