Methodological issues in determining the dimensionality of composite health measures using principal component analysis:: Case illustration and suggestions for practice

During the early steps of the construction of composite health measures, principal component analysis (PCA) is commonly used to identify 'latent' factors that underlie observed variables and to determine the dimensionality of the instruments. The determination of the number of components to retain is critical to PCA: it markedly influences the factorial model identified and further conditions the validity of the constructed instrument. However, many researchers developing composite health measures seem to be unaware of the importance of this determination. The purposes of the paper are to illustrate (1) the variability of the factorial models obtained by using different published rules (n = 10) for determining the number of components to retain in PCA applied to two quality-of-life datasets, and (2) the value of a careful and diversified approach to the problem of the number of components to retain in PCA that we suggest, instead of the unsatisfactory 'rule-of-thumb' that many researchers use. This involves: (1) using robust rules (including parallel analysis and minimum average partial procedure) to generate a set of possible values for the number of components to retain, (2) repeating the analysis across samples, (3) comprehensively assessing the models obtained, and (4) considering complementary methods to PCA and especially confirmatory factor analysis.