Variantiecomponentenanalyse

Variantiecomponentenanalyse, in English often called variance component analysis, is a statistical method used to estimate how much of the observed variation in a trait can be attributed to different random sources. It is widely used in fields such as genetics, animal and plant breeding, psychology, and quality control to understand the structure of variability and to quantify contributions from factors like genotype, environment, and measurement error.

The standard framework uses linear mixed models. A typical model for observed data y is y = Xβ + Zu + e, where β represents fixed effects, u is a vector of random effects with distribution u ~ N(0, G), and e is the residual error with e ~ N(0, R). The covariance of y is Var(y) = ZGZ′ + R, and the parameters of G and R are the variance components to be estimated. These components correspond to sources of variation such as genetic effects, environmental effects, and their interactions.

Estimation is commonly performed by restricted maximum likelihood (REML), though maximum likelihood and Bayesian methods are also used. REML provides unbiased estimates of variance components by accounting for the presence of fixed effects. Once estimated, variance components are interpreted as the portions of total variance attributable to each source. In simple models, heritability can be expressed as h² = σ²_genetic / (σ²_genetic + σ²_residual).

Applications include estimating heritability in breeding programs, partitioning phenotype variance into genotype, environment, and interactions, and assessing measurement reliability. Limitations arise from model misspecification, violations of normality, and data sparsity, which can bias estimates or complicate interpretation.