A multilevel latent Markov model for the evaluation of nursing homes' performance

Estimating random effects in a finite Markov chain with absorbing states: Application to cognitive data

Finite Markov chains with absorbing states are popular tools for analyzing longitudinal data with categorical responses. The one step transition probabilities can be defined in terms of fixed and random effects but it is difficult to estimate these effects due to many unknown parameters. In this article we propose a three-step estimation method. In the first step the fixed effects are estimated by using a marginal likelihood function, in the second step the random effects are estimated after substituting the estimated fixed effects into a joint likelihood function defined as a h-likelihood, and in the third step the covariance matrix for the vector of random effects is estimated using the Hessian matrix for this likelihood function. An application involving an analysis of longitudinal cognitive data is used to illustrate the method.

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.

Spare time use: profiles of Italian Millennials (beyond the media hype)

This paper focuses on a particular population segment, that of Millennials, which has attracted much attention over recent years. Beyond the media hype, little is known about the habits of this generation towards spare time use. The present study builds on a previous work devoted to detect the different ways Italian Millennials interact with spare time, and aims at identifying profiles of Millennials branded with profile-specific time use habits and styles. In so doing, we (i) account for the multidimensional nature of time use attitude and express it into a reduced number of distinct dimensions and (ii) identify and qualify profiles of Millennials as regards the ascertained time use dimensions. By relying on an extended Item Response Theory model applied to the Italian “Multipurpose survey on households”, our main findings reveal that the way Millennials use spare time and interact with technology is much more complex, varied and multifaceted than what claimed by the media.

Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models

In this paper, an ordinal multilevel latent Markov model based on separate random effects is proposed. In detail, two distinct second-level discrete effects are considered in the model, one affecting the initial probability vector and the other affecting the transition probability matrix of the first-level ordinal latent Markov process. To model these separate effects, we consider a bi-dimensional mixture specification that allows to avoid unverifiable assumptions on the random effect distribution and to derive a two-way clustering of second-level units. Starting from a general model where the two random effects are dependent, we also obtain the independence model as a special case. The proposal is applied to data on the physical health status of a sample of elderly residents grouped into nursing homes. A simulation study assessing the performance of the proposal is also included.