This simulation study evaluated how well multilevel structural equation models (ML-SEM) fare in detecting within-person nonuniform measurement bias in intensive longitudinal data. Such a bias would be given if variables would not be equally meaningful and observable within a person across time, thus violating dimensional identity and representing interoccasion variability. Unfortunately, prior simulation studies and studies using intensive longitudinal data show a clear tendency to assume but not test dimensional identity. We simulated 450 conditions with varying sample size, retesting frequency, ICCs, bias type and bias strength and examined Type I error and ML-SEM performance in detecting within-person nonuniform measurement bias. Type I error was well below nominal level. The ²-statistic and CFI outperformed the other fit indices (RMSEA, SRMR-w, SRMR-b). These effects were conditional on all design factors. While ecological momentary assessment motivated our study, findings are applicable to other research settings yielding the same data structure (e.g., ambulatory assessment, daily diary studies, experience sampling methods, and hierarchical data structures in general). We conclude with practical recommendations on samples sizes and re-testing frequencies to ensure adequate power for evaluating model fit.