Why some data points are secretly linked to each other

Health · Published 18 October 2026 Swipe more like this →

In short: Standard statistics often assume every data point is an independent island. But in biology and social science, this is rarely true. If you measure the same person twice, or study students within the same school, the data points are linked. Mixed models are the mathematical tool used to untangle these hidden connections.

Mixed effects models are designed to handle 'non-independent' data structures. In traditional analysis of variance (ANOVA), researchers often assume that every observation is independent. However, many real-world scenarios involve nested or clustered data. For example, in an educational study, individual students are nested within schools. Because students in the same school share a common environment, their outcomes are correlated. Mixed models allow researchers to explicitly account for these hierarchical structures, preventing biased estimations that occur when these dependencies are ignored.

The model works by combining 'fixed' and 'random' effects. Fixed effects are the primary factors of interest, such as a specific treatment or medication. Random effects, however, are used for two main purposes. First, they model sources of variance to match the experimental design—such as accounting for repeated measurements on the same subject, families, or cages to avoid 'pseudo-replication.' Second, random effects can directly address biological research interests. In quantitative genetics, they are used to quantify how much of a trait's variance is caused by genetic versus environmental factors, or to measure phenotypic plasticity in a population.

Despite their utility, mixed models require sophisticated handling, especially in longitudinal studies where subjects are measured repeatedly over time. A common mistake is simply including 'subject' as a random effect without considering 'autocorrelation'—the tendency for measurements taken closer together in time to be more similar than those further apart. Failing to account for this can increase Type 1 errors (false positives). By properly modeling these variance-covariance structures, mixed models provide a flexible framework for analyzing complex diversity in experimental designs, from neuroscience to plant breeding.

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