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Prediction invariance of causal models under heterogeneous settings has been exploited by a number of recent methods for causal discovery, typically focussing on recovering the causal parents of a target variable of interest. When instrumental variables are not available, the causal Dantzig estimator exploits invariance under the more restrictive case of shift interventions. However, also in this case, one requires observational data from a number of sufficiently different environments, which is rarely available. In this paper, we consider a structural equation model where the target variable is described by a generalised additive model conditional on its parents. Besides having finite moments, no modelling assumptions are made on the conditional distributions of the other variables in the system. Under this setting, we characterise the causal model uniquely by means of two key properties: the Pearson residuals are invariant under the causal model and conditional on the causal parents the causal parameters maximise the population likelihood. These two properties form the basis of a computational strategy for searching the causal model among all possible models. Crucially, for generalised linear models with a known dispersion parameter, such as Poisson and logistic regression, the causal model can be identified from a single data environment.

Traditional inference in relational event models from dynamic network data involves only dyadic and node-specific variables, as anything that is global, i.e. constant across dyads, drops out of the partial likelihood. We address this with the use of nested case-control sampling on a time-shifted version of the event process. This leads to a partial likelihood of a degenerate logistic additive model, enabling efficient estimation of global and non-global covariate effects. The method's effectiveness is demonstrated through a simulation study. An application to bike sharing data reveals significant influences of global covariates like weather and time of day on bike-sharing dynamics.

Cultural values vary significantly around the world. Despite a large heterogeneity, similarities across national cultures are present. This paper studies cross-country culture heterogeneity via the joint inference of country-specific copula graphical models from world-wide survey data. To this end, a random graph generative model of the cultural networks is introduced, with a latent space and proximity measures that embed cultural relatedness across countries. Within-country heterogeneity is also accounted for, via parametric modelling of the marginal distributions of each cultural trait. All together, the different components of the model are able to identify several dimensions of culture.

Various processes can be modelled as quasi-reaction systems of stochastic differential equations, such as cell differentiation and disease spreading. Since the underlying data of particle interactions, such as reactions between proteins or contacts between people, are typically unobserved, statistical inference of the parameters driving these systems is developed from concentration data measuring each unit in the system over time. While observing the continuous time process at a time scale as fine as possible should in theory help with parameter estimation, the existing Local Linear Approximation (LLA) methods fail in this case, due to numerical instability caused by small changes of the system at successive time points. On the other hand, one may be able to reconstruct the underlying unobserved interactions from the observed count data. Motivated by this, we first formalise the latent event history model underlying the observed count process. We then propose a computationally efficient Expectation-Maximation algorithm for parameter estimation, with an extended Kalman filtering procedure for the prediction of the latent states. A simulation study shows the performance of the proposed method and highlights the settings where it is particularly advantageous compared to the existing LLA approaches. Finally, we present an illustration of the methodology on the spreading of the COVID-19 pandemic in Italy.

The microbiome constitutes a complex microbial ecology of interacting components that regulates important pathways in the host. Measurements of microbial abundances are key to learning the intricate network of interactions amongst microbes. Microbial communities at various body sites tend to share some overall common structure, while also showing diversity related to the needs of the local environment. We propose a computational approach for the joint inference of microbiota systems from metagenomic data for a number of body sites. The random graphical model (RGM) allows for heterogeneity across the different environments while quantifying their relatedness at the structural level. In addition, the model allows for the inclusion of external covariates at both the microbial and interaction levels, further adapting to the richness and complexity of microbiome data. Our results show how: the RGM approach is able to capture varying levels of structural similarity across the different body sites and how this is supported by their taxonomical classification; the Bayesian implementation of the RGM fully quantifies parameter uncertainty; the microbiome network posteriors show not only a stable core, but also interesting individual differences between the various body sites, as well as interpretable relationships between various classes of microbes.

Hematopoiesis is the process of blood cell formation, through which progenitor stem cells differentiate into mature forms, such as white and red blood cells or mature platelets. While the precursors of the mature forms share many regulatory pathways involving common cellular nuclear factors, specific networks of regulation shape their fate towards one lineage or another. In this study, we aim to analyse the complex regulatory network that drives the formation of mature red blood cells and platelets from their common precursor. To this aim, we develop a dedicated graphical model which we infer from the latest RT-qPCR genomic data. The model also accounts for the effect of external genomic data. A computationally efficient Expectation-Maximization algorithm allows regularised network inference from the high-dimensional and often only partially observed RT-qPCR data. A careful combination of alternating direction method of multipliers algorithms allows achieving sparsity in the individual lineage networks and a high sharing between these networks, together with the detection of the associations between the membrane-bound receptors and the nuclear factors. The approach will be implemented in the R package cglasso and can be used in similar applications where network inference is conducted from high-dimensional, heterogeneous and partially observed data.

