Linear Mixed Model

What is a Linear Mixed Model?

A linear mixed model, also known as a mixed error-component model, is a statistical model that accounts for both fixed and random effects. Mixed model design is most often used in cases in which there are repeated measurements on the same statistical units, such as a longitudinal study. Mixed models have the advantage of handling missing values well and are often used as an alternative to other models like ANOVA.

How does a Linear Mixed Model work?

Mixed models work by incorporating fixed effects and random effects, making this design of statistical model useful when attempting to model effects of the natural world. In the 1950's, Ronald Fisher initially incorporated random effects models into his study of expressed traits between relatives and the correlations between them.

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It can be helpful to conceptualize the model with an example. Imagine trying to compare the differences in academic performance between students of the same class, and those of different classes. One could group students by their classroom, or more specifically the teacher associated with each group, or alternatively one could group the students in total, in which their population is defined as a whole, rather than by assigned teacher. When hoping to  understanding the effects of phenomena on a hierarchal structure, one can turn to a linear mixed model.

Linear Mixed Models and Machine Learning

If a neural network is tasked with understanding the effects of a phenomena on a hierarchal population, a linear mixed model can calculate the results much easier than that of separate linear regressions. Machine learning algorithms can use mixed models to conceptualize data in a way that allows for understanding the effects of phenomena both between groups, and within them.