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The purpose of this study is to examine the accuracy of selecting the correct number of latent classes with growth mixture models using both the traditional latent growth model (LGM) and the second-order latent growth model (SOLGM) under longitudinal non-invariance conditions. Various conditions will be manipulated, including sample size, class separation, mixing proportions, composite reliability, location of non-invariance, magnitude of non-invariance, and number of non-invariant parameters. The enumeration accuracy of three information criteria (i.e., AIC, BIC, NBIC) and three likelihood ratio tests (i.e., VLMR, aVLMR, BLRT) will be evaluated. It is hoped that this paper will provide information for applied researchers interested in using GMMs about conditions in which class enumeration is more accurate.