Measurement bias is defined as a violation of measurement invariance, which can be investigated through multigroup factor analysis (MGFA), by testing across-group differences in intercepts (uniform bias) and factor loadings (nonuniform bias). Restricted factor analysis (RFA) can also be used to detect measurement bias. To also enable nonuniform bias detection, we extend RFA with latent moderated structures (LMS) or use a random slope parameterization (RSP). In a simulation study we compare the MGFA, RFA/LMS, and RFA/RSP methods in detecting measurement bias, varying type of bias (uniform, nonuniform), type of the variable that violates measurement invariance (dichotomous, continuous), and its relationship with the trait that we want to measure (independent, dependent). For each condition, 500 sets of data are generated and analyzed with each of the three detection methods, in single run and in an iterative procedure. The RFA methods outperform MGFA when the violating variable is continuous. (Contains 9 tables.)