Measurement invariance holds when a latent construct is measured in the same way across different levels of background variables (continuous or categorical) while controlling for the true value of that construct. Using Monte Carlo simulation, this paper compares the multiple indicators, multiple causes (MIMIC) model and MIMIC-interaction to a novel use of alignment optimization (AO) for detecting measurement noninvariance when the violator is a continuous variable. Results showed that MIMIC and MIMIC-interaction in sequential likelihood ratio tests and Wald tests with a Bonferroni correction provided a good balance between identifying invariant and noninvariant (linear violations) items when n=500 in terms of classification accuracy (CA). AO (CA = 0.86) was as competitive as MIMIC and MIMIC-interaction to linear invariance violations but was far better under nonlinear quadratic violations when n= 1,000 (i.e., 100 per group for 10 groups).