Multivariadas

Multivariadas, in statistics, refers to a family of methods designed to analyze multiple dependent variables simultaneously. Rather than examining each outcome separately, multivariadas exploit the correlations among several measurements to improve inference, detect shared structure, and provide a more integrated view of the data. They are used when outcomes are related and when a joint analysis can yield more information than a series of univariate analyses.

The data for multivariadas consist of observations measured on several related variables. Analyses typically start with describing the dependence structure through a covariance or correlation matrix, and they rely on assumptions such as linear relationships and, in some methods, multivariate normality. The objectives include testing group differences on a vector of outcomes, reducing dimensionality, identifying latent constructs that explain shared variance, and modeling relationships among several outcomes and predictors.

Common techniques include multivariate analysis of variance (MANOVA), multivariate regression, principal component analysis (PCA), factor analysis, canonical correlation analysis, discriminant analysis, cluster analysis, and structural equation modeling. Some methods, like multivariate time series analysis, extend these ideas to data collected over time. The choice of method depends on the research question, data structure, and assumptions about distributions and relationships among variables.

Interpretation in multivariadas emphasizes the joint behavior of multiple outcomes and the interdependencies among them. Challenges include larger sample size requirements, sensitivity to assumption violations, and complexity of results. Multivariadas are widely used in psychology, education, economics, ecology, medicine, and social sciences, with common software implementations in R, Python, SAS, and SPSS.