High dimensional and heterogeneous count data are collected in various applied fields. In this paper, we look closely at high-resolution sequencing data on the microbiome, which have enabled researchers to study the genomes of entire microbial communities. Revealing the underlying interactions between these communities is of vital importance to learn how microbes influence human health. To perform structural learning from multivariate count data such as these, we develop a novel Gaussian copula graphical model with two key elements. Firstly, we employ parametric regression to characterize the marginal distributions. This step is crucial for accommodating the impact of external covariates. Neglecting this adjustment could potentially introduce distortions in the inference of the underlying network of dependences. Secondly, we advance a Bayesian structure learning framework, based on a computationally efficient search algorithm that is suited to high dimensionality. The approach returns simultaneous inference of the marginal effects and of the dependence structure, including graph uncertainty estimates. A simulation study and a real data analysis of microbiome data highlight the applicability of the proposed approach at inferring networks from multivariate count data in general, and its relevance to microbiome analyses in particular. The proposed method is implemented in the R package BDgraph.

Making use of the information from the World Value Survey (WVS), and operationalizing a definition of national culture that encompasses both the relevance of specific cultural traits and the interdependence among them, this paper proposes a methodology to reveal the latent structure of national culture and to measure cultural distance between countries that takes into account both the difference in cultural traits and the difference in the network structure of national cultures. Exploiting the possibilities offered by copula graphical models for discrete data, this paper infers the cultural networks of all the countries included in the WVS (Wave 6) and proposes a novel unifying framework to measure national culture and international cultural distances. The Jeffreys' divergence between copula graphical models, taken as the measure of cultural distance between countries, captures the orthogonality of the two components of cultural distance: the one based on cultural traits and the one based on the network structure among them. Moreover, the two components are shown to correlate with different national and structural characteristics of cultural networks, thus encompassing the different informational sets related to national cultures., Comment: 27 pages, 12 figures, 4 tables

With the advent of ubiquitous monitoring and measurement protocols, studies have started to focus more and more on complex, multivariate and heterogeneous datasets. In such studies, multivariate response variables are drawn from a heterogeneous population often in the presence of additional covariate information. In order to deal with this intrinsic heterogeneity, regression analyses have to be clustered for different groups of units. Up until now, mixture model approaches assigned units to distinct and non-overlapping groups. However, not rarely these units exhibit more complex organization and clustering. It is our aim to define a mixture of generalized linear models with overlapping clusters of units. This involves crucially an overlap function, that maps the coefficients of the parent clusters into the the coefficient of the multiple allocation units. We present a computationally efficient MCMC scheme that samples the posterior distribution of the parameters in the model. An example on a two-mode network study shows details of the implementation in the case of a multivariate probit regression setting. A simulation study shows the overall performance of the method, whereas an illustration of the voting behaviour on the US supreme court shows how the 9 justices split in two overlapping sets of justices., Comment: 24 pages, 3 figures

Motivated by reasons such as altruism, managers from different hospitals may engage in cooperative behaviours, which shape the networked healthcare economy. In this paper we study the determinants of hospital cooperation and its association with the quality delivered by hospitals, using Italian administrative data. We explore the impact on patient transfers between hospitals (cooperation/network) of a set of demand-supply factors, as well as distance-based centrality measures. We then use this framework to assess how such cooperation is related to the overall quality for the hospital of origin and of destination of the patient transfer. The over-dispersed Poisson mixed model that we propose, inspired by the literature on social relations models, is suitably defined to handle network data, which are rarely used in health economics. The results show that distance plays an important role in hospital cooperation, though there are other factors that matter such as geographical centrality. Another empirical finding is the existence of a positive relationship between hospital cooperation and the overall quality of the connected hospitals. The absence of a source of information on the quality of hospitals accessible to all providers, such as in the form of star ratings, may prevent some hospitals to engage and cooperate with other hospitals of potentially higher quality. This may result in a lower degree of cooperation among hospitals and a reduction in quality overall.

In many applied fields, such as genomics, different types of data are collected on the same system, and it is not uncommon that some of these datasets are subject to censoring as a result of the measurement technologies used, such as data generated by polymerase chain reactions and flow cytometer. When the overall objective is that of network inference, at possibly different levels of a system, information coming from different sources and/or different steps of the analysis can be integrated into one model with the use of conditional graphical models. In this paper, we develop a doubly penalized inferential procedure for a conditional Gaussian graphical model when data can be subject to censoring. The computational challenges of handling censored data in high dimensionality are met with the development of an efficient Expectation-Maximization algorithm, based on approximate calculations of the moments of truncated Gaussian distributions and on a suitably derived two-step procedure alternating graphical lasso with a novel block-coordinate multivariate lasso approach. We evaluate the performance of this approach on an extensive simulation study and on gene expression data generated by RT-qPCR technologies, where we are able to integrate network inference, differential expression detection and data normalization into one model.

