Implications of confounding from unmodeled interactions between explanatory variables when using latent variable regression models to make inferences

Abstract

With linear dependency between the explanatory variables, partial least squares (PLS) regression is commonly used for regression analysis. If the response variable correlates to a high degree with the explanatory variables, a model with excellent predictive ability can usually be obtained. Ranking of variable importance is commonly used to interpret the model and sometimes this interpretation guides further experimentation. For instance, when analyzing natural product extracts for bioactivity, an underlying assumption is that the highest ranked compounds represent the best candidates for isolation and further testing. A problem with this approach is that in most cases, the number of compounds is larger than the number of samples (and usually much larger) and that the concentrations of the compounds correlate. Furthermore, compounds may interact as synergists or as antagonists. If the modeling process does not account for this possibility, the interpretation can be thoroughly wrong because unmodeled variables that strongly influence the response will give rise to confounding of a first-order PLS model and send the experimenter on a wrong track. We show the consequences of this by a practical example from natural product research. Furthermore, we show that by including the possibility of interactions between explanatory variables, visualization using a selectivity ratio plot may provide model interpretation that can be used to make inferences.