All model parameters were estimated by the expectation-maximumization algorithm using a maximum likelihood estimator with robust standard errors (MLR; Muthén and Muthén, 1998–2007). Models were estimated using automatically generated starting values with random perturbations (100 random sets of starting values with 50 optimizations in the final stage of estimation) to protect against convergence to local optima (Hipp and Bauer, 2006). For all nested model comparisons, the scaled likelihood ratio test was used to test the difference in log-likelihood between a null model in which certain parameters were fixed to equivalence across time (or treatment arms) with an alternative model in which the parameters were freely estimated across time (or treatment arms). As compared with the G2 statistic, which has been used previously to test nested models in LTA, a scaled likelihood ratio test is necessary when comparing nested models that are estimated using MLR (Muthén and Muthén, 1998–2007). Calculations for this test are provided by Satorra (2000).
