Although anger is an important emotion that underlies much overt aggression at great social cost, little is known about how to quantify anger or to specify the relationship between anger and the overt behaviors that express it. This paper proposes a novel statistical model which provides both a metric for the intensity of anger and an approach to determining the quantitative relationship between anger intensity and the specific behaviors that it controls. From observed angry behaviors, we reconstruct the time course of the latent anger intensity and the linkage between anger intensity and the probability of each angry behavior. The data on which this analysis is based consist of observed tantrums had by 296 children in the Madison WI area during the period 1994–1996. For each tantrum, eight angry behaviors were recorded as occurring or not within each consecutive 30-second unit. So, the data can be characterized as a multivariate, binary, longitudinal (MBL) dataset with a latent variable (anger intensity) involved. Data such as these are common in biomedical, psychological and other areas of the medical and social sciences. Thus, the proposed modeling approach has broad applications.
"Statistical modeling of the time course of tantrum anger." Ann. Appl. Stat. 3 (3) 1013 - 1034, September 2009. https://doi.org/10.1214/09-AOAS242