multivariat

Multivariat is an adjective used in statistics to describe analyses, models, and data that involve more than one random variable. It focuses on the joint behavior and interdependencies among several variables, rather than examining them in isolation. The term is commonly used in Swedish and related languages as a direct counterpart to the English 'multivariate'. In practice, multivariat methods analyze the structure of the data through relationships among variables, often via a covariance or correlation matrix.

Core ideas include the joint distribution of multiple variables and how they covary. A central object is the covariance (or correlation) matrix, which summarizes pairwise relationships and underpins many techniques. When assumptions such as normality hold, models can describe the data succinctly using a lower-dimensional representation or a set of simultaneous outcome variables. Multivariat analysis seeks to understand relationships, reduce dimensionality, classify observations, or test for effects across several outcomes.

Common methods include principal component analysis (PCA) for reducing dimensionality while preserving variance; factor analysis for uncovering latent constructs; multivariate analysis of variance (MANOVA) for comparing groups on several dependent variables; canonical correlation for relating two sets of variables; discriminant analysis and cluster analysis for classification and grouping; and multivariate regression for modeling several dependent variables together. More specialized approaches exist for time-series, spatial data, or nonparametric contexts.

Applications span psychology, genetics, ecology, finance, marketing, and social sciences. Analyses generally assume adequate sample size and, in many cases, some form of multivariate normality. Results are interpreted through patterns in loadings, score plots, and the structure of the covariance matrix. When assumptions are not met, robust, nonparametric, or permutation-based alternatives are used.