La valutazione della qualità dei servizi ospedalieri: applicazione dei modelli ad equazioni strutturali ad un caso concreto

Studi applicativi finalizzati all’attivazione del sistema di monitoraggio delle acque marino costiere della Regione Sicilia. Standardizzazione di descrittori biotici in Posidonia oceanica e nelle comunità meiobentoniche di fondi mobili e predisposizione di criteri per il posizionamento di reti di sorveglianza della qualità dell’acqua (D. Lgs. 152/99 e Direttiva 2000/60/UE)

L’Informazione Statistica per le Politiche Ambientali: Stato e Prospettive

On Rao Score and Pearson X2 Statistics in Generalized Linear Models

The identity of the Rao score and PearsonX 2 statistics is well known in the areas where the latter was first introduced: goodness-of-fit in contingency tables and binary responses. We show in this paper that the same identity holds when the two statistics are used for testing goodness-of-fit of Generalized Linear Models. We also highlight the connections that exist between the two statistics when they are used for the comparison of nested models. Finally, we discuss some merits of these unifying results.

Regression diagnostics to analyze complex ecological systems through Generalized Linear Mixed Models

An alternative representation of Altham's multiplicative-binomial distribution

Abstract Cox (1972) introduced a log-linear representation for the joint distribution of n binary-dependent responses. Altham (1978) derived the distribution of the sum of such responses, under a multiplicative, rather than log-linear, representation and called it multiplicative-binomial. We propose here an alternative form of the multiplicative-binomial, which is derived from the original Cox's representation and is characterized by intuitively meaningful parameters, and compare its first two moments with those of the standard binomial distribution.

Using Zero-Inflated Models to analyze environmental data sets with many zeroes

Estimating COVID-19-induced Excess Mortality in Lombardy

AbstractWe compare the expected all-cause mortality with the observed one for different age classes during the pandemic in Lombardy, which was the epicenter of the epidemic in Italy and still is the region most affected by the pandemic. A generalized linear mixed model is introduced to model weekly mortality from 2011 to 2019, taking into account seasonal patterns and year-specific trends. Based on the 2019 year-specific conditional best linear unbiased predictions, a significant excess of mortality is estimated in 2020, leading to approximately 35000 more deaths than expected, mainly arising during the first wave. In 2021, instead, the excess mortality is not significantly different from z…

Spatio-temporal modelling of COVID-19 incident cases using Richards’ curve: An application to the Italian regions

Abstract We introduce an extended generalised logistic growth model for discrete outcomes, in which spatial and temporal dependence are dealt with the specification of a network structure within an Auto-Regressive approach. A major challenge concerns the specification of the network structure, crucial to consistently estimate the canonical parameters of the generalised logistic curve, e.g. peak time and height. We compared a network based on geographic proximity and one built on historical data of transport exchanges between regions. Parameters are estimated under the Bayesian framework, using Stan probabilistic programming language. The proposed approach is motivated by the analysis of bot…

Stato di Qualità Ecologica (EcoQ) delle acque costiere in Mediterraneo mediante l’indice biotico POSIX (POSidonia IndeX)

Model interpretation from the additive elements of the PWRSS in GLMMs

Generalized Linear Mixed models(GLMMs)have rapidly become a widely used tool for modelling clustered and longitudinal data with non-Normal responses. Although a large amount of work has been done in the literature on likelihood-based inference on GLMMs,little seems to have been done on the decomposition of the total variability associated to the different components of a mixed model.In this work we try to generalize the idea of likelihood additive elements Whittaker,1984), proposed in the context of GLMs,to the case of GLMMs by using the Penalized Weighted Residual Sum of Squares(PWRSS). The proposal is illustrated by means of areal application.

