Nonparametric inference of stability landscapes from intensive longitudinal data

Psychological processes are characterized by constant change and complex underlying dynamics and are often researched using intensive longitudinal data (ILD). Although such data are often analyzed with parametric models, these models impose strong and simplified assumptions about the system’s dynamic rules that can be unrealistic and may fail to capture phenomena such as multistability. Recent work has enabled estimation of the stability landscape of psychological systems from ILD, yet drawing statistical inferences from such landscapes remains challenging. In this work, we present a new method for statistical inference based on stability landscapes. The core of the method is bootstrapping, complemented by specialized techniques applied before and after the bootstrap procedure to make computation feasible and to effectively summarize information across bootstrap samples. Across three simulation studies with different data-generating mechanisms, we evaluated the method and, in particular, four approaches for summarizing information about the locations and depths of local minima. Overall, we found that using fixed reference points, such as the local minima from the original sample, helps guide the assignment of bootstrapped minima. When the data-generating mechanism differs from the estimated stability landscape, directional bias may occur; however, the relative locations of minima can still be retrieved. The method generally shows higher precision, whereas achieving high recall may require clear separation between minima, longer time series, and lower measurement noise. We also provide an empirical illustration using an existing dataset. An implementation is available in the latest version of the R package fitlandr.