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Background: Latent class models can be used to estimate diagnostic accuracy without a gold standard test. Early studies often assumed independence between tests given the true disease state, however this can lead to biased estimates when there are inter-test dependencies. Residual correlation plots and chi-squared statistics have been commonly utilized to assess the validity of the conditional independence assumption and, when it does not hold, identify which test pairs are conditionally dependent. We aimed to assess the performance of these tools with a simulation study covering a wide range of scenarios. Methods: We generated data sets from a model with four tests and a dependence between tests 1 and 2 within the diseased group. We varied sample size, prevalence, covariance, sensitivity and specificity, with 504 combinations of these in total, and 1000 data sets for each combination. We fitted the conditional independence model in a Bayesian framework, and reported absolute bias, coverage, and how often the residual correlation plots, G 2 and χ 2 statistics indicated lack-of-fit globally or for each test pair. Results: Across all settings, residual correlation plots, pairwise G 2 and χ 2 detected the correct correlated pair of tests only 12.1%, 10.3%, and 10.3% of the time, respectively, but incorrectly suggested dependence between tests 3 and 4 64.9%, 49.7%, and 49.5% of the time. We observed some variation in this across parameter settings, with these tools appearing to perform more as intended when tests 3 and 4 were both much more accurate than tests 1 and 2. Residual correlation plots, G 2 and χ 2 statistics identified a lack of overall fit in 74.3%, 64.5% and 67.5% of models, respectively. The conditional independence model tended to overestimate the sensitivities of the correlated tests (median bias across all scenarios 0.094, 2.5th and 97.5th percentiles -0.003, 0.397) and underestimate prevalence and the specificities of the uncorrelated tests. Conclusions: Residual correlation plots and chi-squared statistics cannot be relied upon to identify which tests are conditionally dependent, and also have relatively low power to detect lack of overall fit. This is important since failure to account for conditional dependence can lead to highly biased parameter estimates. [ABSTRACT FROM AUTHOR]

Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointly learning their independence structures. We consider the case where there are exactly two dependent groups and the association structure is represented by a family of coloured Gaussian graphical models suited to deal with paired data problems. To learn the two dependent graphs, together with their across-graph association structure, we implement a fused graphical lasso penalty. We carry out a comprehensive analysis of this approach, with special attention to the role played by some relevant submodel classes. In this way, we provide a broad set of tools for the application of Gaussian graphical models to paired data problems. These include results useful for the specification of penalty values in order to obtain a path of lasso solutions and an ADMM algorithm that solves the fused graphical lasso optimization problem. Finally, we carry out a simulation study to compare our method with the traditional graphical lasso, and present an application of our method to cancer genomics where it is of interest to compare cancer cells with a control sample from histologically normal tissues adjacent to the tumor. All the methods described in this article are implemented in the R package pdglasso available at . [ABSTRACT FROM AUTHOR]

Motivation Valid statistical inference is crucial for decision-making but difficult to obtain in supervised learning with multimodal data, e.g. combinations of clinical features, genomic data, and medical images. Multimodal data often warrants the use of black-box algorithms, for instance, random forests or neural networks, which impede the use of traditional variable significance tests. Results We address this problem by proposing the use of COvariance MEasure Tests (COMETs), which are calibrated and powerful tests that can be combined with any sufficiently predictive supervised learning algorithm. We apply COMETs to several high-dimensional, multimodal data sets to illustrate (i) variable significance testing for finding relevant mutations modulating drug-activity, (ii) modality selection for predicting survival in liver cancer patients with multiomics data, and (iii) modality selection with clinical features and medical imaging data. In all applications, COMETs yield results consistent with domain knowledge without requiring data-driven pre-processing, which may invalidate type I error control. These novel applications with high-dimensional multimodal data corroborate prior results on the power and robustness of COMETs for significance testing. Availability and implementation COMETs are implemented in the comets R package available on CRAN and pycomets Python library available on GitHub. Source code for reproducing all results is available at https://github.com/LucasKook/comets. All data sets used in this work are openly available. [ABSTRACT FROM AUTHOR]

This paper introduces an algorithm to construct a bidirectional causal graph using an augmented graph. The algorithm decomposes the augmented graph, significantly reducing the size of the variable set required for conditional independence testing. Simultaneously, it preserves the fundamental structure of the augmented graph after decomposition, saving time and cost in constructing a global skeleton graph. Through experiments on discrete and continuous datasets, the algorithm demonstrates a clear advantage in runtime compared to traditional methods. In large-scale sparse networks, the training time is only about one-tenth of traditional methods. Additionally, the algorithm shows improvement in terms of construction error. Since the input to the algorithm is an augmented graph, this paper also discusses the impact on construction error when using both real and generated augmented graphs as input. Furthermore, the concept of markov blanket is extended to multivariate regression chain graphs, providing a method for rapidly constructing augmented graphs given certain prior knowledge. [ABSTRACT FROM AUTHOR]

