Francesco Lagona

Model-based clustering of multivariate skew data with circular components and missing values

Motivated by classification issues that arise in marine studies, we propose a latent-class mixture model for the unsupervised classification of incomplete quadrivariate data with two linear and two circular components. The model integrates bivariate circular densities and bivariate skew normal densities to capture the association between toroidal clusters of bivariate circular observations and planar clusters of bivariate linear observations. Maximum-likelihood estimation of the model is facilitated by an expectation maximization (EM) algorithm that treats unknown class membership and missing values as different sources of incomplete information. The model is exploited on hourly observations of wind speed and direction and wave height and direction to identify a number of sea regimes, which represent specific distributional shapes that the data take under environmental latent conditions.

Maximum likelihood estimation of bivariate circular Hidden Markov models from incomplete data

In this paper, we propose a hidden Markov model for the analysis of the time series of bivariate circular observations, by assuming that the data are sampled from bivariate circular densities, whose parameters are driven by the evolution of a latent Markov chain. The model segments the data by accounting for redundancies due to correlations along time and across variables. A computationally feasible expectation maximization (EM) algorithm is provided for the maximum likelihood estimation of the model from incomplete data, by treating the missing values and the states of the latent chain as two different sources of incomplete information. Importance-sampling methods facilitate the computation of bootstrap standard errors of the estimates. The methodology is illustrated on a bivariate time series of wind and wave directions and compared with popular segmentation models for bivariate circular data, which ignore correlations across variables and/or along time.

Symmetrically dividing cells of the fission yeast schizosaccharomyces pombe do age.

Theories of the evolution of senescence state that symmetrically dividing organisms do not senesce. However, this view is challenged by experimental evidence. We measured by immunofluorescence the occurrence and intensity of protein carbonylation in single and symmetrically dividing cells of Schizosaccharomyces pombe. Cells of S. pombe show different levels of carbonylated proteins. Most cells have little damage, a few show a lot, an observation consistent with the gradual accumulation of carbonylation over time. At reproduction, oxidized proteins are shared between the two resulting cells. These results indicate that S. pombe does age, but does so in a different way from other studied species. Damaged cells give rise to damaged cells. The fact that cells with no or few carbonylated proteins constitute the main part of the population can explain why, although age is not reset to zero in one of the cells during division, the pool of young cells remains large enough to prevent the rapid extinction of the population.

A hidden Markov approach to the analysis of space–time environmental data with linear and circular components

The analysis of bivariate space–time series with linear and circular components is complicated by (1) multiple correlations, across time, space and between variables, (2) different supports on which the variables are observed, the real line and the circle, and (3) the periodic nature of circular data. We describe a multivariate hidden Markov model that includes these features of the data within a single framework. The model integrates a circular von Mises Markov field and a Gaussian Markov field, with parameters that evolve in time according to a latent (hidden) Markov chain. It allows to describe the data by means of a finite number of time-varying latent regimes, associated with easily interpretable components of large-scale and small-scale spatial variation. It can be estimated by a computationally feasible expectation–maximization algorithm. In a case study of sea currents in the Northern Adriatic Sea, it provides a parsimonious representation of the sea surface in terms of alternating environmental states.

Plasticity of death rates in stationary phase in Saccharomyces cerevisiae

For the species that have been most carefully studied, mortality rises with age and then plateaus or declines at advanced ages, except for yeast. Remarkably, mortality for yeast can rise, fall and rise again. In the present study we investigated (i) if this complicated shape could be modulated by environmental conditions by measuring mortality with different food media and temperature; (ii) if it is triggered by biological heterogeneity by measuring mortality in stationary phase in populations fractionated into subpopulations of young, virgin cells, and replicatively older, non‐virgin cells. We also discussed the results of a staining method to measure viability instead of measuring the number of cells able to exit stationary phase and form a colony. We showed that different shapes of age‐specific death rates were observed and that their appearance depended on the environmental conditions. Furthermore, biological heterogeneity explained the shapes of mortality with homogeneous populations of young, virgin cells exhibiting a simple shape of mortality in conditions under which more heterogeneous populations of older cells or unfractionated populations displayed complicated death rates. Finally, the staining method suggested that cells lost the capacity to exit stationary phase and to divide long before they died in stationary phase. These results explain a phenomenon that was puzzling because it appeared to reflect a radical departure from mortality patterns observed for other species.

