Extended Bayesian Information Criterion Research Articles

Exploring the complexity of commonly held attitudes and beliefs of low back pain-a network analysis.

The current study used a network analysis approach to explore the complexity of attitudes and beliefs held in people with and without low back pain (LBP). The study aimed to (1) quantify the adjusted associations between individual items of the Back Pain Attitudes Questionnaire (Back-PAQ), and (2) identify the items with the strongest connectivity within the network. This is a secondary data analysis of a previously published survey using the Back-PAQ (n = 602). A nonparametric Spearman's rank correlation matrix was used as input to the network analysis. We estimated an unregularised graphical Gaussian model (GGM). Edges were added or removed in a stepwise manner until the extended Bayesian information criterion (EBIC) did not improve. We assessed three measures of centrality measures of betweenness, closeness, and strength. The two pairwise associations with the greatest magnitude of correlation were between Q30-Q31 [0.54 (95% CI 0.44 to 0.60)] and Q15-Q16 [0.52 (95% CI 0.43 to 0.61)]. These two relationships related to the association between items exploring the influence of attentional focus and expectations (Q30-Q31), and feelings and stress (Q15-Q16). The three items with the greatest average centrality values, were Q22, Q25, and Q10. These items reflect beliefs about damaging the back, exercise, and activity avoidance, respectively. Beliefs about back damage, exercise, and activity avoidance are factors most connected to all other beliefs within the network. These three factors may represent candidate targets that clinicians can focus their counseling efforts on to manage unhelpful attitudes and beliefs in people experiencing LBP.

Multiple-hypothesis testing rules for high-dimensional model selection and sparse-parameter estimation

We consider the problem of model selection for high-dimensional sparse linear regression models. We pose the model selection problem as a multiple-hypothesis testing problem and employ the methods of false discovery rate (FDR) and familywise error rate (FER) to solve it. We also present the reformulation of the FDR/FER-based approaches as criterion-based model selection rules and establish their relation to the extended Bayesian Information Criterion (EBIC), which is a state-of-the-art high-dimensional model selection rule. We use numerical simulations to show that the proposed FDR/FER method is well suited for high-dimensional model selection and performs better than EBIC.

Quantile forward regression for high-dimensional survival data.

Despite the urgent need for an effective prediction model tailored to individual interests, existing models have mainly been developed for the mean outcome, targeting average people. Additionally, the direction and magnitude of covariates' effects on the mean outcome may not hold across different quantiles of the outcome distribution. To accommodate the heterogeneous characteristics of covariates and provide a flexible risk model, we propose a quantile forward regression model for high-dimensional survival data. Our method selects variables by maximizing the likelihood of the asymmetric Laplace distribution (ALD) and derives the final model based on the extended Bayesian Information Criterion (EBIC). We demonstrate that the proposed method enjoys a sure screening property and selection consistency. We apply it to the national health survey dataset to show the advantages of a quantile-specific prediction model. Finally, we discuss potential extensions of our approach, including the nonlinear model and the globally concerned quantile regression coefficients model.

Prevalence of depression and its association with quality of life among guardians of hospitalized psychiatric patients during the COVID-19 pandemic: a network perspective.

The COVID-19 pandemic has greatly affected treatment-seeking behaviors of psychiatric patients and their guardians. Barriers to access of mental health services may contribute to adverse mental health consequences, not only for psychiatric patients, but also for their guardians. This study explored the prevalence of depression and its association with quality of life among guardians of hospitalized psychiatric patients during the COVID-19 pandemic. This multi-center, cross-sectional study was conducted in China. Symptoms of depression and anxiety, fatigue level and quality of life (QOL) of guardians were measured with validated Chinese versions of the Patient Health Questionnaire - 9 (PHQ-9), Generalized Anxiety Disorder Scale - 7 (GAD-7), fatigue numeric rating scale (FNRS), and the first two items of the World Health Organization Quality of Life Questionnaire - brief version (WHOQOL-BREF), respectively. Independent correlates of depression were evaluated using multiple logistic regression analysis. Analysis of covariance (ANCOVA) was used to compare global QOL of depressed versus non-depressed guardians. The network structure of depressive symptoms among guardians was constructed using an extended Bayesian Information Criterion (EBIC) model. The prevalence of depression among guardians of hospitalized psychiatric patients was 32.4% (95% CI: 29.7-35.2%). GAD-7 total scores (OR = 1.9, 95% CI: 1.8-2.1) and fatigue (OR = 1.2, 95% CI: 1.1-1.4) were positively correlated with depression among guardians. After controlling for significant correlates of depression, depressed guardians had lower QOL than non-depressed peers did [F(1, 1,101) = 29.24, p < 0.001]. "Loss of energy" (item 4 of the PHQ-9), "concentration difficulties" (item 7 of the PHQ-9) and "sad mood" (item 2 of the PHQ-9) were the most central symptoms in the network model of depression for guardians. About one third of guardians of hospitalized psychiatric patients reported depression during the COVID-19 pandemic. Poorer QOL was related to having depression in this sample. In light of their emergence as key central symptoms, "loss of energy," "concentration problems," and "sad mood" are potentially useful targets for mental health services designed to support caregivers of psychiatric patients.

