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Psychomotor retardation in depression has been associated with speech timing changes from dyadic clinical interviews. In this work, we investigate speech timing features from free-living dyadic interactions. Apart from the possibility of continuous monitoring to complement clinical visits, a study in free-living conditions would also allow inferring sociability features such as dyadic interaction frequency implicated in depression. We adapted a speaker count estimator as a dyadic interaction detector with a specificity of 89.5% and a sensitivity of 86.1% in the DIHARD dataset. Using the detector, we obtained speech timing features from the detected dyadic interactions in multi-day audio recordings of 32 participants comprised of 13 healthy individuals, 11 individuals with depression, and 8 individuals with psychotic disorders. The dyadic interaction frequency increased with depression severity in participants with no or mild depression, indicating a potential diagnostic marker of depression onset. However, the dyadic interaction frequency decreased with increasing depression severity for participants with moderate or severe depression. In terms of speech timing features, the response time had a significant positive correlation with depression severity. Our work shows the potential of dyadic interaction analysis from audio recordings of free-living to obtain markers of depression severity.