Reporting linear mixed model (LMM) results requires you to present fixed effects, random effects, model fit information, and assumption checks. Unlike standard regression, mixed models have a layered structure that reviewers expect to see fully documented. Missing any of these layers is one of the most common reasons for revision requests. Here’s how to report each component clearly.
What to Include in the Methods Section
Before presenting any numbers, your methods section needs to specify several decisions you made when fitting the model. State the outcome variable, the fixed effects (and why you included them), and the random effects structure, including which grouping variable defines your clusters (e.g., participants, schools, hospitals). If you allowed random slopes in addition to random intercepts, say so explicitly and explain why.
You also need to name the software package and version you used. This matters more for mixed models than for standard regression because packages differ in how they estimate parameters and compute p-values. If you used the lme4 package in R, note that it does not produce p-values by default. You must specify which method you used to obtain them: the Satterthwaite approximation, the Kenward-Roger approximation, or likelihood ratio tests. Each gives slightly different results, and reviewers will want to know which one you chose. Packages like nlme in R or PROC MIXED in SAS handle this differently, so the key is transparency about your specific workflow.
Finally, state the estimation method: restricted maximum likelihood (REML) or full maximum likelihood (ML). If you compared nested models using likelihood ratio tests or information criteria, note that ML estimation is required for those comparisons.
Reporting Fixed Effects
Fixed effects are the core findings of your model, the equivalent of regression coefficients in standard regression. For each fixed effect, report the estimate (b or β), the standard error, the test statistic (t-value or F-value), degrees of freedom, the p-value, and ideally a 95% confidence interval. The confidence intervals from a mixed model already account for the correlation among clustered observations, which makes them more appropriate than intervals from a standard regression applied to the same data.
In running text, this typically looks something like: “Participants in the sleep deprivation condition had significantly higher error thresholds than those in the control condition (b = 3.42, SE = 0.87, t(45.3) = 3.93, p < .001, 95% CI [1.67, 5.17]).” Notice the degrees of freedom are not a whole number. That’s normal for mixed models when using approximations like Satterthwaite or Kenward-Roger, and you should report them as given rather than rounding to an integer.
When you have several fixed effects, a table is cleaner than listing everything in the text. A well-structured table includes one row per predictor, with columns for the estimate, standard error, degrees of freedom, t-value, p-value, and confidence interval. Summarize the key findings in the text and let the table carry the full detail.
Reporting Random Effects
Random effects capture how much variability exists across your grouping units, such as individual differences in a repeated-measures study or school-level differences in an education study. For each random effect, report the variance (σ²) and its square root, the standard deviation. If your model includes both a random intercept and a random slope, also report the correlation between them.
A common way to contextualize the random effects is with the intraclass correlation coefficient (ICC), which tells readers what proportion of the total variance sits at the cluster level. An ICC of 0.30 means 30% of the variability in your outcome is attributable to differences between clusters rather than differences within them. The ICC from a null model (one with no predictors) is especially useful because it justifies using a mixed model in the first place. If the ICC is near zero, a standard regression might have sufficed.
You can present random effects in the same table as fixed effects, separated into their own panel, or in a dedicated table. The LEVEL reporting guidelines from BMC Medical Research Methodology recommend a summary table that includes fixed effect estimates and variance components (or ICCs) for the null model, any intermediate models, and the final model. This lets readers see how the variance components changed as you added predictors.
Effect Sizes for Mixed Models
Standard R² doesn’t apply directly to mixed models, but an adapted version developed by Shinichi Nakagawa and Holger Schielzeth has become widely accepted. It produces two values. The marginal R² reflects the variance explained by fixed effects alone. The conditional R² reflects the variance explained by the entire model, fixed and random effects together. Reporting both gives readers a sense of how much your predictors explain versus how much the clustering structure itself accounts for.