Associations between post-traumatic stress symptoms and quality of life among psychiatric healthcare personnel in China during the COVID-19 pandemic: A network approach.

Post-traumatic stress symptoms (PTSS) are commonly reported by psychiatric healthcare personnel during the coronavirus disease 2019 (COVID-19) pandemic and negatively affect quality of life (QOL). However, associations between PTSS and QOL at symptom level are not clear. This study examined the network structure of PTSS and its connection with QOL in psychiatric healthcare personnel during the COVID-19 pandemic. This cross-sectional study was carried out between March 15 and March 20, 2020 based on convenience sampling. Self-report measures including the 17-item Post-Traumatic Stress Disorder Checklist - Civilian version (PCL-C) and World Health Organization Quality of Life Questionnaire - Brief Version (WHOQOL-BREF) were used to measure PTSS and global QOL, respectively. Network analysis was used to investigate the central symptoms of PTSS and pattern of connections between PTSS and QOL. An undirected network was constructed using an extended Bayesian Information Criterion (EBIC) model, while a directed network was established based on the Triangulated Maximally Filtered Graph (TMFG) method. Altogether, 10,516 psychiatric healthcare personnel completed the assessment. "Avoidance of thoughts" (PTSS-6), "Avoidance of reminders" (PTSS-7), and "emotionally numb" (PTSS-11) were the most central symptoms in the PTSS community, all of which were in the Avoidance and Numbing domain. Key bridge symptoms connecting PTSS and QOL were "Sleep disturbances" (PTSS-13), "Irritability" (PTSS-14) and "Difficulty concentrating" (PTSS-15), all of which were within the Hyperarousal domain. In this sample, the most prominent PTSS symptoms reflected avoidance while symptoms of hyper-arousal had the strongest links with QOL. As such, these symptom clusters are potentially useful targets for interventions to improve PTSS and QOL among healthcare personnel at work under pandemic conditions.

Variable Screening and Model Averaging for Expectile Regressions

Expectile regression is a useful tool in modelling data with heterogeneous conditional distributions. This paper introduces two new concepts, i.e. the expectile correlation and expectile partial correlation, which can measure the contribution from each regressor to the response in expectile regression. In ultra‐high dimensional setting, the expectile partial correlation, which provides an importance ranking of the predictors, is found useful for variable screening. Theoretical results indicate that the proposed screening procedure can achieve the sure screening set. Additionally, a model selection method via extended Bayesian information criterion (EBIC) and a jackknife model averaging (JMA) method are suggested after the screening step to address model uncertainty. The screening consistency of EBIC, the asymptotic optimality of JMA in the sense of minimizing out‐of‐sample expectile final prediction error, and the sparsity of JMA weight are then established. Finally, numerical results demonstrate the nice performance of our proposed methods.

The backbone symptoms of depression: a network analysis after the initial wave of the COVID-19 pandemic in Macao.

BackgroundThe coronavirus disease 2019 (COVID-19) pandemic disrupted the working lives of Macau residents, possibly leading to mental health issues such as depression. The pandemic served as the context for this investigation of the network structure of depressive symptoms in a community sample. This study aimed to identify the backbone symptoms of depression and to propose an intervention target.MethodsThis study recruited a convenience sample of 975 Macao residents between 20th August and 9th November 2020. In an electronic survey, depressive symptoms were assessed with the Patient Health Questionnaire-9 (PHQ-9). Symptom relationships and centrality indices were identified using directed and undirected network estimation methods. The undirected network was constructed using the extended Bayesian information criterion (EBIC) model, and the directed network was constructed using the Triangulated Maximally Filtered Graph (TMFG) method. The stability of the centrality indices was evaluated by a case-dropping bootstrap procedure. Wilcoxon signed rank tests of the centrality indices were used to assess whether the network structure was invariant between age and gender groups.ResultsLoss of energy, psychomotor problems, and guilt feelings were the symptoms with the highest centrality indices, indicating that these three symptoms were backbone symptoms of depression. The directed graph showed that loss of energy had the highest number of outward projections to other symptoms. The network structure remained stable after randomly dropping 50% of the study sample, and the network structure was invariant by age and gender groups.ConclusionLoss of energy, psychomotor problems and guilt feelings constituted the three backbone symptoms during the pandemic. Based on centrality and relative influence, loss of energy could be targeted by increasing opportunities for physical activity.

