Regarding finite population ratio models, as referenced in the discussion question, see "Application of Efficient Sampling with Prediction for Skewed Data," JSM 2022: 

https://www.researchgate.net/publication/362370770_Application_of_Efficient_Sampling_with_Prediction_for_Skewed_Data. 

Regarding heteroscedasticity being more evident for simple models when appropriate, see https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR.

James, IMO there are two problems here:

1. Statistical inference does not strictly speaking apply to non-probabilty samples.

2. See the references in the paper which is attached below and which as I recall you objected to before.

3.The second problem ls overfitting. You can fit anything you like if you use enough variables. Simply compare polynomial interpolation with lasso regression..

James, apologies. I forget to add the paper and recall that Occam's Razor exists for a reason.

4. And in the cited abstract for the poster they give no real information simply a conclusion. This without solid evidence I wouldn't waste time on it. If the paper appears in JASA PLEASE alert us and we Will see what the real argument is. Best wishes David Booth

David -

Statistical Science is a very prestigious journal, and the authors are with the Joint Program in Survey Methodology out of the Universities of Maryland and Michigan. One is giving the Morris Hansen lecture next week. These are very heavy hitters. Also, they aren't the only ones talking about those methods of inference from nonprobability samples. You're a bit late to be dismissive of that. I am, however, pointing out how the fewer covariates needed the better, as I think you would agree. But to actually get my real point you would probably need to know their methods first.

Thanks - Jim

Jim thanks for the reply if you thought those things were important cite the published paper and not a poster abstract which gives no details . Best wishes, David Booth

BTW if you give the appropriate citation I'd be happy to read the full paper. I had six graduate hours. From Cochran's book from a student of Colin Blythe. Best wishes David Booth

In the discussion question I said

"(That paper is available through Project Euclid, using the DOI found at the link above.)" The link was https://www.researchgate.net/publication/316867475_Inference_for_Nonprobability_Samples. The DOI link is there.

This discussion should be about the problems that may be incurred when multiple covariates are needed, in some way, to arrive at inference from a nonprobability sample, and how much better it is to be able to use a ratio model when the same data item is available, in each case, from a previous census survey, as the lone predictor.  (By "each case" I mean that you do this for each item on the sample survey.)  Of course, this is not always possible. 

Jim, would you please give a summary of what you wish to discuss. The new link is to request a copy through RG, all authors are not on RG and i have to remark that often these requests go unanswered. If you outline what you want to discuss you may well have a better chance of actually having a discussion. David

This is that Project Euclid link:

http://dx.doi.org/10.1214/16-STS598

I am suggesting that when less complex models are required, that works better:

https://www.researchgate.net/publication/362370770_Application_of_Efficient_Sampling_with_Prediction_for_Skewed_Data

"Regarding heteroscedasticity being more evident for simple models when appropriate, see 

Prediction-based inference from finite population sampling is well-established.   See

Valliant, R, Dorfman, A.H., and Royall, R.M.(2000), Finite Population Sampling and Inference: A Prediction Approach, Wiley Series in Probability and Statistics,

and

Chambers, R, and Clark, R(2012), An Introduction to Model-Based Survey Sampling with Applications, Oxford Statistical Science Series. 

This is also in parts of other sampling books such as Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons. 

A classical ratio model is based on less heteroscedasticity than one may usually find in survey data, except when the effective coefficient of heteroscedasticity is reduced by data quality issues from the small responders.  It can be very useful in Official Statistics.  We can estimate sample size requirements for a subpopulation or a population modeled well by a single such model, using a sample drawn in any way which does not miss any important subdivision which would indicate more than one model is needed.  The format for the "formula" for estimating the sample size in such a case is similar to what is found for a simple random sample in Cochran, W.G.(1977), Sampling Techniques, 3rd ed, John Wiley & Sons.  See https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements.  Both cutoff/quasi-cutoff sampling and balanced sampling are discussed. 

Thus we can estimate the sample size required here to make satisfactory inference from a population or subpopulation which falls under the purview of one model-based classical ratio estimator.  This simple result is relatively easily verified. 

So we can see that when a simple model is appropriate, as when a single predictor is the same data item in a previous census, we may more feasibly infer from a nonprobability sample.  

[Note:  Please also see https://www.researchgate.net/post/Can_we_use_inferential_statistics_when_we_have_used_non-probability_sampling.] 

Does anyone have any other experience to discuss?