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Chromosomal inversions are associated with reproductive isolation and adaptation in insects such as Drosophila melanogaster and the malaria vectors Anopheles gambiae and Anopheles coluzzii. While methods based on read alignment have been useful in humans for detecting inversions, these methods are less successful in insects due to long repeated sequences at the breakpoints. Alternatively, inversions can be detected using principal component analysis (PCA) of single nucleotide polymorphisms (SNPs). We apply PCA-based inversion detection to a simulated data set and real data from multiple insect species, which vary in complexity from a single inversion in samples drawn from a single population to analyzing multiple overlapping inversions occurring in closely-related species, samples of which that were generated from multiple geographic locations. We show empirically that proper analysis of these data can be challenging when multiple inversions or populations are present, and that our alternative framework is more robust in these more difficult scenarios.