Associations between depressive symptoms and quality of life among residents of Wuhan, China during the later stage of the COVID-19 pandemic: A network analysis

BackgroundVarious populations have experienced significant increases in depression and decreased quality of life (QOL) during the coronavirus disease 2019 (COVID-19) pandemic. This network analysis study was designed to elucidate interconnections between particular depressive symptoms and different aspects of QOL and identify the most clinically important symptoms in this network among adults in Wuhan China, the initial epicenter of the COVID-19 pandemic. MethodsThis cross-sectional, convenience-sampling study (N = 2459) was conducted between May 25 to June 18, 2020, after the lockdown policy had been lifted in Wuhan. Depressive symptoms and QOL were measured with the Patient Health Questionnaire-9 (PHQ-9) and first two items of the World Health Organization Quality of Life Questionnaire - brief version (WHOQOL-BREF), respectively. A network structure was constructed from the extended Bayesian Information Criterion (EBIC) model. Network centrality strength and bridge strength were evaluated along with the stability of the derived network model. ResultsLoss of energy (DEP-4) and Guilt feelings (DEP-6) were the two central symptoms with the highest strength as well as the two most prominent bridge symptoms connecting the clusters of depression and quality of life (QOL) in tandem with the two nodes from the QOL cluster. Network structure and bridge strengths remained stable after randomly dropping 75 % of the sample. ConclusionInterventions targeting “Loss of energy” and “Guilt feelings” should be evaluated as strategies for reducing depressive symptoms and promoting improved QOL in COVID-19-affected populations.

High-dimensional variable selection via low-dimensional adaptive learning

A stochastic search method, the so-called Adaptive Subspace (AdaSub) method, is proposed for variable selection in high-dimensional linear regression models. The method aims at finding the best model with respect to a certain model selection criterion and is based on the idea of adaptively solving low-dimensional sub-problems in order to provide a solution to the original high-dimensional problem. Any of the usual $\ell_0$-type model selection criteria can be used, such as Akaike's Information Criterion (AIC), the Bayesian Information Criterion (BIC) or the Extended BIC (EBIC), with the last being particularly suitable for high-dimensional cases. The limiting properties of the new algorithm are analysed and it is shown that, under certain conditions, AdaSub converges to the best model according to the considered criterion. In a simulation study, the performance of AdaSub is investigated in comparison to alternative methods. The effectiveness of the proposed method is illustrated via various simulated datasets and a high-dimensional real data example.

A network analysis of symptoms of obsessive compulsive disorder and depression in a clinical sample

McNally, Mair, Mugno, and Riemann (2017) provide preliminary evidence for the hypothesis that obsessive compulsive disorder (OCD) and depression symptoms co-occur because they create a network of interacting symptoms. Given the need to understand comorbidity between these symptoms and replicating network models, the aim of the current study was to examine a cross-sectional network of OCD and depression symptoms in an adult clinical sample diagnosed with OCD (n = 290). Participants completed self-report measures of OCD and depression symptoms. A network of regularized partial correlation coefficients was estimated using the graphical least absolute shrinkage and selection operator (GLASSO) with the Extended Bayesian Information Criterion (EBIC). Parameter estimates were also compared between McNally and colleagues’ (2017) results and the current findings to determine the consistency of trends. OCD and depression symptom clusters were bridged by an association between interference from obsessions and low energy, suggesting this is a key feature in the development of comorbidity. Distress related to obsessions emerged as the most highly central node in the network. Low energy, interference from compulsions, and resisting compulsions were also central to the network. These symptoms may be important targets for treatment. Overall, the majority of comparable parameters were consistent with previous work.

Insight-related beliefs and controllability appraisals contribute little to hallucinated voices: a transdiagnostic network analysis study

Hallucinated voices cause high levels of distress and disability. Current theories suggest that insight-related beliefs, about internal or external origin, perceived source location, and appraisals of controllability are important in mediating the impact of these experiences but previous findings have been mixed. We report two open code and open data network analytic studies of items in the Psychotic Symptoms Ratings Scale for auditory verbal hallucinations (PSYRATS-AH) in a large sample of patients with hallucinated voices to examine the network structure of items at (1) first assessment, and (2) differences over two consecutive assessments during a wait-list period. Networks were generated using least absolute shrinkage and selection operator (LASSO) and extended Bayesian information criterion (EBIC) with node predictability. In Study 1 (N = 386), we report that insight-related items made a negligible contribution to hallucinated voices and the controllability appraisal made at most a modest contribution. Items relating to distress and negative content were the most central and most predicted by the wider network. In Study 2 (N = 204), we tested the longitudinal stability of the structure of hallucinated voices over a period of several months, finding a small change in total hallucination score and global strength but no clear evidence for an alteration in the structural relationship. The insight-related and controllability items remained as least influential over time. Insight-related beliefs and controllability appraisals may contribute less than previously thought to distressing hallucinated voices although we do not discount that other appraisals may remain important.

