Uncommon Ground

You really need to check your statistical models, not just fit them

I haven’t had a chance to read the paper I mention below yet, but it looks like a very good guide to model checking – a step that is too often forgotten. It doesn’t do us much good to estimate parameters of a statistical model that doesn’t do well at fitting the data we have. That’s what model checking is all about. In a Bayesian context, posterior predictive model checking is particularly useful.1 If the parameters and the model you used to estimate them can’t reproduce the data you collected reasonably well, the model isn’t doing a good job of fitting the data, and you shouldn’t trust the parameter estimates.

If you happen to be using Stan (via rstan) or rstanarm, posterior predictive model checking is either immediately available (rstanarm) or easy to make available (rstan) in Shinystan. It’s built on the functions in bayesplot, which provides the underlying functions for posterior prediction for virtually any package (provided you coerce the result into the right format). I’ve been using bayesplot lately, because it integrates nicely with R Notebooks, meaning that I can keep a record of my model checking in the same place that I’m developing and refining the code that I’m working on.

Here’s the title, abstract, and a link:

A guide to Bayesian model checking for ecologists

Paul B. Conn, Devin S. Johnson, Perry J. Williams, Sharon R. Melin, Mevin B. Hooten

Ecological Mongraphs doi: 10.1002/ecm.1314

Checking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously accounting for observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack of fit when applying Bayesian methods than when applying more traditional modes of inference such as maximum likelihood. There are also multiple ways of assessing the fit of Bayesian models, each of which has strengths and weaknesses. For instance, Bayesian P values are relatively easy to compute, but are well known to be conservative, producing P values biased toward 0.5. Alternatively, lesser known approaches to model checking, such as prior predictive checks, cross‐validation probability integral transforms, and pivot discrepancy measures may produce more accurate characterizations of goodness‐of‐fit but are not as well known to ecologists. In addition, a suite of visual and targeted diagnostics can be used to examine violations of different model assumptions and lack of fit at different levels of the modeling hierarchy, and to check for residual temporal or spatial autocorrelation. In this review, we synthesize existing literature to guide ecologists through the many available options for Bayesian model checking. We illustrate methods and procedures with several ecological case studies including (1) analysis of simulated spatiotemporal count data, (2) N‐mixture models for estimating abundance of sea otters from an aircraft, and (3) hidden Markov modeling to describe attendance patterns of California sea lion mothers on a rookery. We find that commonly used procedures based on posterior predictive P values detect extreme model inadequacy, but often do not detect more subtle cases of lack of fit. Tests based on cross‐validation and pivot discrepancy measures (including the “sampled predictive P value”) appear to be better suited to model checking and to have better overall statistical performance. We conclude that model checking is necessary to ensure that scientific inference is well founded. As an essential component of scientific discovery, it should accompany most Bayesian analyses presented in the literature.

  1. Andrew Gelman introduced the idea more than 20 year ago (link), but it’s only really caught on since his Stan group made some general purpose packages available that simplify the process of producing the predictions. (See the next paragraph for references.)

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