Introduction to Multivariate Statistics

Multivariate statistics is a branch of statistics that deals with the analysis of data sets that have more than one variable. In other words, it is the study of the relationships between multiple variables in a data set.

Multivariate analysis techniques are used to understand the complex interactions among different variables and how they influence each other. These techniques include methods for describing and summarizing data, testing hypotheses about relationships between variables, and predicting the values of one variable based on the values of others.

Examples of multivariate analysis techniques include principal component analysis, factor analysis, cluster analysis, discriminant analysis, canonical correlation analysis, and multiple regression analysis.

Here are some of the most commonly used multivariate analysis techniques and the corresponding R packages:

  1. Principal Component Analysis (PCA): The prcomp function in base R can be used to perform PCA. The FactoMineR package also provides functions for PCA.

  2. Canonical Correlation Analysis (CCA): The canoncorr function in base R can be used to perform CCA. The CCA package also provides functions for CCA.

  3. Cluster Analysis: The stats package in base R provides functions for hierarchical clustering (hclust) and k-means clustering (kmeans). The cluster package also provides additional clustering functions.

  4. Discriminant Analysis: The MASS package provides function for Linear Discriminant Analysis (lda) and Quadratic Discriminant Analysis (qda).

  5. Multivariate Analysis of Variance (MANOVA): The stats package provides the manova function for MANOVA.

  6. Multidimensional Scaling (MDS): The MASS package provides functions for MDS (cmdscale).