Graphical models are pivotal in studying the conditional independence structure of a set of random variables. Circular variables, arising in several contexts and fields, are characterized by periodicity. Models for studying the dependence/independence structure of circular variables are under-explored but of increasing interest. This paper delves into two multivariate circular distributions, the Wrapped Normal and the Inverse Stereographic Normal distribution as undirected graphical models. For each of these distributions, we study their key properties with respect to conditional independence and introduce specific classes of graphical models. The usefulness of the proposal is shown by modelling the conditional independence among dihedral angles that play a critical role in defining the three-dimensional structure and functionality of proteins. This can provide valuable insights, for instance, into the multiform protein folding understanding. [ABSTRACT FROM AUTHOR]

Multiple imputation is a practical approach in analyzing incomplete data, with multiple imputation by chained equations (MICE) being popularly used. MICE specifies a conditional distribution for each variable to be imputed, but estimating it is inherently a high-dimensional problem for large-scale data. Existing approaches propose to utilize regularized regression models, such as lasso. However, the estimation of them occurs iteratively across all incomplete variables, leading to a considerable increase in computational burden, as demonstrated in our simulation study. To overcome this computational bottleneck, we propose a novel method that estimates the conditional independence structure among variables before the imputation procedure. We extract such information from an undirected graphical model, leveraging the graphical lasso method based on the inverse probability weighting estimator. Our simulation study verifies the proposed method is way faster against the existing methods, while still maintaining comparable imputation performance. [ABSTRACT FROM AUTHOR]

Abstract Background Latent class models can be used to estimate diagnostic accuracy without a gold standard test. Early studies often assumed independence between tests given the true disease state, however this can lead to biased estimates when there are inter-test dependencies. Residual correlation plots and chi-squared statistics have been commonly utilized to assess the validity of the conditional independence assumption and, when it does not hold, identify which test pairs are conditionally dependent. We aimed to assess the performance of these tools with a simulation study covering a wide range of scenarios. Methods We generated data sets from a model with four tests and a dependence between tests 1 and 2 within the diseased group. We varied sample size, prevalence, covariance, sensitivity and specificity, with 504 combinations of these in total, and 1000 data sets for each combination. We fitted the conditional independence model in a Bayesian framework, and reported absolute bias, coverage, and how often the residual correlation plots, $${G}^{2}$$ G 2 and $${\chi }^{2}$$ χ 2 statistics indicated lack-of-fit globally or for each test pair. Results Across all settings, residual correlation plots, pairwise $${G}^{2}$$ G 2 and $${\chi }^{2}$$ χ 2 detected the correct correlated pair of tests only 12.1%, 10.3%, and 10.3% of the time, respectively, but incorrectly suggested dependence between tests 3 and 4 64.9%, 49.7%, and 49.5% of the time. We observed some variation in this across parameter settings, with these tools appearing to perform more as intended when tests 3 and 4 were both much more accurate than tests 1 and 2. Residual correlation plots, $${G}^{2}$$ G 2 and $${\chi }^{2}$$ χ 2 statistics identified a lack of overall fit in 74.3%, 64.5% and 67.5% of models, respectively. The conditional independence model tended to overestimate the sensitivities of the correlated tests (median bias across all scenarios 0.094, 2.5th and 97.5th percentiles -0.003, 0.397) and underestimate prevalence and the specificities of the uncorrelated tests. Conclusions Residual correlation plots and chi-squared statistics cannot be relied upon to identify which tests are conditionally dependent, and also have relatively low power to detect lack of overall fit. This is important since failure to account for conditional dependence can lead to highly biased parameter estimates.

We introduce an algebraic concept of the frame for abstract conditional independence (CI) models, together with basic operations with respect to which such a frame should be closed: copying and marginalization. Three standard examples of such frames are (discrete) probabilistic CI structures, semi-graphoids and structural semi-graphoids. We concentrate on those frames which are closed under the operation of set-theoretical intersection because, for these, the respective families of CI models are lattices. This allows one to apply the results from lattice theory and formal concept analysis to describe such families in terms of implications among CI statements. The central concept of this paper is that of self-adhesivity defined in algebraic terms, which is a combinatorial reflection of the self-adhesivity concept studied earlier in context of polymatroids and information theory. The generalization also leads to a self-adhesivity operator defined on the meta-level of CI frames. We answer some of the questions related to this approach and raise other open questions. The core of the paper is in computations. The combinatorial approach to computation might overcome some memory and space limitation of software packages based on polyhedral geometry, in particular, if SAT solvers are utilized. We characterize some basic CI families over 4 variables in terms of canonical implications among CI statements. We apply our method in information-theoretical context to the task of entropic region demarcation over 5 variables. [ABSTRACT FROM AUTHOR]

