Examining therapy dynamics and session outcome using differential equations model and multilevel data disaggregation

Objective: This study used Ordinary Differential Equations (ODE) model in a multilevel framework to investigate how the dyadic dynamics between therapist and client in perceiving working alliance (WA) was associated with the clients' session evaluation. Method: Participants were 33 therapists and their 180 clients. Therapists' and clients' WA ratings after each session were entered into the ODE model to estimate four coefficients capturing their consistency of perceptions of WA, and the levels to which one's perception influenced and was influenced by the other's perception. These dynamic coefficients were disaggregated into between-therapist and within-therapist components and entered into the Hierarchical Linear Model to predict client's session evaluation. Results: First, when therapists were generally more stable/consistent in perceiving their WA with all clients, they tended to have higher client evaluations of session quality. Second, when therapists were generally not influential on clients or not receptive to clients' influence, therapists' higher influence or openness to being influenced with a particular client was related to better session outcome. Third, when a therapist was generally highly influential, the more that therapist was influential to a particular client, that client reported worse session outcome. Conclusion: Implications about therapy dynamics and the use of ODE models were discussed.