A note on adjusted responses, fitted values and residuals in Generalized Linear Models

Adjusted responses, adjusted fitted values and adjusted residuals are known to play in Generalized Linear Models the role played in Linear Models by observations, fitted values and ordinary residuals. We think this parallelism, which was widely recognized and used in the early literature on Generalized Linear Models, has been somewhat overlooked in more recent presentations. We revise this parallelism, systematizing and proving some results that are either scattered or not satisfactorily spelled out in the literature. In particular, we formally derive the asymptotic dispersion matrix of the (scaled) adjusted residuals, by proving that in Generalized Linear Models the fitted values are asym…

Analysing the mediating role of a network: a Bayesian latent space approach

The use of network analysis for the investigation of social structures has recently seen a rise, due both to the high availability of data and to the numerous insights it can provide into different fields. Most analyses focus on the topological characteristics of networks and the estimation of relationships between the nodes. We adopt a different point of view, by considering the whole network as a random variable conveying the effect of an exposure on a response. This point of view represents a classical mediation setting, where the interest lies in the estimation of the indirect effect, that is, the effect propagated through the mediating variable. We introduce a latent space model mappin…

Modeling Posidonia oceanica growth data: from linear to generalized linear mixed models

The statistical analysis of annual growth of Posidonia oceanica is traditionally carried out through Gaussian linear models applied to untransformed, or log-transformed, data. In this paper, we claim that there are good reasons for re-considering this established practice, since real data on annual growth often violate the assumptions of Gaussian linear models, and show that the class of Generalized Linear Models (GLMs) represents a useful alternative for handling such violations. By analyzing Sicily PosiData-1, a real dataset on P. oceanica growth data gathered in the period 2000–2002 along the coasts of Sicily, we find that in the majority of cases Normality is rejected and the effect of …

Heterogeneity of obesity-asthma association disentangled by latent class analysis, the SAPALDIA cohort

Although evidence for the heterogeneity of asthma accumulated, consensus for definitions of asthma phenotypes is still lacking. Obesity may have heterogeneous effects on various asthma phenotypes. We aimed to distinguish asthma phenotypes by latent class analysis and to investigate their associations with different obesity parameters in adults using a population-based Swiss cohort (SAPALDIA). We applied latent class analysis to 959 self-reported asthmatics using information on disease activity, atopy, and age of onset. Associations with obesity were examined by multinomial logistic regression, after adjustments for age, sex, smoking status, educational level, and study centre. Body mass ind…

The “ThreePlusOne” Likelihood-Based Test Statistics: Unified Geometrical and Graphical Interpretations

The presentation of the well known Likelihood Ratio, Wald and Score test statistics in textbooks appears to lack a unified graphical and geometrical interpretation. We present two simple graphical representations on a common scale for these three test statistics, and also the recently proposed Gradient test statistic. These unified graphical displays may favour better understanding of the geometrical meaning of the likelihood based statistics and provide useful insights into their connections.

Unreliable predictions about COVID‐19 infections and hospitalizations make people worry: The case of Italy

Estimating COVID-19-induced Excess Mortality in Lombardy, Italy.

We compare the expected all-cause mortality with the observed one for different age classes during the pandemic in Lombardy, which was the epicenter of the epidemic in Italy. The first case in Italy was found in Lombardy in early 2020, and the first wave was mainly centered in Lombardy. The other three waves, in Autumn 2020, March 2021 and Summer 2021 are also characterized by a high number of cases in absolute terms. A generalized linear mixed model is introduced to model weekly mortality from 2011 to 2019, taking into account seasonal patterns and year-specific trends. Based on the 2019 year-specific conditional best linear unbiased predictions, a significant excess of mortality is estima…

A penalized approach for the bivariate ordered logistic model with applications to social and medical data

Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the number of global odds ratios to be estimated also increases, and estimation gets problematic. In this work we propose a non-parametric approach for the maximum likelihood (ML) estimation of a BOLM, wherein penalties to the differences between adjacent row and column effects are applied. Our proposal is then compared to the Goodman and Dale models. Some simulation results as well as analyses of two real data sets are presented and discussed.

