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Principal component analysis (PCA) is commonly used in genetics to infer andvisualize population structure and admixture between populations. PCA is ofteninterpreted in a way similar to inferred admixture proportions, where it isassumed that individuals belong to one of several possible populations or areadmixed between these populations. We propose a new method to assess thestatistical fit of PCA (interpreted as a model spanned by the top principalcomponents) and to show that violations of the PCA assumptions affect the fit.Our method uses the chosen top principal components to predict the genotypes.By assessing the covariance (and the correlation) of the residuals (thedifferences between observed and predicted genotypes), we are able to detectviolation of the model assumptions. Based on simulations and genome wide humandata we show that our assessment of fit can be used to guide the interpretationof the data and to pinpoint individuals that are not well represented by thechosen principal components. Our method works equally on other similar models,such as the admixture model, where the mean of the data is represented bylinear matrix decomposition.

Evaluation of population structure inferred by principal component analysis or the admixture model