Latent Transition Analysis (LTA) is increasingly utilized to model person-centered longitudinal change, yet researchers frequently assume longitudinal measurement invariance (LMI) without adequate testing or when the assumption is violated. Longitudinal measurement non-invariance (LMNI), specifically item-level differential item functioning (DIF) over time, is known to bias other longitudinal latent variable models, but its specific consequences on categorical LTA parameter recovery remain underexplored. This dissertation addresses this gap through a Monte Carlo simulation study grounded in the ADEMP framework, within a context where configural invariance holds while individual items exhibit DIF across waves. By manipulating factors including sample size, latent profile ambiguity, transition density, and DIF characteristics, the study explored 456 simulation conditions to evaluate the accuracy, efficiency, and inferential validity of three analytical LTA strategies: the Constrained model (assumed LMI), the Unconstrained model (freely estimated), and the Correctly Specified model (partial MI).

Results reveal that forcing a fully constrained model in the presence of LMNI fundamentally compromises the LTA. Targeted Constrained-only ANOVAs demonstrated that unmodeled DIF introduces extreme systematic bias into both the measurement thresholds and the structural pathways (class proportions and transition probabilities), particularly when severe non-invariance interacts with structurally ambiguous latent profiles. This bias is coupled with a failure of confidence interval coverage, leading to highly confident but completely invalid longitudinal inferences. Conversely, while the fully unconstrained model successfully protects against systematic bias, Unconstrained-only ANOVAs revealed it suffers from statistical inefficiency and empirical under-identification when sample sizes are small or profiles are ambiguous. Furthermore, the omnibus Likelihood Ratio Test (LRT) demonstrated inadequate detection power in smaller samples or under mild DIF, proving to be an unreliable gatekeeper for model selection.

Based on these findings, this study strongly recommends that applied researchers should routinely test LMNI when using LTA and adopt a partial measurement invariance (MI) model when LMNI is empirically found or theoretically anticipated. By freeing only the specific non-invariant items while anchoring the remaining indicators, the partial MI model effectively prevents systematic bias, avoids large sampling variance inflation, and critically preserves the conceptual equivalence of the latent classes across time. The dissertation concludes with practical guidelines for handling LMNI in LTA and outlines critical directions for future methodological development.