As the number of elderly people in our society increases, the need of assistive technologies in home becomes urgent. Existing techniques allow elderly people to be better assisted through monitoring what goes on in smart homes and inferring their activities from sensor data via a recognition model. However, there are various cases that existing models have difficulties in accommodating relational data. In this paper, we present an application of probabilistic graphical model – Latent-Dynamic Conditional Random Field – to detect the goals of the individual subjects when observations have long range dependencies or multiple overlapping features. To validate the proposed method, we apply it to recognize activities in two different datasets which were collected in smart homes. The results demonstrate that Latent-Dynamic Conditional Random Fields favorably outperform other models, especially when there are extrinsic dynamic activities changes and intrinsic actions (subactivities).