Mediation analysis is used to study the relationship between stimulus and response in the presence of intermediate, generative variables. The traditional approach to the analysis utilizes the results of an aggregate regression model, which assumes that all respondents go through the same data-generating mechanism. We introduce a new approach that is able to uncover the heterogeneity in mediating mechanisms and provides more informative insights from mediation studies. The proposed approach provides individual-specific probabilities to mediate as well as a new measure of the degree of mediation as the prevalence of mediation in the sample. Covariates in the proposed model help describe the variation in the probability to mediate among respondents. The empirical examination of published studies demonstrates the presence of heterogeneity in mediating processes and supports the need for this new approach. We present evidence that the results of our more flexible heterogeneous mediation analysis do not necessarily agree with the traditional aggregate measures. We find that the conclusions from the aggregate analysis are neither sufficient nor necessary to claim mediation in the presence of heterogeneity. A web-based application allowing researchers to analyze the data with the proposed model in a user-friendly environment is developed. [ABSTRACT FROM AUTHOR]

Testing multiple hypotheses of conditional independence with provable error rate control is a fundamental problem with various applications. To infer conditional independence with family-wise error rate (FWER) control when only summary statistics of marginal dependence are accessible, we adopt GhostKnockoff to directly generate knockoff copies of summary statistics and propose a new filter to select features conditionally dependent on the response. In addition, we develop a computationally efficient algorithm to greatly reduce the computational cost of knockoff copies generation without sacrificing power and FWER control. Experiments on simulated data and a real dataset of Alzheimer's disease genetics demonstrate the advantage of the proposed method over existing alternatives in both statistical power and computational efficiency. [ABSTRACT FROM AUTHOR]

Network psychometrics uses graphical models to assess the network structure of psychological variables. An important task in their analysis is determining which variables are unrelated in the network, i.e., are independent given the rest of the network variables. This conditional independence structure is a gateway to understanding the causal structure underlying psychological processes. Thus, it is crucial to have an appropriate method for evaluating conditional independence and dependence hypotheses. Bayesian approaches to testing such hypotheses allow researchers to differentiate between absence of evidence and evidence of absence of connections (edges) between pairs of variables in a network. Three Bayesian approaches to assessing conditional independence have been proposed in the network psychometrics literature. We believe that their theoretical foundations are not widely known, and therefore we provide a conceptual review of the proposed methods and highlight their strengths and limitations through a simulation study. We also illustrate the methods using an empirical example with data on Dark Triad Personality. Finally, we provide recommendations on how to choose the optimal method and discuss the current gaps in the literature on this important topic. [ABSTRACT FROM AUTHOR]

Conditional Independence (CI) testing is fundamental in statistical analysis. For example, CI testing helps validate causal graphs or longitudinal data analysis with repeated measures in causal inference. CI testing is difficult, especially when testing involves categorical variables conditioned on a mixture of continuous and categorical variables. Current parametric and non-parametric testing methods are designed for continuous variables and can quickly fall short in the categorical case. This paper presents a computational approach for CI testing suited for categorical data types, which we call computational conditional independence (CCI) testing. The test procedure is based on permutation and combines machine learning prediction algorithms and Monte Carlo cross-validation. We evaluated the approach through simulation studies and assessed the performance against alternative methods: the generalized covariance measure test, the kernel conditional independence test, and testing with multinomial regression. We find that the computational approach to testing has utility over the alternative methods, achieving better control over type I error rates. We hope this work can expand the toolkit for CI testing for practitioners and researchers. [ABSTRACT FROM AUTHOR]

Collapsibility is a practical and useful technique for dimension reduction in multidimensional contingency tables. In this paper, we consider marginal log‐linear models for studying collapsibility and related aspects in such tables. These models generalize ordinary log‐linear and multivariate logistic models, besides several others. First, we obtain some characteristic properties of marginal log‐linear parameters. Then we define collapsibility and strict collapsibility of these parameters in a general sense. Several necessary and sufficient conditions for collapsibility and strict collapsibility are derived based on simple functions of only the cell probabilities, which are easily verifiable. These include results for an arbitrary set of marginal log‐linear parameters having some common effects. The connections of strict collapsibility to various forms of independence of the variables are explored. We analyze some real‐life datasets to illustrate the above results on collapsibility and strict collapsibility. Finally, we obtain a result relating parameters with the same effect, but different margins for an arbitrary table, and demonstrate smoothness of marginal log‐linear models under collapsibility conditions. [ABSTRACT FROM AUTHOR]