For example, a model might have a marginal R² of 0.30 and a conditional R² of 0.93. That tells you the fixed effects explain about 30% of the variance in the outcome, but once you account for cluster-level differences, the model captures 93% of the total variance. In R, the performance package calculates both values directly. In your results, you can report these as: “The fixed effects explained 30.3% of the variance (marginal R² = .303), and the full model including random effects explained 93.3% (conditional R² = .933).”
Model Comparison and Selection
If you compared multiple models to arrive at your final one, report the logic and statistics behind those comparisons. The two most common approaches are information criteria (AIC and BIC) and likelihood ratio tests.
AIC balances model fit against complexity: it penalizes models with more parameters so you don’t overfit. Lower AIC indicates a better trade-off. BIC applies a harsher penalty for additional parameters, especially with larger sample sizes, so it tends to favor simpler models. When comparing models, report the AIC and BIC for each, along with the difference in AIC (ΔAIC) between competing models. A ΔAIC greater than 2 is often treated as meaningful support for the better-fitting model, though this threshold is more liberal than a traditional p = .05 cutoff.
For nested models (where one model is a simplified version of the other), likelihood ratio tests provide a direct statistical comparison. Report the chi-square statistic, the degrees of freedom (equal to the difference in the number of parameters), and the p-value. For instance: “A likelihood ratio test indicated that the model with a random slope for time fit significantly better than the random-intercept-only model (χ²(2) = 12.4, p = .002).”
Present these comparisons in a table when you tested more than two models. Include columns for the number of parameters, log-likelihood, AIC, BIC, and the results of any pairwise likelihood ratio tests.
Documenting Assumption Checks
Mixed models assume that residuals are normally distributed with constant variance and that random effects are normally distributed. Reviewers expect you to state that you checked these assumptions, even if briefly.
The standard diagnostic tools are a Q-Q plot of residuals (checking normality) and a plot of fitted values versus residuals (checking constant variance). Residuals should fall roughly along the diagonal in the Q-Q plot and show no fan-shaped or curved pattern in the fitted-versus-residuals plot. Perfect diagnostics are rare, and slight departures from normality are generally acceptable. If you found a meaningful violation, report what you did about it. Transforming the outcome variable (such as taking the square root) is a common fix for non-constant variance. If you applied a transformation, state it clearly so readers can interpret your coefficients correctly.
You don’t need to include the diagnostic plots in your main results section, but mention that you inspected them and note any corrective steps. Many journals accept diagnostic plots as supplementary material.
Structuring the Results Table
A well-organized results table is the backbone of your LMM reporting. Here’s what to include:
- Fixed effects panel: One row per predictor, with columns for estimate, SE, df, t-value, p-value, and 95% CI.
- Random effects panel: One row per variance component (e.g., random intercept variance, random slope variance, their correlation), plus the residual variance.
- Model-level statistics: ICC, marginal R², conditional R², AIC, BIC, and number of observations and clusters.
If you built your model in steps, show the null model alongside the final model so readers can see how adding predictors shifted the variance components and improved fit. The LEVEL guidelines specifically recommend this progression format for multilevel analyses.
Putting It Together in Text
Your running text should walk the reader through the key findings without duplicating every number from the table. A typical results paragraph might read: “We fit a linear mixed model with reaction time as the outcome, condition and trial number as fixed effects, and participant as a random effect (random intercept and random slope for trial number). The ICC from the null model was .45, indicating substantial between-participant variability. In the final model, condition significantly predicted reaction time (b = 28.3, SE = 7.1, t(22.6) = 3.99, p < .001), with participants in the experimental condition responding approximately 28 ms slower. The marginal R² was .18 and the conditional R² was .72. Full model estimates are presented in Table 1.”
This structure gives readers the essential findings at a glance and directs them to the table for complete detail. The critical elements are naming your random effects structure, providing the ICC to justify the mixed model, reporting fixed effects with full inferential statistics, and quantifying overall model performance with effect sizes.