Statnote 27: Principal components analysis (PCA)

In Statnotes 24 and 25, multiple linear regression, a statistical method that examines the relationship between a single dependent variable (Y) and two or more independent variables (X), was described. The principle objective of such an analysis was to determine which of the X variables had a significant influence on Y and to construct an equation that predicts Y from the X variables. ‘Principal components analysis’ (PCA) and ‘factor analysis’ (FA) are also methods of examining the relationships between different variables but they differ from multiple regression in that no distinction is made between the dependent and independent variables, all variables being essentially treated the same. Originally, PCA and FA were regarded as distinct methods but in recent times they have been combined into a single analysis, PCA often being the first stage of a FA. The basic objective of a PCA/FA is to examine the relationships between the variables or the ‘structure’ of the variables and to determine whether these relationships can be explained by a smaller number of ‘factors’. This statnote describes the use of PCA/FA in the analysis of the differences between the DNA profiles of different MRSA strains introduced in Statnote 26.