Linear Mixed Models: Part I
Jiming Jiang, Thuan Nguyen
Abstract
The best way to understand a linear mixed modelLinear mixed model , or mixed linear model in some earlier literature, is to first recall a linear regression model. The latter can be expressed as y = Xβ + 𝜖, where y is a vector of observations, X is a matrix of known covariates, β is a vector of unknown regression coefficients, and 𝜖 is a vector of (unobservable random) errors. In this model, the regression coefficients are considered as fixed, unknown constants. However, there are cases in which it makes sense to assume that some of these coefficients are random.
Topics & Concepts
Mixed modelUnobservableCovariateMathematicsGeneralized linear mixed modelProper linear modelLinear regressionLinear modelMultivariate random variableApplied mathematicsStatisticsRandom effects modelLinear predictor functionEconometricsRandom variableBayesian multivariate linear regressionMeta-analysisInternal medicineMedicineAdvanced Statistical Methods and ModelsStatistical Methods and Bayesian InferenceGenetic and phenotypic traits in livestock