GLMM: Gaussian and Binomial

How to fit a generalized linear mixed model in Licklider, which families are supported, and when to use a GLMM instead of a simpler model.

A generalized linear mixed model (GLMM) extends standard regression by including both fixed effects — the predictors whose coefficients you want to estimate — and random effects, which account for the correlation structure in the data.

GLMMs are used when observations are not independent: when multiple measurements come from the same subject, when subjects are nested within groups, or when there is another clustering structure in the data that should be accounted for.

When to use a GLMM

A GLMM is appropriate when:

  • The same subject contributes multiple observations (repeated measures)
  • Observations are nested within groups that are not of direct interest (for example, animals within litters, patients within clinics)
  • The outcome is binary and the data has a clustering structure

If the data is independent and ungrouped, a standard linear or logistic regression is simpler and preferable.

Supported families

Licklider supports two distribution families:

Gaussian (identity link)

For continuous outcomes. The model is equivalent to a linear mixed model (LMM). This is the appropriate choice when the outcome is numeric and approximately normally distributed within each level of the random effect.

Binomial (logit link)

For binary outcomes. The model is a mixed-effects logistic regression. Each coefficient represents the change in log-odds of the outcome associated with a one-unit change in the predictor, holding the random effect constant.

Random effects

Licklider supports a random intercept model. The random intercept allows the baseline level of the outcome to vary across subjects or clusters.

For example, in a study where the same animals are measured across multiple time points, the random intercept accounts for the fact that some animals are systematically higher or lower than others at baseline.

Random slopes — where the effect of a predictor is allowed to vary across subjects — are not currently supported.

This is a deliberate scope limit. Random intercept models cover many common repeated-measures and clustered-data use cases while keeping the model structure easier to specify and less fragile in smaller applied datasets. However, some designs do require random slopes for valid uncertainty estimates, so a fitted random-intercept model should not be interpreted as proof that the chosen random-effect structure is sufficient.

How to request it

Describe the analysis and the clustering structure in the Chat. For example:

  • "Fit a mixed model with subject as a random effect"
  • "Run a GLMM for this binary outcome with subject ID as the grouping variable"
  • "Use a linear mixed model to account for repeated measurements per animal"

What the results include

Coefficient table

One row per fixed-effect predictor. Each row shows the estimate, standard error, z- or t-statistic, p-value, and 95% confidence interval.

For Gaussian models, coefficients are interpreted on the original outcome scale. For Binomial models, coefficients are interpreted on the log-odds scale.

Model structure summary

The output identifies the model family (Gaussian or Binomial) and the grouping variable used for the random intercept, so readers can see which clustering structure the fit is attempting to account for.

Convergence status

Whether the fitting algorithm reached a stable solution. Non-convergence may indicate that the model is too complex for the data, or that the random effect structure is not supported.

Warnings

Any numerical issues encountered during fitting are reported alongside the results.

At minimum, a reader should expect the page to tell them which family was used, which grouping variable was treated as the random intercept, whether the model converged, and whether numerical warnings were raised.

Gaussian vs Binomial: choosing the right family

Specify the outcome type in your request. If the outcome is continuous, Licklider will use Gaussian by default. If the outcome is binary, specify this in the Chat or ensure the outcome column contains only two distinct values.

The family choice follows the scale of the outcome because the Gaussian model targets continuous measurements, while the Binomial model targets binary event probabilities. Using the wrong family can distort both interpretation and uncertainty, so the outcome type is the first decision Licklider needs to get right.

What Licklider does not decide for you

Licklider can fit a GLMM once you specify the clustering structure, but it does not automatically determine whether the grouping variable you provided is scientifically correct. If the true dependence is at the donor, animal, litter, plate, clinic, or batch level and the wrong grouping variable is supplied, the model may still converge while reporting standard errors and p-values that are too optimistic.

Licklider also does not automatically determine whether a random intercept is enough for your design. If the effect of time, treatment, or another predictor varies systematically across subjects or clusters, a random-slope structure may be scientifically necessary even though the current product does not support it.

Convergence alone is not a guarantee that the model is well specified. A converged fit can still be inappropriate if the family is wrong, the grouping structure is incomplete, or the fixed-effect specification does not match the study design.

If you are unsure about the observation unit, grouping variable, or whether repeated structure is present, review Repeated Measures and Mixed Models, Repeated Measures Model Suggestion, and Pseudoreplication Detection before relying on the output.

Design rationale and references

Licklider currently supports Gaussian and Binomial mixed models because these cover the most common researcher-facing use cases in this product: continuous repeated outcomes and clustered binary outcomes. The family choice is therefore tied directly to the outcome scale rather than exposed as an open-ended modeling menu.

Licklider currently limits the random-effect structure to a random intercept because this is the most common first-step correction for within-subject or within-cluster dependence, and it is easier for non-specialist users to specify correctly. More complex structures can be scientifically important, but they are also easier to mis-specify and more likely to produce unstable fits in smaller datasets.

That design means the current GLMM page should be read as a supported mixed-model entry point, not as a complete mixed-effects modeling system. When the design likely requires random slopes or a more elaborate covariance structure, the limitation should be treated as substantive rather than cosmetic.

References

  1. Bolker, B. M., Brooks, M. E., Clark, C. J., Geange, S. W., Poulsen, J. R., Stevens, M. H. H., & White, J.-S. S. (2009). Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology & Evolution, 24(3), 127-135. https://doi.org/10.1016/j.tree.2008.10.008
  2. Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255-278. https://doi.org/10.1016/j.jml.2012.11.001

What this page does not cover