Incorporation of Covariates Through Principal Components in Analysis of Covariance: A Simulation Study

Abstract

This study examined the use of the Principal Component Analysis (PCA) approach in incorporating covariates in the Analysis of Covariance (ANCOVA) under different experimental setups. Simulated data were used for the study, and the statistical programs were developed in R statistical software to generate the datasets for different experimental setups by varying (i) number of covariates, (ii) degree of correlation among covariates, (iii) number of treatments, (iv) difference between treatment means, and (v) number of replicates. Thousand simulations were performed for each experimental setup, and the impact of the PCA approach was assessed by means of power of the test through the proportion of rejections of H0: no difference between adjusted treatment means, in 1000 simulations. The use of PCs led to a significant gain in the power of the test in ANCOVA when there is a higher number of interrelated covariates with a limited number of observations. The impact was higher with the increase of number of covariates as well as the correlation between covariates. It can be concluded that by accommodating covariates by means of PCs, the efficiency in ANCOVA can be increased, especially if there are many covariates to be included in the analysis with a limited number of observations.