Depression is a major threat to public health and its mitigation is considered to be of utmost importance. Internet-based Cognitive Behavioral Therapy (ICBT) is one of the employed treatments for depression. However, for the approach to be effective, it is crucial that the outcome of the treatment is accurately predicted as early as possible, to allow for its adaptation to the individual patient. Hidden Markov models (HMMs) have been commonly applied to characterize systematic changes in multivariate time series within health care. However, they have limited capabilities in capturing long-range interactions between emitted symbols. For the task of analyzing ICBT data, one such long-range interaction concerns the dependence of state transition on fractional change of emitted symbols. Gated Hidden Markov Models (GHMMs) are proposed as a solution to this problem. They extend standard HMMs by modifying the Expectation Maximization algorithm; for each observation sequence, the new algorithm regulates the transition probability update based on the fractional change, as specified by domain knowledge. GHMMs are compared to standard HMMs and a recently proposed approach, Inertial Hidden Markov Models, on the task of early prediction of ICBT outcome for treating depression; the algorithms are evaluated on outcome prediction, up to 7 weeks before ICBT ends. GHMMs are shown to outperform both alternative models, with an improvement of AUC ranging from 12 to 23%. These promising results indicate that considering fractional change of the observation sequence when updating state transition probabilities may indeed have a positive effect on early prediction of ICBT outcome.