Several methods and approaches have been proposed to assess landslide susceptibility. The likelihood of landslides occurring can be determined by applying statistical models to historical landslides, taking into account controlling factors. Popular methods for predicting the probability of landslides are weights-of-evidence and logistic regression. We discuss the assumptions and interpretations of these methods, the relationships between them, and their strengths and weaknesses in case of categorical factors. Of particular interest is the conditional independence of the controlling factors and its effect on model bias. To avoid lack of conditional independence of factors and model bias, we present a unique conditions model that is always unbiased. To illustrate the theoretical developments, a practical application is given using observed landslides and geo-environmental factors from a previous study. The unique conditions model appears superior to the other models. [ABSTRACT FROM AUTHOR]

When learning the structure of a Bayesian network, the search space expands significantly as the network size and the number of nodes increase, leading to a noticeable decrease in algorithm efficiency. Traditional constraint-based methods typically rely on the results of conditional independence tests. However, excessive reliance on these test results can lead to a series of problems, including increased computational complexity and inaccurate results, especially when dealing with large-scale networks where performance bottlenecks are particularly evident. To overcome these challenges, we propose a Markov blanket discovery algorithm based on constrained local neighborhoods for constructing undirected independence graphs. This method uses the Markov blanket discovery algorithm to refine the constraints in the initial search space, sets an appropriate constraint radius, thereby reducing the initial computational cost of the algorithm and effectively narrowing the initial solution range. Specifically, the method first determines the local neighborhood space to limit the search range, thereby reducing the number of possible graph structures that need to be considered. This process not only improves the accuracy of the search space constraints but also significantly reduces the number of conditional independence tests. By performing conditional independence tests within the local neighborhood of each node, the method avoids comprehensive tests across the entire network, greatly reducing computational complexity. At the same time, the setting of the constraint radius further improves computational efficiency while ensuring accuracy. Compared to other algorithms, this method can quickly and efficiently construct undirected independence graphs while maintaining high accuracy. Experimental simulation results show that, this method has significant advantages in obtaining the structure of undirected independence graphs, not only maintaining an accuracy of over 96% but also reducing the number of conditional independence tests by at least 50%. This significant performance improvement is due to the effective constraint on the search space and the fine control of computational costs. [ABSTRACT FROM AUTHOR]

In functional MRI (fMRI), effective connectivity analysis aims at inferring the causal influences that brain regions exert on one another. A common method for this type of analysis is structural equation modeling (SEM). We here propose a novel method to test the validity of a given model of structural equation. Given a structural model in the form of a directed graph, the method extracts the set of all constraints of conditional independence induced by the absence of links between pairs of regions in the model and tests for their validity in a Bayesian framework, either individually (constraint by constraint), jointly (e.g., by gathering all constraints associated with a given missing link), or globally (i.e., all constraints associated with the structural model). This approach has two main advantages. First, it only tests what is testable from observational data and does allow for false causal interpretation. Second, it makes it possible to test each constraint (or group of constraints) separately and, therefore, quantify in what measure each constraint (or, e..g., missing link) is respected in the data. We validate our approach using a simulation study and illustrate its potential benefits through the reanalysis of published data. [ABSTRACT FROM AUTHOR]

Learning engagement is malleable to environmental change. An important learning environment created by teacher-student interactions is perceived teacher autonomy support, which may trigger learning engagement directly and/or indirectly by enhancing academic self-efficacy. In this study, we apply a network approach to explore the relationships between the specific facets of perceived teacher autonomy support, academic self-efficacy and learning engagement, and a sample consisting of 215 students in the fifth and sixth grades from a primary school in Changchun of China is used. Node centrality indicators and the accuracy and stability of the network are also calculated. The results reveal that there are no edges between the three facets of perceived teacher autonomy support and the three facets of learning engagement, and the shortest path connecting the two constructs is through academic ability self-efficacy. Furthermore, learning support, academic ability self-efficacy, and dedication have the top three strengths in the network, which indicates that the three facets are more closely related to other facets of the network. [ABSTRACT FROM AUTHOR]

