Finite Mixtures of Hidden Markov Models for Longitudinal Responses Subject to Drop out

Multilevel Hidden Markov Models for Behavioral Data: A Hawk-and-Dove Experiment

Motivated by the analysis of behavioral data taken from an economic experiment based on the Hawk-and-Dove game, this article describes a multilevel hidden Markov model, that includes covariates, autoregression, and endogenous initial conditions under a unified framework. The data at hand are affected by multiple sources of latent heterogeneity, due to multilevel unobserved factors that operate in conjunction with observed covariates at all the levels of the data hierarchy. We fit a multilevel logistic regression model for repeated measurements of player behaviors, nested within groups of interacting players. The model integrates discrete random effects at the group level and Markovian sequences of discrete random effects at the player level. Parameters are estimated by a computationally feasible expectation-maximization algorithm. We model the probability of playing the Hawk strategy, which implies fighting aggressively for controlling an asset, and test the role played by initial possession, property, and other player-specific characteristics in driving hawkish behaviors. The results from our study suggest that crucial factors in determining hawkish behavior are both the way possession is achieved - which depends on our treatment manipulation- and possession itself. Furthermore, a clear time-dependence is observed in the data at the player level as accounted for by the Markovian random effects.

Dynamic latent variable models for the analysis of cognitive abilities in the elderly population

Cognitive functioning is a key indicator of overall individual health. Identifying factors related to cognitive status, especially in later life, is of major importance. We concentrate on the analysis of the temporal evolution of cognitive abilities in the elderly population. We propose to model the individual cognitive functioning as a multidimensional latent process that accounts also for the effects of individual-specific characteristics (gender, age, and years of education). The proposed model is specified within the generalized linear latent variable framework, and its efficient estimation is obtained using a recent approximation technique, called dimensionwise quadrature. It provides a fast and streamlined approximate inference for complex models, with better or no degradation in accuracy compared with standard techniques. The methodology is applied to the cognitive assessment data from the Health and Retirement Study combined with the Asset and Health Dynamic study in the years between 2006 and 2010. We evaluate the temporal relationship between two dimensions of cognitive functioning, that is, episodic memory and general mental status. We find a substantial influence of the former on the evolution of the latter, as well as evidence of severe consequences on both cognitive abilities among less-educated and older individuals.