Extracting GLMM Results with broom.mixed

Why Extract Results With a Tidy Method?

A fitted GLMM object contains several kinds of results: population-level coefficients, estimated random-effect variation, and, when requested, cluster-specific random-effect estimates. They are not interchangeable. A table that reports a cluster-level estimate as though it were a population-level coefficient, or labels a standard deviation as a variance, can change the meaning of the analysis even when the numbers were extracted correctly.

The broom.mixed::tidy() function provides a structured way to request and organize these results. The goal is not merely to make a model output look neat. It is to select the intended quantity, retain the information needed to interpret it, and label the result precisely. The examples use a hypothetical logistic random-intercept model; the same distinction among result types applies to other GLMM families.

Model and Extraction Assumptions

Suppose a binary outcome is observed for patients in clinics. Let \(Y_{ij}=1\) indicate improvement for patient \(i\) in clinic \(j\), let \(A_{ij}\) be age in years, and let \(T_{ij}\) indicate a treatment group. A logistic random-intercept GLMM can be written as

This model assumes that, conditional on the clinic random intercept and the stated predictors, the outcomes follow the specified Bernoulli model; the clinic intercepts follow a mean-zero normal distribution with variance \(\sigma_b^2\); and the random intercepts are independent across clinics. The fixed-effect coefficients describe log-odds changes conditional on the random intercept. In particular, \(\exp(\beta_T)\) is a conditional odds ratio for treatment versus its reference group, holding age and the clinic intercept fixed.

Extraction does not establish that these assumptions are reasonable. It also does not remedy a failed fit. Before preparing a results table, check the model fit and the analysis choices that produced it, including convergence warnings, the intended reference categories, and whether the model formula matches the design. A tidy table is a presentation of model output, not an independent validation of the model.

For a fitted glmer object, the usual fixed-effect request is broom.mixed::tidy(fit, effects = "fixed"). Its rows represent fixed-effect terms; typical columns include term, estimate, std.error, statistic, and p.value. The exact available columns can depend on the model and method. Inspect the returned object before selecting columns, rather than assuming every model supplies every inferential quantity.

Choosing Among Fixed and Random Effects

The effects argument controls which part of the fitted object is being tidied. For a mixed model, three useful requests have different interpretations:

For example, broom.mixed::tidy(fit, effects = "ran_pars", scales = "sdcor") requests random-effect parameters on standard-deviation/correlation scales. A random-intercept estimate of 0.50 in the estimate column is a standard deviation on the logit scale, not a variance and not a clinic-specific intercept. Its corresponding variance is \(0.50^2=0.25\) on the logit scale.

By contrast, effects = "ran_vals" requests estimated conditional random-effect values for particular grouping levels. These are often conditional modes or empirical Bayes estimates, not additional fixed coefficients and not directly observed clinic effects. Their estimates depend on the fitted model and are generally shrunk toward the population mean. If the scientific aim is a population-level comparison, these level-specific values do not replace the fixed-effect results.

From Tidy Output to a Publication Table

A useful table is selective but not ambiguous. Keep the term name, estimate, standard error, and whichever inferential columns the model supports. For a logistic model, transformations for a conditional odds-ratio table should be applied to the fixed-effect estimates and their interval limits, not to standard errors or test statistics. A simple Wald interval can be calculated on the coefficient scale and then exponentiated:

This interval uses a large-sample normal approximation for the coefficient estimate. It should be identified as a Wald interval, and it may be unreliable when estimates are poorly determined or the approximation is weak. Random-effect standard deviations require their own appropriate uncertainty method; do not apply the fixed-effect Wald formula to them automatically.

A practical workflow is to save the tidy output, inspect its column names and labels, select the fixed-effect rows, calculate any desired transformed estimates, and then assign reader-facing labels. For example, an R workflow can begin with fixed <- broom.mixed::tidy(fit, effects = "fixed"), followed by dplyr::select(fixed, term, estimate, std.error, statistic, p.value). If the table needs odds ratios and Wald limits, calculate those as new columns from estimate and std.error, and state the interval method in a table note. The symbol <- here is R's assignment operator.

The extracted term names may be machine-oriented, especially for factor contrasts and interactions. Replace them with explicit labels only after confirming the reference level and contrast coding. For example, “Treatment: intervention vs reference” is more informative than a bare factor name. Include units for continuous predictors, such as “Age, per year,” and state that odds ratios are conditional on the random effects. Avoid hiding the intercept or contrasts by filtering rows without a clear reporting reason.

Derivation and Checks Before Reporting

The transformation used above follows directly from the logistic model. For a one-unit increase in a predictor with coefficient \(\beta\), holding the other predictors and random effect fixed, the log odds change from \(\eta\) to \(\eta+\beta\). Since odds are the exponential of log odds, the ratio of the new odds to the old odds is

For an approximate 95% coefficient interval \(\hat{\beta}\pm1.96SE\), exponentiation is valid because the exponential function is increasing: it preserves the order of the lower and upper limits. The resulting interval is therefore on the odds-ratio scale. The same calculation does not make a confidence interval exact, nor does it change the conditional interpretation of the coefficient.

Before exporting a table, verify that the selected rows are the intended effect type; that the grouping variable and term match the model; that standard deviations and variances are not mislabeled; and that transformed estimates and limits are calculated from the same coefficient and standard error. Check the model's convergence messages and whether a random-effect variance is estimated near zero. A singular fit or unstable estimates are reasons to investigate the fit, not reasons to suppress an inconvenient row.

For standard model output, summary(fit) is a direct alternative and is useful for checking what the fitted object reports. It is less convenient for consistent data-frame workflows. broom.mixed::tidy() makes selection and downstream table construction easier, but its flexibility creates opportunities to select the wrong effect or drop essential context. Neither approach decides which results are scientifically relevant or verifies the model assumptions. A publication table should also be checked against the model specification and the intended estimand.

Common Mistakes and Limitations

• Treating all tidy rows as fixed effects. Random-effect parameters and level-specific estimates answer different questions. Select the intended type explicitly with effects.
• Calling a standard deviation a variance. A random-intercept SD of 0.50 corresponds to variance 0.25; report the scale actually returned or calculated.
• Exponentiating the standard error. For an odds-ratio interval, exponentiate coefficient limits. The standard error itself remains a measure on the coefficient scale.
• Assuming a p-value is always available or decisive. Its presence and method depend on the fitted model and tidier. Report it only when supported, and do not interpret it as the probability that the null hypothesis is true.
• Assuming tidy output means a successful analysis. Extraction does not diagnose convergence, singularity, poor coding, or model misspecification.

Tidy results are also not a complete record of an analysis. A table alone may omit the family, link, random-effects structure, reference categories, sample size, and interval method. Include enough model and table-note information for the reader to understand the reported estimand and reproduce the presentation choices.