Eursr data analysis

Data Analysis (eursr-data-analysis)

ESR reviewers are quantitatively demanding and comparative by instinct. Whether your evidence is multilevel coefficients, hazard ratios, growth trajectories, or decompositions, the analysis must be transparent, correctly specified for the data structure, and reproducible. Design decisions live in eursr-research-design; the replication package lives in eursr-transparency-and-data.

When to trigger

• Running main and supporting analyses; building the results section
• A reviewer asked for robustness, the right clustering/level, heterogeneity, or alternative specifications
• Reporting cross-level interactions or country-level effects from few clusters
• Making the analysis reproducible before depositing materials

Analysis norms ESR expects

1. Report uncertainty and magnitude, not just significance — confidence intervals and substantive effect sizes (predicted probabilities, marginal effects), respecting survey design (weights, clustering, strata; design-based SEs).
2. Model the data structure correctly. Multilevel data → random effects or cluster-robust / country fixed effects with the right level; panel data → within estimators matched to the quantity; durations → event-history with correct risk set and time scale.
3. Small macro-N honesty. With ~20-30 countries, country-level SEs are fragile: too few clusters bias cluster-robust SEs, and a single cross-level interaction can rest on a handful of higher-level units. Use df-appropriate methods (e.g., Satterthwaite/Kenward-Roger df, wild cluster bootstrap, or a Bayesian multilevel model) and do not over-interpret macro coefficients.
4. Robustness that probes, not decorates. Alternative measures, samples, codings, and estimators that could break the result; report what you learn, not just that it "holds."
5. Heterogeneity with discipline. Pre-specify or justify subgroups and cross-level interactions; adjust for multiple comparisons; do not mine an interaction and theorize it post hoc.
6. Measurement. Validate latent constructs (CFA, reliability) and, for comparison, report the invariance level reached and what it licenses.

Reproducibility while you work

• One master script regenerates every table/figure from the (constructed) data.
• Set and report seeds for any stochastic step (imputation, bootstrap, MCMC).
• Pin software/package versions (renv.lock, requirements.txt, recorded ssc/net installs).
• Keep the harmonization/recoding code (ISCED/CASMIN, ISCO/ISEI/EGP) auditable — reviewers check it.

What an ESR analyst-reviewer is checking

Reviewer probe	Clears the ESR bar	Triggers a revision flag
"Right level / clustering?"	SEs at the correct level; df-aware macro inference	individual SEs on a country-level claim
"Just a significant coefficient?"	marginal effect + interval tied to the mechanism	stars-only, no interpretation
"Few clusters handled?"	wild bootstrap / Bayesian / df correction	naive cluster SEs on ~20 countries
"Measures comparable?"	invariance reported; partial invariance bounded	latent comparison with no invariance test
"Heterogeneity real or mined?"	pre-specified / MHT-adjusted	one fished cross-level interaction

Worked micro-example (illustrative numbers)

A hypothetical ESR study links active labor-market policy (macro) to unemployment scarring (micro) across 24 countries with harmonized panel data.

Main effect: a past spell lowers later wages 6.1% (95% CI 4.0–8.2), within-person fixed effects
Cross-level interaction: scar is 3.4 pp smaller per 1 SD of activation spending (CI 1.1–5.7) —
  the macro × micro hypothesis from eursr-theory-building
Few-cluster inference: wild cluster bootstrap (countries), p = 0.012; macro claim kept modest (24 df)
Robustness: holds dropping any one country (leave-one-out), and under register- vs survey-measured wages
Reproducible: one master script, seed = 2026, renv.lock pinned; harmonization code archived

The interval carries the micro claim, the cross-level term names the portable mechanism, and the few-cluster inference is handled honestly rather than asserted.

Referee pushback → ESR-specific fix

• "Your country-level SEs are too optimistic." → Re-estimate with a wild cluster bootstrap or a Bayesian multilevel model; report the df and temper the macro claim.
• "Robustness agrees by construction." → Add a spec that could break it (alternative harmonization, leave-one-country-out, placebo period) and report what you learned.
• "Significant but does it matter?" → Give a predicted-probability or marginal-effect scenario and name what changes for the comparative debate.

Calibration anchors

• Get the level right or nothing else counts. ESR's signature error is mismatched SEs/clustering on a multilevel or comparative claim — fix the variance structure first.
• Few clusters demand humility. ~20-30 countries cannot support strong macro-level inference with naive SEs; df-aware methods and modest claims are expected.
• Magnitude over significance. Report marginal effects and intervals a comparative reader can interpret, not stars.

Execution bridge (StatsPAI / Stata MCP)

Run the battery, don't just enumerate it. Full map: execution-with-mcp. ESR is comparative quantitative sociology; cross-country panels with confounded institutions — foreground fixed effects and clustering.

• Many outcomes / specifications: romano_wolf (step-down FWER) or benjamini_hochberg — report the adjusted threshold.
• OVB sensitivity: oster_delta / sensemakr.
• Inference: wild_cluster_bootstrap (few clusters), twoway_cluster / conley; multilevel data → cluster at the right level.
• Re-fit off one handle: audit_result(result_id) lists the missing checks and the exact suggest_function for each.
• Exhibits: etable / did_summary_to_latex from the handle — no retyped numbers.

Keep the decisive checks in the body and the exhaustive battery in the supplement. See the executed chain in the JF execution walkthrough.

Anti-patterns

• Individual-level SEs on a country-level coefficient; naive cluster SEs on ~20 countries
• Stars-only tables with no effect sizes or intervals; ignoring survey weights
• "Robustness" that only reruns near-identical specs to manufacture stability
• p-hacking / HARKing an exploratory cross-level interaction into a hypothesis
• Latent cross-national comparisons reported without an invariance check

Output format

【Main result】marginal effect + interval
【Data structure handled】level / clustering / panel estimator correct? [Y/N]
【Cross-level / macro inference】few-cluster method + df honest? [Y/N]
【Robustness】what held (incl. leave-one-country-out)
【Reproducible】master script + seeds + pinned versions + harmonization code? [Y/N]
【Next】eursr-tables-figures

Supplementary resources

• ../../resources/external_tools.md — multilevel, event-history, SEM, and decomposition packages
• ../../resources/code/ — reproducible estimation skeleton (DiD/IV/RDD/DML + robustness)
• ../../resources/official-source-map.md — ESR replication and reporting norms