This study examined the test of independence of survival time from a covariate in a more general setting using empirical process techniques. Previous research has been extended in several ways: (1) allow incompleteness of observation owing to censoring (2) allow the time-dependent covariate (3) allow the non-uniform covariate (4) prove the validity of weighted bootstrap to implement the proposed testing procedure. Certain classes of test statistics that are functionals of a natural empirical process were studied, and the limiting distribution of these statistics was then derived using the functional delta method. The limiting distributions included some linear functionals of zero mean tight Brownian bridges under the null hypothesis, and the tests were consistent against general alternatives. Tests implemented using weighted bootstrap were shown to be valid. The proposals are illustrated via simulation studies and an application to acute leukemia data. [ABSTRACT FROM AUTHOR]

Experimental and behavioral economists, as well as psychologists, commonly assume conditional independence of choices when constructing likelihood functions for structural estimation of choice functions. I test this assumption using data from a new experiment designed for this purpose. Within the limits of the experiment's identifying restriction and designed power to detect deviations from conditional independence, conditional independence is not rejected. In naturally occurring data, concerns about violations of conditional independence are certainly proper and well-taken (for well-known reasons). However, when an experimenter employs the particular experimental mechanisms and designs used here, the findings suggest that conditional independence is an acceptable assumption for analyzing data so generated. [ABSTRACT FROM AUTHOR]

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X : = X t : t ∈ Z and Y : = Y t : t ∈ Z , which take values in binary alphabets. When the bivariate process (X , Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test—no causal influence—requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons. [ABSTRACT FROM AUTHOR]

We address the problems of causal structure inference from conditional independence facts when latent confounders are admitted. The conditions that allow one to identify latent confounders and fully or partially recognize causal links are described. The updated implicative rules for orienting edges under confounding are suggested. We propose several new rules that are able to reveal bows and confounded causal edges. The rules rely on facts of absence of certain authentic edges (edge absence may be implied by Verma constraint or given in input as a priori requirement). [ABSTRACT FROM AUTHOR]

Unsupervised domain adaptation (UDA) studies how to transfer a learner from a labeled source domain to an unlabeled target domain with different distributions. Existing methods mainly focus on matching marginal distributions of the source and target domains, which probably leads to a misalignment of samples from the same class but different domains. In this paper, we tackle this misalignment issue by achieving the class-conditioned transferring from a new perspective. Specifically, we propose a method named maximizing conditional independence (MCI) for UDA, which maximizes the conditional independence of feature and domain given class in the reproducing kernel Hilbert spaces. The optimization of conditional independence can be viewed as a surrogate for minimizing class-wise mutual information between feature and domain. An interpretable empirical estimation of the conditional dependence measure is deduced and connected with the unconditional case. Besides, we provide an upper bound on the target error by taking the class-conditional distribution into account, which provides a new theoretical insight for class-conditioned transferring. Extensive experiments on six benchmark datasets and various ablation studies validate the effectiveness of the proposed model in dealing with UDA. [ABSTRACT FROM AUTHOR]

We address the problems of causal structure reconstruction given conditional independence facts when latent confounders are allowed. We examine the conditions that allow one to partially or fully identify authentic causal links and latent confounders. The updated implicative rules for orienting edges under confounding are suggested. As demonstrated, it is possible to construct the new rules, which can reveal confounded causal edges and bows. The rules rely on facts of the absence of certain authentic edges (such facts may be justified by non-independence constraints, like Verma constraint, or subject-based requirements). [ABSTRACT FROM AUTHOR]

For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is undesirable, especially for highly multivariate settings, where popular cross-covariance functions such as the multivariate Matérn suffer from a "curse of dimensionality" as the number of parameters and floating point operations scale up in quadratic and cubic order, respectively, in the number of variables. We propose a class of multivariate "Graphical Gaussian Processes" using a general construction called "stitching" that crafts cross-covariance functions from graphs and ensures process-level conditional independence among variables. For the Matérn family of functions, stitching yields a multivariate GP whose univariate components are Matérn GPs, and conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Matérn GP to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling.

Conditions are obtained for a Gaussian vector autoregressive time series of order k, VAR(k), to have univariate margins that are autoregressive of order k or lower‐dimensional margins that are also VAR(k). This can lead to d‐dimensional VAR(k) models that are closed with respect to a given partition {S1,...,Sn} of {1,...,d} by specifying marginal serial dependence and some cross‐sectional dependence parameters. The special closure property allows one to fit the subprocesses of multi‐variate time series before assembling them by fitting the dependence structure between the subprocesses. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR(k) process with non‐Gaussian univariate margins but under the constraint of closure under margins. This construction allows more flexibility in handling higher‐dimensional time series and a multi‐stage estimation procedure can be used. The proposed class of models is applied to a macro‐economic data set and compared with the relevant benchmark models. [ABSTRACT FROM AUTHOR]