Generalized Symmetry Models for Hypercubic Concordance Tables

Summary Frequency data obtained classifying a sample of 'units' by the same categorical variable repeatedly over 'components', can be arranged in a hypercubic concordance table (h.c.t.). This kind of data naturally arises in a number of different areas such as longitudinal studies, studies using matched and clustered data, item-response analysis, agreement analysis. In spite of the substantial diversity of the mechanisms that can generate them, data arranged in a h.c.t. can all be analyzed via models of symmetry and quasi-symmetry, which exploit the special structure of the h.c.t. The paper extends the definition of such models to any dimension, introducing the class of generalized symmetry…

A matrix-valued Bernoulli distribution

AbstractMatrix-valued distributions are used in continuous multivariate analysis to model sample data matrices of continuous measurements; their use seems to be neglected for binary, or more generally categorical, data. In this paper we propose a matrix-valued Bernoulli distribution, based on the log-linear representation introduced by Cox [The analysis of multivariate binary data, Appl. Statist. 21 (1972) 113–120] for the Multivariate Bernoulli distribution with correlated components.

Statistical analysis of P. oceanica growth data: from standard linear models to Generalized Linear Models

Testing for a breakpoint in segmented regression: a pseudo score approach

To overcome the well known oddities in testing for the existence of a breakpoint in segmented regression models, we discuss a novel approach based on the Pearson X2 statistic which can be understood as an approximation of the Score statistic. We describe the method and present results from some simulations.

Analisi delle performance di crescita di Posidonia oceanica attraverso l’uso di modelli lineari generalizzati misti (GLMM)

An ensemble approach to short-term forecast of COVID-19 intensive care occupancy in Italian Regions

Abstract The availability of intensive care beds during the COVID‐19 epidemic is crucial to guarantee the best possible treatment to severely affected patients. In this work we show a simple strategy for short‐term prediction of COVID‐19 intensive care unit (ICU) beds, that has proved very effective during the Italian outbreak in February to May 2020. Our approach is based on an optimal ensemble of two simple methods: a generalized linear mixed regression model, which pools information over different areas, and an area‐specific nonstationary integer autoregressive methodology. Optimal weights are estimated using a leave‐last‐out rationale. The approach has been set up and validated during t…

Separate regression modelling of the Gaussian and Exponential components of an EMG response from respiratory physiology.

If Y1 \sim N(\mu ;\sigma^2) and Y2 \sim Exp(\nu), with Y1 independent of Y2, then their sum Y = Y1 +Y2 follows an Exponentially Modified Gaussian (EMG) distribution. In many applications it is of interest to model the two components separately, in order to investigate their (possibly) different important predictors. We show how this can be done through a GAMLSS with EMG response, and apply this separate regression modelling strategy to a dataset on lung function variables from the SAPALDIA cohort study.

Nowcasting COVID‐19 incidence indicators during the Italian first outbreak

A novel parametric regression model is proposed to fit incidence data typically collected during epidemics. The proposal is motivated by real-time monitoring and short-term forecasting of the main epidemiological indicators within the first outbreak of COVID-19 in Italy. Accurate short-term predictions, including the potential effect of exogenous or external variables are provided. This ensures to accurately predict important characteristics of the epidemic (e.g., peak time and height), allowing for a better allocation of health resources over time. Parameter estimation is carried out in a maximum likelihood framework. All computational details required to reproduce the approach and replica…

Using ZIP models to analyse environmental time series with many zeroes

Dealing with the Pseudo-Replication Problem in Longitudinal Data from Posidonia Oceanica Surveys: Modeling Dependence vs. Subsampling

Posidonia oceanica represents the key species of the most important ecosystem in subtidal habitats of the Mediterranean Sea. Being sensitive to changes in the environment, it is considered a crucial indicator of the quality of coastal marine waters. A peculiarity of P. oceanica is the presence of reiterative modules characterizing its growth, which lend themselves to back-dating techniques, allowing for the reconstruction of past history of growth variables (annual rhizome elongation and diameter, primary production, etc.). Such back-dating techniques provide, for each sampled shoot, a longitudinal series of multivariate data; this is an instance of what Hurlbert (1984) in a seminal paper d…

A new multivariate Biotic Index to assess Ecological Quality status of Mediterranean coastal waters

A penalized approach to the bivariate logistic regression model for the association between ordinal responses

