Estimating Behavioral Transition Rates: Problems and Solutions

Continuous time Markov chain (CTMC) models offer ethologists a powerful tool. The methods are based on well-established procedures for estimating the rates at which one state (e.g. resting) changes to some other set of states (e.g. feeding, fighting, etc.). Unfortunately, ethological data typically differ in a very critical manner from the type of data to which these methods are usually applied: ethological data are usually heavily censored in the sense that each behavioral state shows frequent transitions to several other possible states. This occurs when several competing processes can each end a bout.
We used computer simulation of various behavioral models with known transition rates to investigate the unknown performance of four of the most popular statistical tests for screening data prior to application of CTMC models; this included a modification of one of these tests derived under the assumption of random censoring. Two of the four tests failed completely and would result in rejection of nearly all data even if the model did fit the assumptions of the CTMC methods. Only Barlow's total-time-on test performed with an acceptable α error rate under all conditions. None of the tests were particularly effective at detecting certain types of departures from the CTMC assumptions.
Guidelines are given as to how much confidence should be attached to apparent changes in transition rates.