How To Report Linear Mixed Model Results Apa Style?

Reporting linear mixed model results in APA style means following the same core rules you would use for any statistical test: report the test statistic, degrees of freedom, p-value, and an effect size or confidence interval, all in a consistent format. The American Psychological Association’s Publication Manual does not dedicate a special section to mixed models, so researchers adapt the general APA reporting framework to the specific outputs that mixed model software produces. That adaptation is where most confusion happens.

This article explains what to include, how to format it, and where the guidelines are genuinely clear versus where conventions are still evolving.

What Is a Linear Mixed Model and Why Does Reporting Differ From Standard Regression?

A linear mixed model is a statistical technique for analyzing data where observations are not independent of each other. Standard linear regression assumes every data point is unrelated to every other. Mixed models relax that assumption.

This matters in real research. If you measure the same person’s blood pressure five times over a year, those five measurements are correlated. If students are nested within classrooms, students in the same classroom share influences. Mixed models handle this clustering by including both fixed effects (the population-level predictors you care about) and random effects (the grouping structure that creates the dependency).

APA reporting for mixed models therefore requires something standard regression does not: you must describe the random effects structure. A reader needs to know how you accounted for non-independence, not just what predictors you tested.

How Do You Structure a Results Section for a Mixed Model in APA Format?

A well-organized results section moves through four stages in order.

First, describe the model. State which software you used, how you specified fixed and random effects, and how you handled missing data. For example: “A linear mixed model was fitted using restricted maximum likelihood estimation. The model included fixed effects for time, group, and their interaction, and random intercepts for participant.”

Second, report model fit or comparison. If you compared nested models, report the likelihood ratio test or information criteria (AIC, BIC). If you report only one model, state how you selected the random effects structure.

Third, report fixed effects. This is the core of your results. For each predictor, give the estimate (β), standard error, degrees of freedom, t-value (or z-value), p-value, and a confidence interval.

Fourth, report random effects. Give the variance components and, where relevant, the intraclass correlation coefficient.

Keep this order. Readers expect it. Journals expect it.

How Do You Format Fixed Effects in APA Style?

The APA Publication Manual does not prescribe a single template for mixed model fixed effects, but the general principle for reporting statistical results applies: give the statistic, degrees of freedom, p-value, and an effect size or interval.

A commonly used format looks like this:

“Time significantly predicted the outcome, b = 0.45, SE = 0.12, t(87.3) = 3.75, p < .001, 95% CI [0.21, 0.69].”

Several formatting details follow APA conventions:

• Statistical symbols are italicized: b, SE, t, p, F, M, SD.
• Degrees of freedom go in parentheses immediately after the test statistic letter.
• p-values are reported to two or three decimal places. Values below .001 are reported as p < .001, never as p = .000.
• Confidence intervals are reported in brackets with the confidence level stated: 95% CI [lower, upper].
• No leading zero is used for values that cannot exceed 1, such as p-values and correlations: p = .03, not p = 0.03.

One genuine complication: mixed model software does not always produce a single degrees of freedom value. Different methods — Satterthwaite, Kenward-Roger, or asymptotic — yield different df. Report which method your software used. This is not optional detail; it affects the p-value.

How Do You Report Random Effects and Model Fit?

Random effects reporting is less standardized than fixed effects. The APA manual offers no specific template here, so conventions come from the methodological literature and journal norms.

At minimum, report the variance estimate for each random effect and the residual variance. For example:

“The random intercept for participant had a variance of 0.82, and the residual variance was 1.14.”

If you are reporting an intraclass correlation coefficient, state it clearly: “The intraclass correlation coefficient was .42, indicating that 42% of the total variance was attributable to between-person differences.”

For model comparison, report the statistic and the models being compared:

“A likelihood ratio test indicated that adding the random slope for time significantly improved model fit, χ²(2) = 14.62, p < .001.”

When reporting information criteria, give the exact values: “The model with random slopes showed better fit (AIC = 1245.3, BIC = 1278.9) than the model with random intercepts only (AIC = 1256.1, BIC = 1283.4).”

Lower AIC and BIC values indicate better fit, but the difference between models matters more than the absolute number.

What Should You Include in a Table for Mixed Model Results?

Tables are useful when you have many predictors or multiple models. A well-constructed fixed effects table typically includes these columns:

APA table formatting requires a table number in bold above the table, an italicized title on the next line, and horizontal lines only — no vertical lines. Notes go below the table in italics, beginning with the word Note.

If your table includes many predictors, consider whether a figure showing predicted values or interaction effects communicates the pattern more clearly than additional columns of numbers.

What Are the Most Common Reporting Mistakes?

The most frequent error is omitting the random effects structure entirely. A reader cannot evaluate your model without knowing what random effects you included and why.

Other common mistakes:

• Reporting unstandardized estimates without specifying the units or scale of the outcome variable.
• Using p-values alone without confidence intervals. APA increasingly emphasizes intervals because they convey both precision and practical significance.
• Failing to state which estimation method was used (maximum likelihood or restricted maximum likelihood). This matters because the two methods produce different results, particularly for model comparison.
• Not reporting how missing data were handled. Mixed models can accommodate missing data under certain assumptions, but readers need to know what those assumptions were.
• Reporting degrees of freedom from one method while using p-values computed with another.

One point that is frequently misunderstood: a non-significant p-value in a mixed model does not mean the predictor has no effect. It means the data are consistent with a null effect at the chosen alpha level. The confidence interval tells you what range of effects remains plausible.

Does APA Have Specific Rules for Mixed Model Reporting?

No. The Publication Manual of the American Psychological Association provides general statistical reporting guidelines but does not have a dedicated section for linear mixed models. This is a genuine gap, not a matter of interpretation.

What APA does specify clearly is the general framework: report exact p-values, include effect sizes, use italics for statistical symbols, format tables and figures consistently, and provide enough detail for replication. These principles apply to mixed models just as they apply to t-tests and ANOVA.

Because no single official template exists, journal-specific guidelines and the methodological literature fill the gap. Some journals have their own statistical reporting checklists. When in doubt, follow the most detailed reporting practices from your field and include everything a reader would need to reproduce your analysis.

The trend in methodological recommendations is toward more transparency, not less. Report your model specification, your estimation method, your random effects structure, and your software version. Over-reporting is far less problematic than under-reporting.