Sensor systems can be deployed in the homes of older adults living alone for functional health assessments. Their information is very useful for health care specialists. The problem lies in developing person independent models while facing a large variability in behavior. We address this problem by, first, proposing a new feature extraction method for data from ambient motion sensors. The method uses functional similarities between houses and daily structure to extract meaningful features. Second, we propose a change-based approach for analyzing data, taking difference scores of both the sensor features and health metrics. To evaluate our approach, experiments on longitudinal data were conducted, where the relationship between sensor data and health measurements was modeled with linear regression and (nonlinear) regression forests. These experiments show that the change-based approach yields better results and that the resulting models can be used as a reliable metric for (functional) health. In addition, feature analysis can help health care specialists understand relevant aspects of behavior. Prediction of health metrics is possible even with simple sensors. With such sensors, it is possible to detect problems and health decline in an early stage. This will have great impact on clinical practice.