Mixed Probit models are widely applied in many fields where prediction of a binary response is of interest. Typically, the random effects are assumed to be independent but this is seldom the case for many real applications. In the credit risk application considered in this paper, random effects are present at the level of industrial sectors and they are expected to be correlated due to inter-firm credit links inducing dependencies in the firms' risk to default. Unfortunately, existing inferential procedures for correlated mixed Probit models are computationally very intensive already for a moderate number of effects. Borrowing from the literature on large network inference, we propose an efficient Expectation-Maximization algorithm for unconstrained and penalised likelihood estimation and derive the asymptotic standard errors of the estimates. An extensive simulation study shows that the proposed approach enjoys substantial computational gains relative to standard Monte Carlo approaches, while still providing accurate parameter estimates. Using data on nearly 64,000 accounts for small and medium-sized enterprises in the United Kingdom in 2013 across 14 industrial sectors, we find that accounting for network effects via a correlated mixed Probit model increases significantly the default prediction power of the model compared to conventional default prediction models, making efficient inferential procedures for these models particularly useful in this field.

Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this estimator theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. Typical examples are data generated by polymerase chain reactions and flow cytometer. The combination of censoring and high-dimensionality make inference of the underlying genetic networks from these data very challenging. In this paper we propose an $\ell_1$-penalized Gaussian graphical model for censored data and derive two EM-like algorithms for inference. By an extensive simulation study, we evaluate the computational efficiency of the proposed algorithms and show that our proposal overcomes existing competitors when censored data are available. We apply the proposed method to gene expression data coming from microfluidic RT-qPCR technology in order to make inference on the regulatory mechanisms of blood development.

Fertility plans, measured by the number of planned children, have been found to be affected by education and family background via complex tail dependencies. This challenge was previously met with the use of non-parametric jittering approaches. This paper shows how a novel generalized additive model based on a discrete Weibull distribution provides partial effects of the covariates on fertility plans which are comparable to jittering, without the inherent drawback of crossing conditional quantiles. The model has some additional desirable features: both over- and under-dispersed data can be modelled by this distribution, the conditional quantiles have a simple analytic form and the likelihood is the same of that of a continuous Weibull distribution with interval-censored data. The latter means that efficient implementations are already available, in the R package gamlss, for a range of models and inferential procedures, and at a fraction of the time compared to the jittering and COM-Poisson approaches, showing potential for the wide applicability of this approach to the modelling of count data., Comment: 19 pages, 5 figures, 7 tables

Actor-event data are common in sociological settings, whereby one registers the pattern of attendance of a group of social actors to a number of events. We focus on 79 members of the Noordin Top terrorist network, who were monitored attending 45 events. The attendance or non-attendance of the terrorist to events defines the social fabric, such as group coherence and social communities. The aim of the analysis of such data is to learn about the affiliation structure. Actor-event data is often transformed to actor-actor data in order to be further analysed by network models, such as stochastic block models. This transformation and such analyses lead to a natural loss of information, particularly when one is interested in identifying, possibly overlapping, subgroups or communities of actors on the basis of their attendances to events. In this paper we propose an actor-event model for overlapping communities of terrorists, which simplifies interpretation of the network. We propose a mixture model with overlapping clusters for the analysis of the binary actor-event network data, called {\tt manet}, and develop a Bayesian procedure for inference. After a simulation study, we show how this analysis of the terrorist network has clear interpretative advantages over the more traditional approaches of affiliation network analysis., Comment: 24 pages, 5 figures; related R package (manet) available on CRAN

Pay-for-performance approaches have been widely adopted in order to drive improvements in the quality of healthcare provision. Previous studies evaluating the impact of these programs are either limited by the number of health outcomes or of medical conditions considered. In this paper, we evaluate the effectiveness of a pay-for-performance program on the basis of five health outcomes and across a wide range of medical conditions. The context of the study is the Lombardy region in Italy, where a rewarding program was introduced in 2012. The policy evaluation is based on a difference-in-differences approach. The model includes multiple dependent outcomes, that allow quantifying the joint effect of the program, and random effects, that account for the heterogeneity of the data at the ward and hospital level. Our results show that the policy had a positive effect on the hospitals' performance in terms of those outcomes that can be more influenced by a managerial activity, namely the number of readmissions, transfers and returns to the surgery room. No significant changes which can be related to the pay-for-performance introduction are observed for the number of voluntary discharges and for mortality. Finally, our study shows evidence that the medical wards have reacted more strongly to the pay-for-performance program than the surgical ones, whereas only limited evidence is found in support of a different policy reaction across different types of hospital ownership., Comment: 16 pages, 7 figures

