How to report a linear mixed model in a paper

Mixed models are reported inconsistently across the literature, which makes them harder to review. Here is what to include.

Describe the model before the results

State the outcome, the fixed effects, and crucially the random effects structure. This is the part most often omitted and most often queried.

A linear mixed model was fitted with reaction time as the outcome, condition and session as fixed effects, and random intercepts for participant.

If you fitted random slopes, say so and say for which term. Random intercepts only, and random intercepts plus slopes, are different models that can give different answers.

Say which software and estimation method

Models were fitted using restricted maximum likelihood (REML).

REML for estimating variance components, ML when comparing models with different fixed effects via likelihood ratio tests. Name which you used and why if you switched.

Report the fixed effects

Estimate, standard error, degrees of freedom, t or z, p-value, and a confidence interval for each. The estimate and its interval carry the science; the p-value alone does not.

Condition significantly predicted reaction time, b = -24.3, SE = 6.1, 95% CI [-36.3, -12.3], t(112.4) = -3.98, p < .001.

Report the random effects

Variance and standard deviation for each random term, plus the residual variance. This tells your reader how much variation sat between participants versus within them.

Explain the degrees of freedom

Mixed models do not have exact degrees of freedom, so software approximates them, commonly by Satterthwaite or Kenward-Roger. Fractional df in your output is normal. Name the method.

Mention convergence

If the model failed to converge with your intended random structure and you simplified it, say so. Reviewers would far rather read that than discover it.

In Plotara

Linear, logistic and Poisson mixed models, with the random effects structure, variance components and fixed effects reported together, and Python export for the full specification.