The plateau of human mortality: Demography of longevity pioneers

Mortality rates level off at extreme age The demography of human longevity is a contentious topic. On the basis of high-quality data from Italians aged 105 and older, Barbi et al. show that mortality is constant at extreme ages but at levels that decline somewhat across cohorts. Human death rates increase exponentially up to about age 80, then decelerate, and plateau after age 105. Science, this issue p. 1459 A study of centenarians in Italy suggests that human mortality is approximately constant in extreme old age. Theories about biological limits to life span and evolutionary shaping of human longevity depend on facts about mortality at extreme ages, but these facts have remained a matter of debate. Do hazard curves typically level out into high plateaus eventually, as seen in other species, or do exponential increases persist? In this study, we estimated hazard rates from data on all inhabitants of Italy aged 105 and older between 2009 and 2015 (born 1896–1910), a total of 3836 documented cases. We observed level hazard curves, which were essentially constant beyond age 105. Our estimates are free from artifacts of aggregation that limited earlier studies and provide the best evidence to date for the existence of extreme-age mortality plateaus in humans.

Latent time-varying factors in longitudinal analysis: a linear mixed hidden Markov model for heart rates.

Longitudinal data are often segmented by unobserved time-varying factors, which introduce latent heterogeneity at the observation level, in addition to heterogeneity across subjects. We account for this latent structure by a linear mixed hidden Markov model. It integrates subject-specific random effects and Markovian sequences of time-varying effects in the linear predictor. We propose an expectationŰ-maximization algorithm for maximum likelihood estimation, based on data augmentation. It reduces to the iterative maximization of the expected value of a complete likelihood function, derived from an augmented dataset with case weights, alternated with weights updating. In a case study of the Survey on Stress Aging and Health in Russia, the model is exploited to estimate the influence of the observed covariates under unobserved time-varying factors, which affect the cardiovascular activity of each subject during the observation period.

A missing composite covariate in survival analysis: A case study of the Chinese Longitudinal Health and Longevity Survey

We estimate a Cox proportional hazards model where one of the covariates measures the level of a subjects cognitive functioning by grading the total score obtained by the subject on the items of a questionnaire. A case study is presented where the sample includes partial respondents, who did not answer some questionnaire items. The total score takes, hence, the form of an interval-censored variable and, as a result, the level of cognitive functioning is missing on some subjects. We handle the partial respondents by taking a likelihood-based approach where survival time is jointly modelled with the censored total score and the size of the censoring interval. Estimates are obtained by an E-M-type algorithm that reduces to the iterative maximization of three complete log-likelihood functions derived from two augmented data sets with case weights, alternated with weights updating. This methodology is exploited to assess the Mini-Mental State Examination index as a prognostic factor of survival in a sample of Chinese older adults.

Handling endogeneity and nonnegativity in correlated random effects models: Evidence from ambulatory expenditure

We describe a mixed-effects model for nonnegative continuous cross-sectional data in a two-part modelling framework. A potentially endogenous binary variable is included in the model specification and association between the outcomes is modeled through a (discrete) latent structure. We show how model parameters can be estimated in a finite mixture context, allowing for skewness, multivariate association between random effects and endogeneity. The model behavior is investigated through a large-scale simulation experiment. The proposed model is computationally parsimonious and seems to produce acceptable results even if the underlying random effects structure follows a continuous parametric (e.g. Gaussian) distribution. The proposed approach is motivated by the analysis of a sample taken from the Medical Expenditure Panel Survey. The analyzed outcome, that is ambulatory health expenditure, is a mixture of zeros and continuous values. The effects of socio-demographic characteristics on health expenditure are investigated and, as a by-product of the estimation procedure, two subpopulations (i.e. high and low users) are identified.

A time-dependent extension of the projected Normal regression model for longitudinal circular data based on a hidden Markov heterogeneity structure

The modelling of animal movement is an important ecological and environmental issue. It is well-known that animals change their movement patterns over time, according to observable and unobservable factors. To trace the dynamics of behaviors, to identify factors influencing these dynamics and unobserved characteristics driving intra-subjects correlations, we introduce a time-dependent mixed effects projected normal regression model. A set of animal-specific parameters following a hidden Markov chain is introduced to deal with unobserved heterogeneity. For the maximum likelihood estimation of the model parameters, we outline an expectation–maximization algorithm. A large-scale simulation study provides evidence on model behavior. The data analysis approach based on the proposed model is finally illustrated by an application to a dataset, which derives from a population of Talitrus saltator from the beach of Castiglione della Pescaia (Italy).