Regularized regression has become very popular nowadays, particularly on high-dimensional problems where the addition of a penalty term to the log-likelihood allows inference where traditional methods fail. A number of penalties have been proposed in the literature, such as lasso, SCAD, ridge and elastic net to name a few. Despite their advantages and remarkable performance in rather extreme settings, where $p \gg n$, all these penalties, with the exception of ridge, are non-differentiable at zero. This can be a limitation in certain cases, such as computational efficiency of parameter estimation in non-linear models or derivation of estimators of the degrees of freedom for model selection criteria. With this paper, we provide the scientific community with a differentiable penalty, which can be used in any situation, but particularly where differentiability plays a key role. We show some desirable features of this function and prove theoretical properties of the resulting estimators within a regularized regression context. A simulation study and the analysis of a real dataset show overall a good performance under different scenarios. The method is implemented in the R package DLASSO freely available from CRAN.

Network enrichment analysis is a powerful method, which allows to integrate gene enrichment analysis with the information on relationships between genes that is provided by gene networks. Existing tests for network enrichment analysis deal only with undirected networks, they can be computationally slow and are based on normality assumptions. We propose NEAT, a test for network enrichment analysis. The test is based on the hypergeometric distribution, which naturally arises as the null distribution in this context. NEAT can be applied not only to undirected, but to directed and partially directed networks as well. Our simulations indicate that NEAT is considerably faster than alternative resampling-based methods, and that its capacity to detect enrichments is at least as good as the one of alternative tests. We discuss applications of NEAT to network analyses in yeast by testing for enrichment of the Environmental Stress Response target gene set with GO Slim and KEGG functional gene sets, and also by testing for associations between GO Slim categories themselves. NEAT is a flexible and efficient test for network enrichment analysis that aims to overcome some limitations of existing resampling-based tests. The method is implemented in the R package neat, which can be freely downloaded from CRAN (http://cran.r-project.org/package=neat)., Comment: The original version of the paper is freely available (Open Access) from the editor's website (https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-016-1203-6)

Discrete data are collected in many application areas and are often characterised by highly skewed and power-lawlike distributions. An example of this, which is considered in this paper, is the number of visits to a specialist, often taken as a measure of demand in healthcare. A discrete Weibull regression model was recently proposed for regression problems with a discrete response and it was shown to possess two important features: the ability to capture over and under-dispersion simultaneously and a closed-form analytical expression of the quantiles of the conditional distribution. In this paper, we propose the first Bayesian implementation of a discrete Weibull regression model. The implementation considers a novel parameterization, where both parameters of the discrete Weibull distribution can be made dependent on the predictors. In addition, prior distributions can be imposed that encourage parameter shrinkage and that lead to variable selection. As with Bayesian procedures, the full posterior distribution of the parameters is returned, from which credible intervals can be readily calculated. A simulation study and the analysis of four real datasets of medical records show promises for the wide applicability of this approach to the analysis of count data. The method is implemented in the R package BDWreg.

Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion, which typically occurs in count datasets. It is highly desirable to have a unified model that can automatically adapt to the underlying dispersion and that can be easily implemented in practice. In this paper, a discrete Weibull regression model is shown to be able to adapt in a simple way to different types of dispersions relative to Poisson regression: overdispersion, underdispersion and covariate-specific dispersion. Maximum likelihood can be used for efficient parameter estimation. The description of the model, parameter inference and model diagnostics is accompanied by simulated and real data analyses.

Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average residuals. The addition of the moving average component results in a complex model with a very challenging implementation. In this paper, we propose to account for the time dependency in the data by explicitly adding autoregressive terms of the response variable in the linear model. In addition, we consider an autoregressive process for the errors in order to capture complex dynamic relationships parsimoniously. To broaden the application of the model, we present an $l_1$ penalized likelihood approach for the estimation of the parameters and show how the adaptive lasso penalties lead to an estimator which enjoys the oracle property. Furthermore, we prove the consistency of the estimators with respect to the mean squared prediction error in high-dimensional settings, an aspect that has not been considered by the existing time-dependent regression models. A simulation study and real data analysis show the successful applications of the model on financial data on stock indexes.

Chromatin ImmunoPrecipitation-sequencing (ChIP-seq) experiments have now become routine in biology for the detection of protein binding sites. In this paper, we present a Markov random field model for the joint analysis of multiple ChIP-seq experiments. The proposed model naturally accounts for spatial dependencies in the data, by assuming first order Markov properties, and for the large proportion of zero counts, by using zero-inflated mixture distributions. In contrast to all other available implementations, the model allows for the joint modelling of multiple experiments, by incorporating key aspects of the experimental design. In particular, the model uses the information about replicates and about the different antibodies used in the experiments. An extensive simulation study shows a lower false non-discovery rate for the proposed method, compared to existing methods, at the same false discovery rate. Finally, we present an analysis on real data for the detection of histone modifications of two chromatin modifiers from eight ChIP-seq experiments, including technical replicates with different IP efficiencies.