We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three-way statistical relation that shares similar properties with conditional independence by satisfying the semi-graphoid axioms. Based on this relation we build an additive graphical model for discrete variables that does not suffer from the restriction of a parametric model such as the Ising model. We develop an estimator of the new graphical model via the penalized estimation of the discrete version of the additive precision operator and establish the consistency of the estimator under the ultrahigh-dimensional setting. Along with these methodological developments, we also exploit the properties of discrete random variables to uncover a deeper relation between additive conditional independence and conditional independence than previously known. The new graphical model reduces to a conditional independence graphical model under certain sparsity conditions. We conduct simulation experiments and analysis of an HIV antiretroviral therapy dataset to compare the new method with existing ones. for this article are available online. [ABSTRACT FROM AUTHOR]

The key assumption of conditional independence of item responses given latent ability in item response theory (IRT) models is addressed for multistage adaptive testing (MST) designs. Routing decisions in MST designs can cause patterns in the data that are not accounted for by the IRT model. This phenomenon relates to quasi-independence in log-linear models for incomplete contingency tables and impacts certain types of statistical inference based on assumptions on observed and missing data. We demonstrate that generalized residuals for item pair frequencies under IRT models as discussed by Haberman and Sinharay (J Am Stat Assoc 108:1435–1444, 2013. https://doi.org/10.1080/01621459.2013.835660) are inappropriate for MST data without adjustments. The adjustments are dependent on the MST design, and can quickly become nontrivial as the complexity of the routing increases. However, the adjusted residuals are found to have satisfactory Type I errors in a simulation and illustrated by an application to real MST data from the Programme for International Student Assessment (PISA). Implications and suggestions for statistical inference with MST designs are discussed. [ABSTRACT FROM AUTHOR]

Bayesian networks are widely used to learn and reason about the dependence structure of discrete variables. However, they can only formally encode symmetric conditional independence, which is often too strict to hold in practice. Asymmetry-labeled DAGs have been recently proposed to extend the class of Bayesian networks by relaxing the symmetric assumption of independence and denoting the dependence between the variables of interest. Here, we introduce novel structural learning algorithms for this class of models, which, whilst efficient, allow for a straightforward interpretation of the underlying dependence structure. A comprehensive computational study highlights the efficiency of the algorithms. A real-world data application using data from the Fear of COVID-19 Scale collected in Italy showcases their use in practice. [ABSTRACT FROM AUTHOR]

A prior distribution for the underlying graph is introduced in the framework of Gaussian graphical models. Such a prior distribution induces a block structure in the graph's adjacency matrix, allowing learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for learning block structured graphs under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single edge of the graph but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional dependence structure. Since the elements of a B-Spline basis have compact support, the conditional dependence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among portions of the domain and improve the interpretability of the results. for this article are available online. [ABSTRACT FROM AUTHOR]

Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms, yet it remains a highly challenging problem due to dimensionality and complex relationships presented in data. In this study, we introduce LCIT (Latent representation-based Conditional Independence Test)—a novel method for conditional independence testing based on representation learning. Our main contribution involves a hypothesis testing framework in which to test for the independence between X and Y given Z, we first learn to infer the latent representations of target variables X and Y that contain no information about the conditioning variable Z. The latent variables are then investigated for any significant remaining dependencies, which can be performed using a conventional correlation test. Moreover, LCIT can also handle discrete and mixed-type data in general by converting discrete variables into the continuous domain via variational dequantization. The empirical evaluations show that LCIT outperforms several state-of-the-art baselines consistently under different evaluation metrics, and is able to adapt really well to both nonlinear, high-dimensional, and mixed data settings on a diverse collection of synthetic and real data sets. [ABSTRACT FROM AUTHOR]

Conditional Independence (CI) testing is fundamental in statistical analysis. For example, CI testing helps validate causal graphs or longitudinal data analysis with repeated measures in causal inference. CI testing is difficult, especially when testing involves categorical variables conditioned on a mixture of continuous and categorical variables. Current parametric and non-parametric testing methods are designed for continuous variables and can quickly fall short in the categorical case. This paper presents a computational approach for CI testing suited for categorical data types, which we call computational conditional independence (CCI) testing. The test procedure is based on permutation and combines machine learning prediction algorithms and Monte Carlo cross-validation. We evaluated the approach through simulation studies and assessed the performance against alternative methods: the generalized covariance measure test, the kernel conditional independence test, and testing with multinomial regression. We find that the computational approach to testing has utility over the alternative methods, achieving better control over type I error rates. We hope this work can expand the toolkit for CI testing for practitioners and researchers.

