Shoppers of statistics, take note: readers and researchers are increasingly turning to multilevel regression and poststratification (MRP) to move from noisy individual surveys to clear, state‑level stories , and why that matters when you want to link public opinion to policy. This piece looks at a classic example and what to learn if you plan to use MRP in follow‑up analyses.

Essential Takeaways

  • What MRP does: MRP smooths survey responses across demographic and geographic cells, producing stable small‑area estimates like state support rates that feel less jumpy and more plausible.
  • Classic use case: Lax & Phillips (2009) used MRP to estimate state‑level support for gay‑rights protections and then related those estimates to whether states adopted protections.
  • Model ingredients matter: The multilevel model included individual covariates (age, race, education, gender), state effects and poll effects, plus state‑level predictors such as percent religious conservatives.
  • Poststratification practicalities: You must weight model predictions to the population structure , census counts by demographic cells , so estimates reflect real populations, not just survey composition.
  • Caveat for later analyses: Treat MRP outputs as estimates with uncertainty; propagating that uncertainty into policy‑level regressions is essential to avoid overconfident conclusions.

Why Lax & Phillips remains a go‑to example for MRP in applied research

The paper feels tactile , you can almost see the state maps and the colourful trend lines. Lax & Phillips wanted to know whether states with higher public support for anti‑discrimination laws were more likely to adopt such laws. They couldn’t rely on raw survey proportions because sample sizes varied wildly by state, so they used MRP to produce smoother state estimates that borrow strength across demographics and polls. According to the authors, this approach produced more credible E(y | state) estimates than simple weighting.

How the multilevel regression was built: the anatomy of the “MR”

Lax & Phillips modelled individual support (y_i) as a function of age, race, gender, education, the respondent’s state, and poll id. The state term itself was partially explained by state‑level covariates like the share of religious conservatives and the 2004 Democratic vote. This two‑stage thinking , individuals nested in states, plus contextual predictors , is exactly where multilevel models shine: they control for individual composition while letting state contexts do explanatory work. If you’re building your own, include poll effects when combining multiple surveys, and think about interactions you suspect matter.

Poststratification: why it’s not just a weighting trick

After fitting the model, the authors poststratified: they predicted support for every demographic–state cell in the population frame and averaged those predictions using population counts. That step moves you from modelled cell probabilities to an estimate of the state’s overall public opinion, E(y | s). Practically, you need decent population margins , census or administrative counts , and a clear cell structure. Too many cells with sparse population data and your poststratified average becomes unstable, so keep the cell grid sensible.

Using MRP estimates as predictors: do it, but carry the uncertainty

Lax & Phillips then regressed state policy adoption on their MRP state‑level opinion estimates, modelling Pr(policy_s = 1) = logistic(a + b * y_s^pred). It’s a neat way to ask whether public opinion predicts action, but there’s a statistical gotcha: y_s^pred is estimated, not observed, so treating it as fixed ignores uncertainty and can bias inference. Modern practice is to propagate the posterior draws of y_s through the policy model or fit a joint model in one go. Researchers today often use Bayesian workflows to keep uncertainty intact.

What changed since 2009 and practical tips for today’s analysts

MRP has gone mainstream: researchers use it for estimates at substate levels, for new outcomes like consumer preferences, and in policy work. Online resources and primers explain the steps and pitfalls. If you’re trying this yourself, start with a modest cell structure, include relevant demographic and poll effects, check model fit with held‑out data, and always map estimated margins against known aggregates. And if you want to link estimates to later outcomes, run the policy model across posterior draws or build a unified hierarchical model so uncertainty travels where it should.

A quick checklist before you report MRP‑based analyses

Decide your cell scheme and ensure you have population counts; include poll and sampling‑frame effects; check that state effects can be partially explained by sensible covariates; visualise maps and uncertainty; and propagate uncertainty into any downstream regressions. These steps keep your story honest and your conclusions defensible.

It's a small change in workflow that makes later analyses clearer and more believable , and your maps a lot easier on the eye.

Source Reference Map

Story idea inspired by: [1]

Sources by paragraph: