Graphical Chain Models Research Articles

Chain Graph Models to Elicit the Structure of a Bayesian Network

Bayesian networks are possibly the most successful graphical models to build decision support systems. Building the structure of large networks is still a challenging task, but Bayesian methods are particularly suited to exploit experts' degree of belief in a quantitative way while learning the network structure from data. In this paper details are provided about how to build a prior distribution on the space of network structures by eliciting a chain graph model on structural reference features. Several structural features expected to be often useful during the elicitation are described. The statistical background needed to effectively use this approach is summarized, and some potential pitfalls are illustrated. Finally, a few seminal contributions from the literature are reformulated in terms of structural features.

Chain graph models of multivariate regression type for categorical data

We discuss a class of chain graph models for categorical variables defined by what we call a multivariate regression chain graph Markov property. First, the set of local independencies of these models is shown to be Markov equivalent to those of a chain graph model recently defined in the literature. Next we provide a parametrization based on a sequence of generalized linear models with a multivariate logistic link function that captures all independence constraints in any chain graph model of this kind.

Properties of graphical regression models for multidimensional categorical data

We propose a two-component graphical chain model, the discrete regression distribution, where a set of discrete random variables is modeled as a response to a set of categorical and continuous covariates. The proposed model is useful for modeling a set of discrete variables measured at multiple sites along with a set of continuous and/or discrete covariates. The proposed model allows for joint examination of the dependence structure of the discrete response and observed covariates and also accommodates site-to-site variability. We develop the graphical model properties and theoretical justifications of this model. Our model has several advantages over the traditional logistic normal model used to analyze similar compositional data, including site-specific random effect terms and the incorporation of discrete and continuous covariates.

Probabilistic Image Modeling With an Extended Chain Graph for Human Activity Recognition and Image Segmentation

Chain graph (CG) is a hybrid probabilistic graphical model (PGM) capable of modeling heterogeneous relationships among random variables. So far, however, its application in image and video analysis is very limited due to lack of principled learning and inference methods for a CG of general topology. To overcome this limitation, we introduce methods to extend the conventional chain-like CG model to CG model with more general topology and the associated methods for learning and inference in such a general CG model. Specifically, we propose techniques to systematically construct a generally structured CG, to parameterize this model, to derive its joint probability distribution, to perform joint parameter learning, and to perform probabilistic inference in this model. To demonstrate the utility of such an extended CG, we apply it to two challenging image and video analysis problems: human activity recognition and image segmentation. The experimental results show improved performance of the extended CG model over the conventional directed or undirected PGMs. This study demonstrates the promise of the extended CG for effective modeling and inference of complex real-world problems.

Hypothermia in neonatal piglets: Interactions and causes of individual differences

Hypothermia is a major cause of mortality in neonatal piglets. However, there are considerable individual differences in the successful recovery from postnatal hypothermia in the common farrowing environment, and so far the causes and interactions of causes have not been studied in detail. Using 635 crossbred neonatal piglets, the aim of this study was to identify the links among different physiological and behavioral measures and their connections to the ability of piglets to overcome initial postnatal hypothermia, with rectal temperature at 2 h as the response variable. The data included birth weight, hypoxia at birth (viability score and lactate in umbilical cord blood), latency to first udder contact and first suckle, scans of individual piglet position during the first 2 h after birth, and rectal temperature at birth and 2 h postpartum. A graphical chain model was used to analyze data. The statistical variables were divided into blocks according to level (design and litter) and chronological order (prenatal, birth, perinatal, and thermoregulatory success at 2 h) before applying the graphical model to the data. Bayesian information criteria (BIC) was used for model selection. The BIC relates to maximum likelihood, but introduces an additional penalty term for the number of variables. The strength of an association between 2 variables is reported as the increase in BIC (BICinc) due to removing the link. Results indicate that at 2 h, 22.1% of the piglets had a rectal temperature below 37 °C. Out of the 16 variables included in the model, only 3 had direct links to the response variable of rectal temperature at 2 h. There was a positive relationship between rectal temperature at 2 h and birth weight (BICinc=26), and between being observed more often by the udder as opposed to alone during both the first (BICinc=8) and second hours (BICinc=19) after birth. Lighter piglets and piglets that had experienced hypoxia took longer to achieve first suckle, which in turn affected where the piglet positioned itself during the first and second hours after birth. Variables related to the birth process had no direct connection to thermoregulatory success, but were additive in the explanation of piglet behavior. The rectal temperature of individual piglets at 2 h depends largely on piglet birth weight and on piglet position in relation to sow and littermates. Birth weight is the most important single factor in successful recovery from postnatal hypothermia.

Selecting and fitting graphical chain models to longitudinal data

The aim of this paper is to demonstrate how graphical chain models can be used as effective tools in life course research focusing in particular on models for longitudinal prospective data. The substantive research question focuses on whether young motherhood is a pathway through which socio-economic disadvantage in childhood is related to poor self-reported health in adulthood among the 1970 British birth cohort. By breaking down large multivariate systems into simpler more tractable subcomponents and analysing them via local regressions, graphical models help the understanding of complicated life course processes, show the intermediate relationships between predictors, and aid the understanding of the mechanisms through which potential confounding and mediating factors affect the outcome of interest.

A Graphical Diagnostic for Identifying Influential Model Choices in Bayesian Hierarchical Models

Abstract. Real‐world phenomena are frequently modelled by Bayesian hierarchical models. The building‐blocks in such models are the distribution of each variable conditional on parent and/or neighbour variables in the graph. The specifications of centre and spread of these conditional distributions may be well motivated, whereas the tail specifications are often left to convenience. However, the posterior distribution of a parameter may depend strongly on such arbitrary tail specifications. This is not easily detected in complex models. In this article, we propose a graphical diagnostic,the Local critique plot, which detects such influential statistical modelling choices at the node level. It identifies the properties of the information coming from the parents and neighbours (the local prior) and from the children and co‐parents (the lifted likelihood) that are influential on the posterior distribution, and examines local conflict between these distinct information sources. The Local critique plot can be derived for all parameters in a chain graph model.

Orphanhood and vulnerability: a conduit to poor child health outcomes in Rwanda

The HIV epidemic in sub-Saharan Africa has caused many children to become orphaned and vulnerable. Recent studies show that orphaned and vulnerable children (OVC) lack the basic necessities for survival and development. These children are particularly at high risk of poor health and poverty. Although the poor health outcomes of these children are well documented, the complexities of the factors that mediate their health outcomes have not been systematically studied. The aim of this paper is to examine how the complex relationships between and within the proximate and socio-economic determinants mediate the poor health outcomes of children through their OVC status. The analyses considered graphical chain modelling of morbidity data from a sample of 3745 children aged below five years from the 2005 Rwandan Demographic and Health Survey. The results show that OVC status influences the risk of childhood morbidity both directly and indirectly and also as a conduit through which other significant proximate factors and socio-economic factors operate.

The impact of different dietary patterns on nutritional status and metabolic integrity in asymptomatic individuals living with HIV infection (PLWH) in South Africa

Adequate nutritional status promotes optimal structure and function. In PLWH, few studies on the impact of dietary intake on nutritional and metabolic status have been undertaken. This cross-sectional secondary data analysis examined how different dietary patterns influenced nutritional and metabolic integrity in asymptomatic PLWH in the North-West Province of South Africa. Dietary data were collected using validated QFFQ. Data analysis was by SPSS version 14. Dietary and nutrient patterns were generated using Principal Component Analysis. Though asymptomatic, marked biochemical differences depicting altered metabolism and inflammation were observed in PLWH compared to the uninfected. PLWH also showed an anthropometric profile that depicted altered body composition and abnormal fat distribution. Four dietary patterns: animal-based, ‘recommended’, staple, and the Carbohydrate, Vegetable and Legumes (CVL) based were observed in both PLWH and the uninfected with slight differences. In PLWH, the animal-based similar to the CVL pattern was associated with better overall nutrient intake (r=0.5, p<0.001) and selected nutrients, including energy (r=0.3, p<0.001), protein (r=0.6, p<0.001), iron (r=0.5, p<0.001), zinc (r=0.6, p<0.001) and vitamin A (r=0.5, p<0.001), compared to the other dietary patterns. The animal based dietary pattern also predicted higher BMI (OR=2.2, 95% CI=0.9-5.0), LBM (3.6, 1.3-10.4), serum albumin (1.5, 0.9-2.4) and lower liver enzymes AST (0.5, 0.3-0.8) and ALT (0.6, 0.4-0.9). Using Graphical Chain Modelling, higher intake of the animal-based but lower staple-based dietary patterns were associated with better overall nutrient intake, serum vitamins A, E, lipid score, albumin, BMI and LBM suggesting that intake of this diet may provide better nutrient quality, enhancing nutritional status and metabolic proficiency, which may ultimately influence disease progression. The findings have implications for dietary guidelines for this population but further research is required. However, if these findings are true, then a predominantly animal-based diet may be ‘recommended’ for this population. Moreover, the longer term implications of high fat intake associated with the animal based dietary pattern on obesity and associated risks should be considered. This poses a challenge to imperatively weigh up the longer term risks of the overall population profile crucial for public health.

Discrete chain graph models

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous and multivariate normal, and it is also known that one model class, referred to as models of LWF (Lauritzen–Wermuth–Frydenberg) or block concentration type, yields discrete models for categorical data that are smooth. This paper considers the structural properties of the discrete models based on the three alternative Markov properties. It is shown by example that two of the alternative Markov properties can lead to non-smooth models. The remaining model class, which can be viewed as a discrete version of multivariate regressions, is proven to comprise only smooth models. The proof employs a simple change of coordinates that also reveals that the model’s likelihood function is unimodal if the chain components of the graph are complete sets.

Transitions to adulthood and psychological distress in young adults born 12 years apart: constraints on and resources for development

Later transitions to adult roles and responsibilities have been linked with better psychological well-being yet psychological distress has risen despite young people making the transition to adulthood at older ages over recent years. We examine the role of structural constraints and adolescent resources in the relationship between the timing of transitions and psychological distress in early adult life in the 1958 National Child Development Study and the 1970 British Cohort Study. Graphical chain models were used to examine the influences on timing of four key transitions and their relationship with psychological distress (Malaise Inventory). The role of structural factors at birth (gender, social class) and adolescent resources (psychosocial problems, exam grades) were modelled. An earlier transition to adult roles was associated with an increased risk for psychological distress but so was failing to make some key transitions. Structural constraints had negative effects on successful development. Persistent social class and gender inequalities in psychological distress were evident in both cohorts. Social class constraints were mediated by educational resources whereas gender constraints were mediated by psychosocial resources. The influence of structural constraints on the timing of transitions to adult roles was more complex with evidence of positive and negative mediation and moderation effects. Delaying transition to adulthood promotes psychological health but failure of transition to independent living is associated with psychological distress. Life-course transitions are constrained by social origin and gender and possibly economic environment. Adolescent resources help young adults to make timely transitions to adult roles.

Using graphical chain models to analyze differences in structural correlates of undernutrition in Benin and Bangladesh

Undernutrition among children is one of the most important health problems in developing countries. In order to understand the complex pathways affecting undernutrition which is crucial for policy interventions, one needs to explicitly model the dependence chain of immediate, intermediate, and underlying factors affecting undernutrition. Graphical chain models are used here to investigate the determinants of undernutrition in Benin and Bangladesh. While the dependence chain affecting undernutrition contains many common elements, the influence of demographic, cultural, and socioeconomic factors seems to have stronger direct and indirect influences in Benin than in Bangladesh, where many socioeconomic and gender related factors have a more direct influence on undernutrition.

Handling the effect of non-response in graphical models for longitudinal data

In this paper we investigated the use of attrition weights to cope with non-response when selecting graphical chain models for longitudinal data. We proposed a parametric bootstrap approach to account for the extra variability introduced by the estimation of the weights and compared this with results using standard test procedures.

A Graphical Chain Model for Reciprocal Relationships Between Women’s Gender Role Attitudes and Labour Force Participation

SummaryWe use a graphical chain model to investigate the reciprocal relationships between changes in women’s labour force participation following entry into parenthood and changes in gender role attitude. Results suggest that attitudes are not fixed and that revision of these attitudes in the light of recent life course events is an important process. The adaptation of attitudes to events appears to be stronger than the selection of individuals on the basis of attitudes. We show that it is not entry into parenthood as such, but the change in economic activity that is related to this event that is associated with attitude change.

Modeling Gene-Gene Interactions Using Graphical Chain Models

Objective: To investigate whether graphical chain models are suitable to detect gene-gene interaction under different biological models. Methods: We conducted a simulation study comparing graphical chain models with logistic regression models regarding their ability to detect underlying biological interaction models. For both methods, we attempted to capture simulation data following 12 different biological models. We used 10 statistical models for both methods. Of the 12 different biological models, four contained no interaction effects, two were multiplicative, and six were epistasis models. For each situation, the choice for a statistical model was based on global model fit as judged by two different information criteria, the BIC and the AIC. Results: Both methods failed in most of the scenarios to capture the gene-gene interaction present in the simulation data. Only in very specific cases, when disease risk was high and both genes had a dominant effect, present gene-gene interaction was detected. Conclusions: Graphical chain models are, similar to logistic regression models, not able to capture gene-gene interactions for arbitrary biological models underlying the data.

Prevalence of and Risk Factors for Pubic Lipoma Development in HIV-Infected Persons

The natural history of HIV-associated body habitus changes is unclear. In this report, we describe a novel manifestation of HIV-associated lipoaccumulation. We noted the presence of suprapubic fat pads (pubic lipomas [PLs]) in several patients with preexisting HIV-associated body habitus abnormalities. Subsequently, we evaluated the prevalence of and associated risk factors for development of PLs by undertaking an observational cross-sectional study among patients with known lipodystrophy who attended a metabolic clinic in northern Italy. Inclusion criteria were a physician-confirmed diagnosis of lipodystrophy according to the Multicenter AIDS Cohort Study definition and, for those affected with PL, a readily noticeable PL on physical examination. We evaluated 582 patients with lipodystrophy: 214 female (36.7%) and 368 male (63.3%). The overall PL prevalence was 9.4% (95% confidence interval [CI]: 7.2% to 12.1%; P < 0.0001). PLs were more common among obese than nonobese individuals (34.5%, 95% CI: 17.9% to 5l.3% vs. 8%, 95% CI: 5.9% to 10.6%, respectively; P < 0.0001) and those with preexisting dorsocervical fat pads, commonly called "buffalo humps" (BHs) (18.5%, 95% CI: 12.7% to 25.4% vs. 6.1%, 95% CI: 4.03% to 8.83%, respectively, P < 0.0001; relative risk = 3.02, 95% CI: 1.84% to 4.96%, P < 0.0001). The PL prevalence in the nonobese HIV-infected population (body mass index [BMI] <30, n = 550) was 8.0% (95% CI: 5.9% to 10.6%; P < 0.0001). Logistic regression analyses identified the following factors as associated with a greater likelihood for PL: BMI >30 (beta = 0.18, SE = 0.04; P < 0.001), female gender (beta = 1.06, SE = 0.31; P < 0.001), and shorter duration of HIV infection (beta = -0.005, SE = 0.003; P = 0.04). We used a chain graph model to evaluate risk factors for BH and PL simultaneously. A nonnull interaction between these entities was evident, and this association seemed to be independent of factors positively associated with both (BMI and gender). PL is a newly recognized manifestation of HIV-associated lipoaccumulation that is more likely to occur among those with coexisting dorsocervical fat pads, suggesting the possibility of a common pathogenesis between the 2 entities. Likewise, PLs are more common among women, obese individuals, and those with a shorter duration of HIV infection. We suggest that PL should be considered part of the HIV-associated lipodystrophy syndrome.

Discrete Variable Chain Graphical Modelling for Assessing the Effects of Fund Managers’ Characteristics on Incentives Satisfaction and Size of Returns

The relevance of a fund manager’s educational and experience profile to the size of investment portfolio return has been the subject of recurrent research in the last decade. While previous research considered an external reference point of view analysing industry-wide aggregated data, little research, if any, has been directed at revealing the inside story of what influences the subjective perception of the risk framework the managers at a financial institution have to work under or whether managers consider incentives they receive to be satisfactory. This survey-based study analyses the answers of 120 fund managers from one of the world’s largest banks to a set of questions designed to unveil the links between the objective and more subjective factors that contribute to the investment activity in the banking industry. This context is different from previous studies because information has been collected not only on objective characteristics such as age, size of portfolio, and size of incentives but also on whether investment decisions are based on subjective judgment or analytic tools and on the level of satisfaction with incentives and the bank’s risk management system. This paper provides a methodology capable of exploring the links among the variables obtained from the interviews, graphical chain modelling, which offers an elegant solution to the problem caused by the sparsity of the data, testing with categorical ordinal variables, and model selection. The results may help senior management of financial institutions identify possible linkages that determine a stable and encouraging working environment for fund managers.

Isomorphic chain graphs for modeling spatial dependence in ecological data

Graphical models (alternatively, Bayesian belief networks, path analysis models) are increasingly used for modeling complex ecological systems (e.g., Lee, In: Ferson S, Burgman M(eds) Quantative methods for conservation biology. Springer, Berlin Heilin Heideslperk New York, pp.127–147, 2000; Borsuk et al., J Water Res Plann Manage 129:271–282, 2003). Their implementation in this context leverages their utility in modeling interrelationships in multivariate systems, and in a Bayesian implementation, their intuitive appeal of yielding easily interpretable posterior probability estimates. However, methods for incorporating correlational structure to account for observations collected through time and/or space—features of most ecological data—have not been widely studied; Haas et al. (AI Appl 8:15–27, 1994) is one exception. In this paper, an “isomorphic” chain graph (ICG) model is introduced to account for correlation between samples by linking site-specific Bayes network models. Several results show that the ICG preserves many of the Markov properties (conditional and marginal dependencies) of the site-specific models. The ICG model is compared with a model that does not account for spatial correlation. Data from several stream networks in the Willamette River valley, Oregon (USA) are used. Significant correlation between sites within the same stream network is shown with an ICG model.

A Graphical Representation of Equivalence Classes of AMP Chain Graphs

This paper deals with chain graph models under alternative AMP interpretation. A new representative of an AMP Markov equivalence class, called the largest deflagged graph, is proposed. The represen...

On the inclusion of bivariate marked point processes in graphical models

Graphical models use graphs to represent conditional independence relationships among random variables of a multivariate probability distribution. This paper introduces a new kind of chain graph models in which nodes also represent marked point processes. This is relevant to the analysis of event history data, i.e. data consisting of random sequences of events or time durations of states. Survival analysis and duration models are particular cases. This article considers the case of two marked point processes. The idea consists of representing a whole process by a single node and a conditional independence statement by a lack of connection. We refer to the resulting models as graphical duration models.