You should use a mixed effects model whenever your data has a grouping structure that makes observations non-independent. This includes repeated measurements on the same subjects, data collected from multiple sites or clusters, and any design where observations are nested within higher-level units like classrooms, hospitals, or geographic regions. If you ran a standard linear regression on this kind of data, you’d violate the assumption of independent observations and end up with misleadingly small standard errors and inflated false-positive rates.
The “mixed” in mixed effects refers to the combination of fixed effects (the variables you care about estimating, like treatment group or age) and random effects (grouping variables that introduce non-independence, like subject ID or study site). Choosing between a standard regression and a mixed model isn’t really a matter of preference. It’s determined by your experimental design.
Repeated Measures and Longitudinal Data
The most common reason to reach for a mixed effects model is repeated measurements on the same individuals over time. If you measured blood pressure in 50 patients at four time points, those four observations within each patient are correlated. A mixed model handles this by estimating a random intercept (and optionally a random slope) for each patient, capturing the fact that some people start higher and some respond faster.
Mixed models have four key advantages over traditional repeated measures ANOVA for longitudinal data. First, they accommodate missing data naturally. If a patient drops out after the second visit, the model still uses their available measurements rather than discarding the entire case. Second, subjects don’t need the same number of observations. Third, time can be treated as a continuous variable rather than a fixed set of measurement points. Fourth, the correlation structure among repeated measures can be specified flexibly. These features make mixed models the default choice for clinical trials, cohort studies, and any experiment where you follow individuals over time.
Nested and Hierarchical Designs
Data is nested when lower-level units sit inside higher-level units. Students are nested within classrooms, classrooms within schools, schools within districts. Plots are nested within field sites. Patients are nested within hospitals. In each case, observations within the same group tend to be more similar to each other than observations from different groups, and ignoring that clustering produces unreliable results.
Consider a study measuring plant biomass across multiple field sites, with several plots sampled within each site and replicate extractions taken from each plot. Plots are nested in sites, and extractions are nested in plots. A mixed model accounts for this hierarchy by including random effects at each level, correctly partitioning the variance and giving you honest confidence intervals on your fixed effects.
Multicenter clinical trials follow the same logic. Treatments are fixed effects (you want to estimate their impact), while centers are random effects (you want to generalize beyond the specific hospitals that happened to participate). This is the standard analytical approach for trials conducted across multiple sites.
Crossed Random Effects
Not all grouping structures are nested. In many experiments, particularly in psychology and linguistics, subjects respond to a set of stimuli. Each subject sees every stimulus, and each stimulus is seen by every subject. Subjects and stimuli are “crossed” rather than nested. A mixed model with crossed random effects accounts for both sources of variability simultaneously: some subjects are generally faster or more accurate, and some stimuli are inherently easier or harder.
Ignoring either source of variation can dramatically inflate your false-positive rate. If you average over items and analyze only by-subject means (the traditional approach), you’re pretending that the specific stimuli you chose don’t matter. A mixed model with crossed random effects for subjects and items avoids this problem.
How Partial Pooling Improves Estimates
One of the most useful properties of mixed models is partial pooling, sometimes called shrinkage. When you estimate a separate mean for each group using a standard model, groups with very few observations produce noisy, unreliable estimates. When you ignore groups entirely and estimate a single overall mean, you lose real differences between groups. Partial pooling splits the difference.
A mixed model pulls each group’s estimate toward the overall mean, and the amount of pulling depends on how much data that group has. A group with hundreds of observations barely moves, because its own data is informative. A group with only three observations gets pulled substantially toward the grand mean, because the model recognizes that the group estimate is unreliable on its own. This borrowing of information across groups produces more accurate predictions, especially for small or poorly sampled groups.
When a Standard Regression Is Fine
If your observations are genuinely independent, you don’t need a mixed model. A one-time survey where each person responds once, with no clustering by household, school, or region, can be analyzed with ordinary regression. The same goes for a simple experiment where each subject contributes a single data point and there’s no site or batch structure.
