Quick answer: Ordinary tests and regression assume each observation is independent. That assumption is often false when the same person, site, class, or unit is measured more than once. In those cases, the data have structure that must be modeled or adjusted for. Repeated-measures models and mixed-effects models exist for exactly this reason: they account for within-unit correlation so the unit of analysis matches the unit of design.
Part 5 of a practical statistics series for researchers. If the basics are new, start with p-values, effect sizes, and confidence intervals.
Table of Contents
The independence assumption is doing a lot of work
Most introductory methods rely on a quiet assumption: each row of data provides separate information.
That assumption is fine when it is true. It is a problem when it is not.
Repeated measurements on the same person are not independent. Measurements on the same school are not independent. Repeated visits, repeated trials, repeated tests, repeated sites, repeated eyes, repeated limbs — all of these can create dependence.
When dependence is ignored, two things often go wrong:
- standard errors can be too small,
- and the effective sample size can be overstated.
That can make results look more certain than they really are.
The simplest mistake: treating repeats as replicates
A common beginner mistake is to average repeated measurements and then treat each subject as one observation, or to treat every measurement as if it came from a different subject.
Averaging can be reasonable in some settings, but it throws away information about within-subject patterns and can be misleading if the number of measurements differs across subjects.
Treating every measurement as independent is worse when there is real within-unit correlation. If the same person tends to give similar responses across time, then multiple measurements from that person do not each add a full unit of independent information.
The right approach depends on the question. Sometimes you want to model the within-subject change directly. Sometimes you want to account for clustering. Sometimes you want both.
What repeated-measures models do
A repeated-measures model is designed for situations where the same units are observed under multiple conditions, times, or occasions.
The key idea is that the model recognizes that measurements from the same unit are related. That recognition changes how uncertainty is estimated and how effects are interpreted.
Repeated-measures ANOVA is one classical tool. It can work for balanced designs with a small number of time points or conditions, but it has limitations. It can be awkward when there are missing measurements, uneven timing, or more complex covariance patterns.
That is where mixed-effects models often help.
What mixed models add
Mixed models include both fixed effects and random effects.
- Fixed effects are the systematic effects you want to estimate, such as treatment, time, or condition.
- Random effects capture structure such as subject-to-subject variation or cluster-to-cluster variation.
In a repeated-measures context, a random intercept for subject says: each subject has their own baseline level, and those baselines vary.
That simple change can improve the model in several ways:
- it accounts for within-subject correlation,
- it can handle unequal numbers of measurements per subject,
- it can accommodate missing measurements more naturally than some classical methods,
- and it lets you separate within-unit and between-unit variation more clearly.
A random slope can go further: it allows the effect of time or another predictor to vary across subjects.
When mixed models are useful
Mixed models are especially useful when:
- the same units are measured repeatedly,
- measurements are clustered within groups,
- the design is unbalanced,
- there are missing data patterns that are not simple,
- or you want to model variation across subjects or clusters rather than treating it as noise.
They are not always necessary. If the design is very simple and the correlation structure is minimal, a simpler method may be enough. But once the data have repeated structure, it is worth using a method that respects it.
Independence and the unit of analysis
A useful principle is to match the unit of analysis to the unit of design.
If the intervention was assigned to clinics, then clinics are a clustering unit. If students are nested in classrooms, then classrooms matter. If a person contributes multiple observations over time, that person matters.
Ignoring that structure can lead to overconfident conclusions. This is one reason that “more data points” is not always the same as “more information.”
How to think about the correlation
The core practical question is: how similar are repeated measurements from the same unit?
If the correlation is high, then each additional measurement adds less new information. If it is low, the measurements are closer to independent.
You do not always need to specify the full correlation structure perfectly. But you should not assume away the dependence. At minimum, the model should reflect that measurements are grouped.
A simple example
Suppose you measure blood pressure in 30 people at baseline, after 4 weeks, and after 8 weeks.
If you treat all 90 measurements as independent, you are pretending that the three measurements from the same person are unrelated. They are not.
A repeated-measures or mixed approach can:
- model the change over time,
- account for person-to-person variation,
- and give a more honest estimate of uncertainty.
That matters even if the average change looks similar under both approaches. The average may be similar, but the uncertainty and interpretation are not.
A second example
Suppose you compare two teaching methods across 10 classrooms, with 20 students per classroom.
If you treat all 200 students as independent, you ignore classroom-level clustering. Students in the same classroom share teachers, environment, and routines, so their outcomes may be correlated.
In that case, the classroom is the more relevant clustering unit for the intervention comparison. A model that accounts for clustering can keep the analysis from overstating the effective sample size.