Bivariate ordered logistic models (BOLMs) are appealing to jointly model the marginal distribution of two ordered responses and their association, given a set of covariates. When the number of categories of the responses increases, the number of global odds ratios (or their re-parametrizations) to be estimated also increases and estimating the association structure becomes crucial for this type of data. In fact, such data could be too "rich" to be fully modelled with an ordinary BOLM while, sometimes, the well-known Dale's model could be too parsimonious to provide a good fit. In addition, when the cross-tabulation of the responses contains some zeros, for a number of model configurations, …

Modelling the relationship between sexual reproduction and rhizome growth in Posidonia oceanica (L.) Delile

The relationship between flowering and growth performance of Posidonia oceanica (L.) Delile in meadows distributed along the south-eastern coast of Sicily (Italy) was investigated by means of a statistical model (generalized linear mixed model) combined with the lepidochronological analysis. Over a 28-year period, 67 floral stalk remains were observed. The highest flowering index was recorded in lepidochronological year 1998 (10.1%) and the Inflorescence Frequency per age showed a clear decrease corresponding to 15-year-old shoots. The sexual reproductive event had positive effects on rhizome elongation (cm year−1) and leaf production (no. leaves year−1) in the same flowering year, whilst n…

Le fanerogame marine in Sicilia

A generalization of the Binomial distribution based on the dependence ratio

We propose a generalization of the Binomial distribution, called DR-Binomial, which accommodates dependence among units through a model based on the dependence ratio (Ekholm et al., Biometrika, 82, 1995, 847). Properties of the DR-Binomial are discussed, and the constraints on its parameter space are studied in detail. Likelihood-based inference is presented, using both the joint and profile likelihoods; the usefulness of the DR-Binomial in applications is illustrated on a real dataset displaying negative unit-dependence, and hence under-dispersion compared with the Binomial. Although the DR-Binomial turns out to be a reparameterization of Altham's Additive-Binomial and Kupper-Haseman's Cor…

Dealing with dependence in retrospective ecological data through longitudinal models

DNA Methylation in Inflammatory Pathways Modifies the Association between BMI and Adult-Onset Non-Atopic Asthma

A high body mass (BMI) index has repeatedly been associated with non-atopic asthma, but the biological mechanism linking obesity to asthma is still poorly understood. We aimed to test the hypothesis that inflammation and/or innate immunity plays a role in the obesity-asthma link. DNA methylome was measured in blood samples of 61 non-atopic participants with asthma and 146 non-atopic participants without asthma (non-smokers for at least 10 years) taking part in the Swiss Cohort Study on Air Pollution and Lung and Heart Diseases in Adults (SAPALDIA) study. Modification by DNA methylation of the association of BMI or BMI change over 10 years with adult-onset asthma was examined at each CpG sit…

A generalization of the Binomial distribution based on the dependence ratio

We propose a generalization of the Binomial distribution, called DR-Binomial, which accommodates dependence among units through a model based on the dependence ratio (Ekholm et al., Biometrika, 82, 1995, 847). Properties of the DR-Binomial are discussed, and the constraints on its parameter space are studied in detail. Likelihood-based inference is presented, using both the joint and profile likelihoods; the usefulness of the DR-Binomial in applications is illustrated on a real dataset displaying negative unit-dependence, and hence under-dispersion compared with the Binomial. Although the DR-Binomial turns out to be a reparameterization of Altham's Additive-Binomial and Kupper–Haseman's Cor…

Effetto a breve termine dell'inquinamento sulla salute: Palermo 1997-2002

Residential greenness-related DNA methylation changes

Abstract Background Residential greenness has been associated with health benefits, but its biological mechanism is largely unknown. Investigation of greenness-related DNA methylation profiles can contribute to mechanistic understanding of the health benefits of residential greenness. Objective To identify DNA methylation profiles associated with greenness in the immediate surroundings of the residence. Methods We analyzed genome-wide DNA methylation in 1938 blood samples (982 participants) from the Swiss Cohort Study on Air Pollution and Lung and Heart Diseases in Adults (SAPALDIA). We estimated residential greenness based on normalized difference vegetation index at 30 × 30 m cell (green3…

Confondimento dell’età nell’analisi degli effetti di perturbazioni antropiche su variabili biometriche di Posidonia oceanica (L.) Delile

Potenzialità e vantaggi dell’uso di Modelli Lineari Generalizzati e di Modelli Lineari Generalizzati Misti nell’analisi statistica della crescita di Posidonia oceanica.

