Graphical models, regression graphs, and recursive linear regression in a unified way

Bolla, Marianna; Abdelkhalek, Fatma; Baranyi, Máté

doi:10.14232/actasm-018-331-4

Cited by 5 publications

(6 citation statements)

References 18 publications

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“…Here, we include a short description on the relation between directed and undirected graphical models, with emphases on the Gaussian case, based on Lauritzen (2004) and Bolla et al (2019). Directed and undirected models have many properties in common, and under some conditions, there are important correspondences between them.…”

Section: The Restricted Causal Var(p) Modelmentioning

confidence: 99%

“…If this undirected graph is triangulated, then in a convenient (so-called perfect) ordering of the nodes, the zeros of the adjacency matrix form an RZP. We can find such a (not necessarily unique) ordering of the nodes with the maximal cardinality search (MCS) algorithm, together with cliques and separators of a so-called junction tree (JT); see Lauritzen (2004), Koller andFriedman (2009), andBolla et al (2019). In this ordering (labeling) of the nodes, a DAG can also be constructed, which is Markov equivalent to the undirected one (it has no so-called sink V configuration); for further details, see Section 3.2.…”

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confidence: 99%

“…With the covariance selection method of Dempster (1972), the starting concentration matrix is re-estimated by imposing zero constraints for its entries in the RZP positions (symmetrically). By the theory (see, e.g., Bolla et al (2019)), this will result in zero entries of A in the no directed edge positions.…”

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confidence: 99%

“…If the desired zeros form an RZP, the covariance selection has a closed form (see Lauritzen (2004)). In the lack of an RZP, the covariance selection still works, but it needs an infinite (convergent) iteration, called iterative proportional scaling (IPS), see Lauritzen (2004) and Bolla et al (2019). Other possibility is to moralize the DAG (connect parents that are not connected and thus eliminate the sink Vs), and work with the so-obtained undirected graph.…”

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confidence: 99%

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Causal Vector Autoregression Enhanced with Covariance and Order Selection

Bolla

Wang

et al. 2023

Econometrics

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A causal vector autoregressive (CVAR) model is introduced for weakly stationary multivariate processes, combining a recursive directed graphical model for the contemporaneous components and a vector autoregressive model longitudinally. Block Cholesky decomposition with varying block sizes is used to solve the model equations and estimate the path coefficients along a directed acyclic graph (DAG). If the DAG is decomposable, i.e., the zeros form a reducible zero pattern (RZP) in its adjacency matrix, then covariance selection is applied that assigns zeros to the corresponding path coefficients. Real-life applications are also considered, where for the optimal order p≥1 of the fitted CVAR(p) model, order selection is performed with various information criteria.

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Section: The Restricted Causal Var(p) Modelmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Causal Vector Autoregression Enhanced with Covariance and Order Selection

Bolla

Wang

et al. 2023

Econometrics

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“…It shows that the log-likelihood of G can be decomposed as the sum of the log-likelihood of local structures of a covariate given its parents. For the estimation of the local structures, existing literature on causal graphical models often assumes a linear model of a covariate on its parents (Spirtes, 2010;Valente et al, 2010;Bolla et al, 2019). Note that in the MPHIA data set, many covariates are categorical, so we assume generalized linear models (GLM) of a covariate given its parents instead of linear models, and we fit the GLM of local structures by MLE.…”

Section: Model Comparisonmentioning

confidence: 99%

Causal Structural Learning on MPHIA Individual Dataset

Bao¹,

Li²,

Li³

et al. 2022

Preprint

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The Population-based HIV Impact Assessment (PHIA) is an ongoing project that conducts nationally representative HIV-focused surveys for measuring national and regional progress toward UNAIDS' 90-90-90 targets, the primary strategy to end the HIV epidemic. We believe the PHIA survey offers a unique opportunity to better understand the key factors that drive the HIV epidemics in the most affected countries in sub-Saharan Africa. In this article, we propose a novel causal structural learning algorithm to discover important covariates and potential causal pathways for 90-90-90 targets. Existing constrained-based causal structural learning algorithms are quite aggressive in edge removal. The proposed algorithm preserves more information about important features and potential causal pathways. It is applied to the Malawi PHIA (MPHIA) data set and leads to interesting results. For example, it discovers age and condom usage to be important for female HIV awareness; the number of sexual partners to be important for male HIV awareness; and knowing the travel time to HIV care facilities leads to a higher chance of being treated for both females and males. We further compare and validate the proposed algorithm using BIC and using Monte Carlo simulations, and show that the proposed algorithm achieves improvement in true positive rates in important feature discovery over existing algorithms.

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Application of Structural Equation Modeling to Infant Mortality Rate in Egypt

Abdelkhalek

Bolla

2020

The Springer Series on Demographic Methods and Population Analysis

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Graphical models, regression graphs, and recursive linear regression in a unified way

Cited by 5 publications

References 18 publications

Causal Vector Autoregression Enhanced with Covariance and Order Selection

Causal Vector Autoregression Enhanced with Covariance and Order Selection

Causal Structural Learning on MPHIA Individual Dataset

Application of Structural Equation Modeling to Infant Mortality Rate in Egypt

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