Several methods and approaches have been proposed to assess landslide susceptibility. The likelihood of landslides occurring can be determined by applying statistical models to historical landslides, taking into account controlling factors. Popular methods for predicting the probability of landslides are weights-of-evidence and logistic regression. We discuss the assumptions and interpretations of these methods, the relationships between them, and their strengths and weaknesses in case of categorical factors. Of particular interest is the conditional independence of the controlling factors and its effect on model bias. To avoid lack of conditional independence of factors and model bias, we present a unique conditions model that is always unbiased. To illustrate the theoretical developments, a practical application is given using observed landslides and geo-environmental factors from a previous study. The unique conditions model appears superior to the other models.

We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables X and Y given a random variable Z. Namely, we investigate asymptotic behaviour of estimates of a vector of probabilities in such settings, establish their asymptotic normality and ordering between asymptotic covariance matrices. The results are used to derive asymptotic distributions of the empirical Conditional Mutual Information in those set-ups. Somewhat unexpectedly, the distributions coincide for the two scenarios, despite differences in the asymptotic distributions of the estimates of probabilities. We also prove validity of permutation p-values for the Conditional Permutation scheme. The above results justify consideration of conditional independence tests based on resampled p-values and on the asymptotic chi-square distribution with an adjusted number of degrees of freedom. We show in numerical experiments that when the ratio of the sample size to the number of possible values of the triple exceeds 0.5, the test based on the asymptotic distribution with the adjustment made on a limited number of permutations is a viable alternative to the exact test for both the Conditional Permutation and the Conditional Randomisation scenarios. Moreover, there is no significant difference between the performance of exact tests for Conditional Permutation and Randomisation schemes, the latter requiring knowledge of conditional distribution of X given Z, and the same conclusion is true for both adaptive tests. [ABSTRACT FROM AUTHOR]

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X:=Xt:t∈Z and Y:=Yt:t∈Z, which take values in binary alphabets. When the bivariate process (X,Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test—no causal influence—requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons.

We study efficient estimation of an interventional mean associated with a point exposure treatment under a causal graphical model represented by a directed acyclic graph without hidden variables. Under such a model, a subset of the variables may be uninformative, in that failure to measure them neither precludes identification of the interventional mean nor changes the semiparametric variance bound for regular estimators of it. We develop a set of graphical criteria that are sound and complete for eliminating all the uninformative variables, so that the cost of measuring them can be saved without sacrificing estimation efficiency, which could be useful when designing a planned observational or randomized study. Further, we construct a reduced directed acyclic graph on the set of informative variables only. We show that the interventional mean is identified from the marginal law by the g-formula (Robins, 1986) associated with the reduced graph, and the semiparametric variance bounds for estimating the interventional mean under the original and the reduced graphical model agree. The g-formula is an irreducible, efficient identifying formula in the sense that the nonparametric estimator of the formula, under regularity conditions, is asymptotically efficient under the original causal graphical model, and no formula with this property exists that depends only on a strict subset of the variables. [ABSTRACT FROM AUTHOR]

We study the joint occurrence of large values of a Markov random field or undirected graphical model associated to a block graph. On such graphs, containing trees as special cases, we aim to generalize recent results for extremes of Markov trees. Every pair of nodes in a block graph is connected by a unique shortest path. These paths are shown to determine the limiting distribution of the properly rescaled random field given that a fixed variable exceeds a high threshold. The latter limit relation implies that the random field is multivariate regularly varying and it determines the max-stable distribution to which component-wise maxima of independent random samples from the field are attracted. When the sub-vectors induced by the blocks have certain limits parametrized by Hüsler–Reiss distributions, the global Markov property of the original field induces a particular structure on the parameter matrix of the limiting max-stable Hüsler–Reiss distribution. The multivariate Pareto version of the latter turns out to be an extremal graphical model according to the original block graph. Thanks to these algebraic relations, the parameters are still identifiable even if some variables are latent. [ABSTRACT FROM AUTHOR]

Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the matrix and its inverse. We study the semi‐algebraic geometry of these models, in particular their dimension, smoothness, and connectedness as well as algebraic and combinatorial properties. [ABSTRACT FROM AUTHOR]

