sekoitemallin

Seikoitemallin, in Finnish often referred to as sekoitemalli, is a statistical framework used to analyze data that exhibit non-independence or hierarchical structure by incorporating both fixed effects and random effects into the model. In a typical sekoitemallin, the observed response y is modeled as y = Xβ + Zb + ε, where Xβ represents fixed effects, Zb represents random effects capturing group- or subject-specific deviations, and ε is the residual error. The random effects b are assumed to follow a multivariate normal distribution with mean zero and covariance matrix G, while ε is assumed to be normal with mean zero and covariance R. This structure allows partitioning of variation into components attributable to measured covariates and to unobserved random factors.

There are two main families: linear mixed models (LMMs) for continuous outcomes and generalized linear mixed models (GLMMs) for non-normal outcomes, using appropriate link functions and distributions. Estimation is commonly performed by maximum likelihood or restricted maximum likelihood (REML) for variance components; Bayesian approaches using MCMC are also used. Model selection and diagnostics cover fixed effects significance, variance components, BLUPs for random effects, and checking assumptions about distributions.

Sekoitemallit are widely used in fields with grouped or hierarchical data, such as agriculture, psychology, education, ecology, genetics, and econometrics, to account for correlations within clusters (e.g., subjects, plots, schools) and to obtain valid inferences. Limitations include sensitivity to distributional assumptions for random effects, potential computational complexity, and the need for sufficient data to estimate variance components. The term reflects the Finnish translation of the broader statistical concept of mixed models and is commonly encountered in statistical software and literature.