Fixed effects can also help
Sometimes you do not need random effects to handle a repeated structure. You can also use fixed effects for subject or cluster when appropriate.
Fixed effects control for all time-invariant differences between units. That can be useful when the unit-to-unit differences are the main concern and you want to focus on within-unit change.
The tradeoff is that fixed effects use more degrees of freedom when there are many units, and they do not directly give you estimates of between-unit variation. Mixed models offer a different balance.
Choosing between simple and complex models
Do not start with the most complex model just because it sounds sophisticated. Start with the structure the data actually have.
Ask:
- Are there repeated measurements?
- Are there clusters?
- Is the design balanced or unbalanced?
- Are there missing measurements?
- Do you care about subject-specific trajectories or just the average pattern?
A model that matches the design is usually better than one that ignores it. But a model that is more complex than the problem requires can be harder to interpret and harder to trust.
What to check after fitting
Even with a mixed model, you should still check fit.
For example:
- Do the residuals look reasonable?
- Is the assumed correlation or random-effects structure plausible?
- Are there influential subjects or clusters?
- Do results change a lot if you simplify or change the random-effects structure?
Mixed models are flexible, not infallible. A flexible model can still be misused.
Reporting the structure clearly
When you report a repeated-measures or mixed analysis, say:
- what the repeated or clustered unit is,
- what fixed effects you included,
- what random effects you used, if any,
- how you handled missing data,
- and what correlation or covariance structure you assumed, if relevant.
That level of detail matters because the same dataset can be analyzed in several ways, and the choice affects conclusions.
Common mistakes
- Treating repeated measurements as independent observations.
- Using the total number of measurements as the sample size when clustering matters.
- Averaging away within-subject patterns without a good reason.
- Using a method that cannot handle missing data gracefully when missingness is present.
- Forgetting to say what the random effects represent.
- Assuming the model fixed the design problems even when the design is weak.
- Ignoring whether the correlation structure is plausible.
Key takeaways
- Repeated measurements are usually correlated, not independent.
- Ignoring that correlation can understate uncertainty and overstate effective sample size.
- Repeated-measures models and mixed models account for within-unit structure.
- Mixed models are helpful for unbalanced data, missing measurements, and clustering.
- The unit of analysis should match the unit of design.
- Fixed effects and random effects solve related but different problems.
- Model choice should follow the design, not habit.
- Always check fit and report the structure clearly.
Challenge
Take a study idea with repeated measurements or clustering and write a short analysis plan that states the unit of design, the unit of analysis, the fixed effects you care about, and whether you would use a repeated-measures model, mixed model, or fixed-effects approach. Explain why.
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FAQ
The main problem is that repeated measurements from the same unit are usually correlated, so they do not provide fully independent information. Ignoring that can distort uncertainty.
- What is the main problem with repeated measures?
When data are clustered or repeatedly measured and you want to account for that structure, especially with unbalanced data or missing measurements.
- When should I use a mixed model?
No. Simpler methods can be fine for simple designs. Mixed models are better when the design really has repeated or clustered structure that simpler methods ignore.
- Are mixed models always better than simpler methods?
It is a term that lets each subject or cluster have its own baseline level. It accounts for differences between units that are constant across measurements.
- What is a random intercept?
It is a term that lets the effect of a predictor vary across subjects or clusters. It is useful when the trajectory or response pattern differs by unit.
- What is a random slope?
Not if the data are correlated within units. Many measurements from the same unit may add less independent information than the same number of measurements from different units.
- Does more data always mean more information?
Say what the repeated or clustered unit is, what fixed and random effects you used, how you handled missing data, and any covariance assumptions that matter.
- How do I report a mixed model?
What is the main problem with repeated measures?
The main problem is that repeated measurements from the same unit are usually correlated, so they do not provide fully independent information. Ignoring that can distort uncertainty.
When should I use a mixed model?
When data are clustered or repeatedly measured and you want to account for that structure, especially with unbalanced data or missing measurements.
Are mixed models always better than simpler methods?
No. Simpler methods can be fine for simple designs. Mixed models are better when the design really has repeated or clustered structure that simpler methods ignore.
What is a random intercept?
It is a term that lets each subject or cluster have its own baseline level. It accounts for differences between units that are constant across measurements.
What is a random slope?
It is a term that lets the effect of a predictor vary across subjects or clusters. It is useful when the trajectory or response pattern differs by unit.
Does more data always mean more information?
Not if the data are correlated within units. Many measurements from the same unit may add less independent information than the same number of measurements from different units.
How do I report a mixed model?
Say what the repeated or clustered unit is, what fixed and random effects you used, how you handled missing data, and any covariance assumptions that matter.