Background Laboratory‐based assessments have shown that stroke recovery is heterogeneous between patients and affected domains such as motor and language function. However, laboratory‐based assessments are not ecologically valid and do not necessarily reflect patients' daily life performance. Therefore, we aimed to give an innovative view on stroke recovery by profiling daily life performance recovery across domains in patients with early subacute stroke and determine their interrelatedness, taking stroke localization into account. Methods and Results Daily life performance was observed at neurorehabilitation admission and weekly thereafter until discharge, using a scale containing 7 daily life domains. Graphical modeling was applied to investigate the conditional independence between recovery of these domains depending on stroke localization. There were 592 patients analyzed. Four clusters of interrelated domains were identified within the first 6 weeks poststroke. The first cluster included recovery in learning and applying knowledge, general tasks and demands, and domestic life. The second cluster comprised recovery in self‐care and general tasks and demands. The third cluster included recovery in mobility and self‐care; it incorporated interpersonal interactions and relationships in left supratentorial stroke, and learning and applying knowledge in right supratentorial stroke. The final cluster included only communication recovery. Conclusions Daily life recovery dynamics early poststroke show that although impairments in body functions are anatomically determined, their impact on performance is comparable. Second, some, but by no means all, domains show an interrelated recovery. Domains requiring cognitive abilities are especially interrelated and seem to be essential for concomitant recovery in mobility and domestic life.

In a recent issue of this journal, Philip Dawid (2021) proposes a framework for causal inference that is based on statistical decision theory and that is, in many aspects, compatible with the familiar framework of causal graphs (e.g., Directed Acyclic Graphs (DAGs)). This editorial compares the methodological features of the two frameworks as well as their epistemological basis.

Let Λ be the collection of all probability distributions for (X , X ˜) , where X is a fixed random vector and X ˜ ranges over all possible knockoff copies of X (in the sense of Candes et al. (2018)). Three topics are developed in this paper: (i) A new characterization of Λ is proved; (ii) A certain subclass of Λ , defined in terms of copulas, is introduced; (iii) The (meaningful) special case where the components of X are conditionally independent is treated in depth. In real problems, after observing X = x , each of points (i)–(ii)–(iii) may be useful to generate a value x ˜ for X ˜ conditionally on X = x. • The paper provides some new theoretical insights on the knockoffs procedure introduced by Barber and Candes (2015). Let Λ be the set of all possible knockofffs. In Section 2, a new characterization of Λ is proved. • In Section 3, a certain (proper) subclass Λ 0 ⊂ Λ is introduced. The elements of Λ 0 admit a simple and explicit representation in terms of copulas. • In Section 4, we focus on the case where the variables X 1 , ... , X p are conditionally independent. Under this assumption, we show how to build a knockoff X ˜. [ABSTRACT FROM AUTHOR]

Graphical models have become a popular tool for representing dependencies within large sets of variables and are crucial for representing causal structures. We provide results for uniform inference on high-dimensional graphical models, in which the number of target parameters |$d$| is potentially much larger than the sample size, under approximate sparsity. Our results highlight how graphical models can be estimated and recovered using modern machine learning methods in high-dimensional complex settings. To construct simultaneous confidence regions on many target parameters, it is crucial to have sufficiently fast estimation rates of the nuisance functions. In this context, we establish uniform estimation rates and sparsity guarantees for the square-root lasso estimator in a random design under approximate sparsity conditions. These might be of independent interest for related problems in high dimensions. We also demonstrate in a comprehensive simulation study that our procedure has good small sample properties in comparison to existing methods, and we present two empirical applications. [ABSTRACT FROM AUTHOR]

In this article, I propose a nonparametric strategy to identify the distribution of heterogeneous causal effects. A set of identification restrictions proposed in this article differs from existing approaches in three ways. First, it extends the random coefficient model by allowing potentially nonlinear interactions between distributional parameters and the set of covariates. Second, the causal effect distributions identified in this article give an alternative to those under the rank invariance assumption. Third, identified distribution lies within the sharp bound of distributions of the treatment effect. I develop a consistent nonparametric estimator exploiting the identifying restriction by extending the conventional statistical deconvolution method to the Rubin causal framework. Results from a Monte Carlo experiment and an application to wage loss of displaced workers suggest that the method yields robust estimates under various scenarios. [ABSTRACT FROM AUTHOR]

Bi-factor and second-order models based on copulas are proposed for item response data, where the items are sampled from identified subdomains of some larger domain such that there is a homogeneous dependence within each domain. Our general models include the Gaussian bi-factor and second-order models as special cases and can lead to more probability in the joint upper or lower tail compared with the Gaussian bi-factor and second-order models. Details on maximum likelihood estimation of parameters for the bi-factor and second-order copula models are given, as well as model selection and goodness-of-fit techniques. Our general methodology is demonstrated with an extensive simulation study and illustrated for the Toronto Alexithymia Scale. Our studies suggest that there can be a substantial improvement over the Gaussian bi-factor and second-order models both conceptually, as the items can have interpretations of discretized maxima/minima or mixtures of discretized means in comparison with discretized means, and in fit to data. [ABSTRACT FROM AUTHOR]