Go Multivariate: Recommendations on Bayesian Multilevel Hidden Markov Models with Categorical Data.

The multilevel hidden Markov model (MHMM) is a promising method to investigate intense longitudinal data obtained within the social and behavioral sciences. The MHMM quantifies information on the latent dynamics of behavior over time. In addition, heterogeneity between individuals is accommodated with the inclusion of individual-specific random effects, facilitating the study of individual differences in dynamics. However, the performance of the MHMM has not been sufficiently explored. We performed an extensive simulation to assess the effect of the number of dependent variables (1-8), number of individuals (5-90), and number of observations per individual (100-1600) on the estimation performance of a Bayesian MHMM with categorical data including various levels of state distinctiveness and separation. We found that using multivariate data generally alleviates the sample size needed and improves the stability of the results. Moreover, including variables only consisting of random noise was generally not detrimental to model performance. Regarding the estimation of group-level parameters, the number of individuals and observations largely compensate for each other. However, only the former drives the estimation of between-individual variability. We conclude with guidelines on the sample size necessary based on the level of state distinctiveness and separation and study objectives of the researcher.

Band reporting rates of waterfowl: does individual heterogeneity bias estimated survival rates?

In capture-recapture studies, the estimation accuracy of demographic parameters is essential to the efficacy of management of hunted animal populations. Dead recovery models based upon the reporting of rings or bands are often used for estimating survival of waterfowl and other harvested species. However, distance from the ringing site or condition of the bird may introduce substantial individual heterogeneity in the conditional band reporting rates (r), which could cause bias in estimated survival rates (S) or suggest nonexistent individual heterogeneity in S. To explore these hypotheses, we ran two sets of simulations (n = 1000) in MARK using Seber's dead recovery model, allowing time variation on both S and r. This included a series of heterogeneity models, allowing substantial variation on logit(r), and control models with no heterogeneity. We conducted simulations using two different values of S: S = 0.60, which would be typical of dabbling ducks such as mallards (Anas platyrhynchos), and S = 0.80, which would be more typical of sea ducks or geese. We chose a mean reporting rate on the logit scale of -1.9459 with SD = 1.5 for the heterogeneity models (producing a back-transformed mean of 0.196 with SD = 0.196, median = 0.125) and a constant reporting rate for the control models of 0.196. Within these sets of simulations, estimation models where σS = 0 and σS > 0 (σS is SD of individual survival rates on the logit scale) were incorporated to investigate whether real heterogeneity in r would induce apparent individual heterogeneity in S. Models where σS = 0 were selected approximately 91% of the time over models where σS > 0. Simulation results showed < 0.05% relative bias in estimating survival rates except for models estimating σS > 0 when true S = 0.8, where relative bias was a modest 0.5%. These results indicate that considerable variation in reporting rates does not cause major bias in estimated survival rates of waterfowl, further highlighting the robust nature of dead recovery models that are being used for the management of harvested species.