Subject-specific odds ratios in binomial GLMMs with continuous response

In a regression context, the dichotomization of a continuous outcome variable is often motivated by the need to express results in terms of the odds ratio, as a measure of association between the response and one or more risk factors. Starting from the recent work of Moser and Coombs (Odds ratios for a continuous outcome variable without dichotomizing, Statistics in Medicine, 2004, 23, 1843-1860), in this article we explore in a mixed model framework the possibility of obtaining odds ratio estimates from a regression linear model without the need of dichotomizing the response variable. It is shown that the odds ratio estimators derived from a linear mixed model outperform those from a binom…

Estimating the Bayesian posterior distribution of indirect effects in causal longitudinal mediation analysis

Many research studies aim to unveil the causal mechanism underlying a particular phenomenon; mediation analysis is increasingly used for this scope, and longitudinal data are particularly suited for mediation since they ensure the correct temporal order among variables and the time spanning allows the causal effects to unfold. This explains the rise of interest in the topic of longitudinal mediation analysis. Many approaches have been proposed to cope with longitudinal mediation (Fosen et al., 2005; Lin et al., 2017), among which mixed-effect modelling. In a recent paper, Bind et al. (Biostatistics, 2016) made use of generalised mixed effect models and provided conditions for the identifiab…

Bayesian causal mediation analysis through linear mixed-effect models

In mediational settings, the main focus is on the estimation of the indirect effect of an exposure on an outcome through a third variable called mediator. The traditional maximum likelihood estimation method presents several problems in the estimation of the standard error and the confidence interval of the indirect effect. In this paper, we propose a Bayesian approach to obtain the posterior distribution of the indirect effect through MCMC, in the context of mediational mixed models for longitudinal data. A simulation study shows that our method outperforms the traditional maximum likelihood approach in terms of bias and coverage rates.

Shoot age as a confounding factor on detecting the effect of human-induced disturbance on Posidonia oceanica growth performance

Abstract The response of orthotropic rhizome elongation and primary production of Posidonia oceanica to anthropogenic perturbations and potential confounding effects of shoot age were assessed using a Linear Multilevel Model (LMM). This model examined the confounding effect of age by comparing the estimates of impact and variance components obtained by excluding and including Age as an explanatory variable. Age had a negative effect on rhizome elongation and primary production with an annual decrease of 0.6 mm y − 1 and 7 mg dw y − 1 respectively. According to the LMM when age effect was omitted, the differences between disturbed and control locations in rhizome elongation and primary produ…

A Comparison between Simple and Multiple Imputation in Applying Logistic Regression Models

A recap on Linear Mixed Models and their hat-matrices

This working paper has a twofold goal. On one hand, it provides a recap of Linear Mixed Models (LMMs): far from trying to be exhaustive, this first part of the working paper focusses on the derivation of theoretical results on estimation of LMMs that are scattered in the literature or whose mathematical derivation is sometimes missing or too quickly sketched. On the other hand, it discusses various definitions that are available in the literature for the hat-matrix of Linear Mixed Models, showing their limitations and proving their equivalence.

Variazioni spaziali e temporali delle performance di crescita nelle praterie di Posidonia oceanica (L.) Delile: fattore endogeno vs. fattori esogeni

Networks as mediating variables: a Bayesian latent space approach

AbstractThe use of network analysis to investigate social structures has recently seen a rise due to the high availability of data and the numerous insights it can provide into different fields. Most analyses focus on the topological characteristics of networks and the estimation of relationships between the nodes. We adopt a different perspective by considering the whole network as a random variable conveying the effect of an exposure on a response. This point of view represents a classical mediation setting, where the interest lies in estimating the indirect effect, that is, the effect propagated through the mediating variable. We introduce a latent space model mapping the network into a …

Second-order interaction in a Trivariate Generalized Gamma Distribution

The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).