To test whether differences in transitions occurred between the treatment groups (CBT, MET, TSF) or treatment arms (outpatient, aftercare), the assumption of invariance of the transition probabilities across treatment was examined by estimating a series of constrained latent transition models. First, for the null model, transition probabilities were constrained to equality across both treatment groups/arms. Second, for the alternative model, the transition probabilities were allowed to vary across treatment groups/arms. The null model is nested within the alternative model, which allows for significance testing using a likelihood ratio test (Muthén and Muthén, 1998–2007) based on the scaled chi-square difference test provided by Satorra (2000). The scaled chi-square difference test is distributed as chi-square with degrees of freedom equal to the difference in parameters between the two models. For the comparison of treatment groups, the null model with transitions held equal across treatment groups was not rejected (outpatient: scaled χ2 = 35.67, 24 df, p = .06; aftercare: scaled χ2 = 34.68, 24 df, p = .07), indicating that the transition matrices were statistically equivalent for the CBT, MET, and TSF