Mixed models also become less necessary when the grouping factor isn’t something you want to generalize beyond. If you ran an experiment at exactly three locations and those three locations are the entire population of interest (not a sample from a larger set), you could treat location as a fixed effect instead. That said, even with few levels, treating a grouping factor as random is often the conceptually correct model of the system, and simulations suggest that using fewer than five levels of a random effect is acceptable when your primary interest is in the fixed effects rather than the variance components themselves.
Random Intercepts vs. Random Slopes
The simplest mixed model includes only a random intercept for each group, meaning each group can have a different baseline level but the effect of your predictor is assumed to be the same everywhere. A random slope model relaxes that assumption, allowing the effect itself to vary across groups. For example, a random intercept for patients says each patient starts at a different weight; adding a random slope for time says each patient also gains or loses weight at a different rate.
There’s ongoing debate about how aggressive to be with random effects structure. One influential recommendation is to keep models “maximal” by including all random slopes justified by the design, because omitting them risks inflated false-positive rates. A more pragmatic view is that maximal models can reduce statistical power and sometimes fail to converge, so you should test whether the data supports each random slope and remove those with clear evidence against them. Including random slopes largely eliminates the risk of strong false positives but reduces your chance of detecting true effects, so the tradeoff depends on whether you’re more worried about Type I or Type II errors.
Assumptions to Check
Mixed models share several assumptions with standard regression: residuals should be approximately normal, variance should be roughly constant across fitted values, and the model should be correctly specified. The additional assumption specific to mixed models is that the random effects themselves follow a normal distribution. In practice, moderate violations of normality in random effects rarely cause serious problems for fixed effect estimates, but severe heterogeneity of variance and violations of independence (beyond what your random effects capture) can bias both parameter estimates and p-values.
One practical advantage is that mixed models give you tools to address some of these violations directly. You can model different variances for different groups, fit alternative correlation structures to handle temporal or spatial dependence, and extend the framework to non-normal outcomes (counts, binary data) through generalized linear mixed models.
Sample Size Considerations
Power in mixed models depends on both the number of groups and the number of observations per group. For reaction time experiments with repeated measures, one detailed power analysis recommended at least 1,600 observations per condition, which can be divided flexibly across participants and items. Forty participants each seeing 40 stimuli, or 20 participants seeing 80 stimuli, both reach that threshold. The key insight is that you can trade off between more subjects and more items per subject, depending on which is easier to recruit.
For designs with fewer groups (say, 5 to 10 study sites), variance estimates for the random effects will be imprecise, but fixed effect estimates remain reasonable. If you have very few groups, be cautious about interpreting the random effects variance itself, though using the random effect to properly account for the grouped structure is still better than ignoring it.
Software Implementation
The most widely used package for fitting mixed models is lme4 in R. A model with a random intercept for each pig in a weight-gain study looks like this: lmer(Weight ~ Time + (1|Pig), data=dietox). Adding a random slope for time: lmer(Weight ~ Time + (1 + Time|Pig), data=dietox).
In Python, the statsmodels library provides MixedLM, which follows the same underlying estimation approach. A random intercept model: smf.mixedlm("Weight ~ Time", data, groups=data["Pig"]). Adding a random slope: smf.mixedlm("Weight ~ Time", data, groups=data["Pig"], re_formula="~Time"). Results from both implementations are consistent, so the choice comes down to your preferred programming environment. SAS and Stata also offer mature mixed model procedures that follow the same statistical framework.
When comparing nested models (for instance, testing whether a random slope improves fit over a random intercept alone), likelihood ratio tests are the standard tool. One important detail: if you’re comparing models with different fixed effects, use maximum likelihood estimation. If you’re comparing models with the same fixed effects but different random effects structures, restricted maximum likelihood (REML) is preferred because it produces less biased variance estimates. Most software defaults to REML, so you’ll need to switch to ML explicitly when comparing fixed effects.