On Penalty Parameter Selection for Estimating Network Models

Network models are gaining popularity as a way to estimate direct effects among psychological variables and investigate the structure of constructs. A key feature of network estimation is determining which edges are likely to be non-zero. In psychology, this is commonly achieved through the graphical lasso regularization method that estimates a precision matrix of Gaussian variables using an -penalty to push small values to zero. A tuning parameter, λ, controls the sparsity of the network. There are many methods to select λ, which can lead to vastly different graphs. The most common approach in psychological network applications is to minimize the extended Bayesian information criterion, but the consistency of this method for model selection has primarily been examined in high dimensional settings (i.e., n < p) that are uncommon in psychology. Further, there is some evidence that alternative selection methods may have superior performance. Here, using simulation, we compare four different methods for selecting λ, including the stability approach to regularization selection (StARS), K-fold cross-validation, the rotation information criterion (RIC), and the extended Bayesian information criterion (EBIC). Our results demonstrate that penalty parameter selection should be made based on data characteristics and the inferential goal (e.g., to increase sensitivity versus to avoid false positives). We end with recommendations for selecting the penalty parameter when using the graphical lasso.

Forward regression for Cox models with high-dimensional covariates

Forward regression, a classical variable screening method, has been widely used for model building when the number of covariates is relatively low. However, forward regression is seldom used in high-dimensional settings because of the cumbersome computation and unknown theoretical properties. Some recent works have shown that forward regression, coupled with an extended Bayesian information criterion (EBIC)-based stopping rule, can consistently identify all relevant predictors in high-dimensional linear regression settings. However, the results are based on the sum of residual squares from linear models and it is unclear whether forward regression can be applied to more general regression settings, such as Cox proportional hazards models. We introduce a forward variable selection procedure for Cox models. It selects important variables sequentially according to the increment of partial likelihood, with an EBIC stopping rule. To our knowledge, this is the first study that investigates the partial likelihood-based forward regression in high-dimensional survival settings and establishes selection consistency results. We show that, if the dimension of the true model is finite, forward regression can discover all relevant predictors within a finite number of steps and their order of entry is determined by the size of the increment in partial likelihood. As partial likelihood is not a regular density-based likelihood, we develop some new theoretical results on partial likelihood and use these results to establish the desired sure screening properties. The practical utility of the proposed method is examined via extensive simulations and analysis of a subset of the Boston Lung Cancer Survival Cohort study, a hospital-based study for identifying biomarkers related to lung cancer patients’ survival.

Robust Variable and Interaction Selection for Logistic Regression and General Index Models

ABSTRACTUnder the logistic regression framework, we propose a forward-backward method, SODA, for variable selection with both main and quadratic interaction terms. In the forward stage, SODA adds in predictors that have significant overall effects, whereas in the backward stage SODA removes unimportant terms to optimize the extended Bayesian information criterion (EBIC). Compared with existing methods for variable selection in quadratic discriminant analysis, SODA can deal with high-dimensional data in which the number of predictors is much larger than the sample size and does not require the joint normality assumption on predictors, leading to much enhanced robustness. We further extend SODA to conduct variable selection and model fitting for general index models. Compared with existing variable selection methods based on the sliced inverse regression (SIR), SODA requires neither linearity nor constant variance condition and is thus more robust. Our theoretical analysis establishes the variable-selection consistency of SODA under high-dimensional settings, and our simulation studies as well as real-data applications demonstrate superior performances of SODA in dealing with non-Gaussian design matrices in both logistic and general index models. Supplementary materials for this article are available online.

Sequential profile Lasso for ultra-high-dimensional partially linear models

ABSTRACTIn this paper, we study ultra-high-dimensional partially linear models when the dimension of the linear predictors grows exponentially with the sample size. For the variable screening, we propose a sequential profile Lasso method (SPLasso) and show that it possesses the screening property. SPLasso can also detect all relevant predictors with probability tending to one, no matter whether the ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a real data example to assess the performance of the proposed method and compare with the existing method.

Variable Screening via Quantile Partial Correlation

ABSTRACT In quantile linear regression with ultrahigh-dimensional data, we propose an algorithm for screening all candidate variables and subsequently selecting relevant predictors. Specifically, we first employ quantile partial correlation for screening, and then we apply the extended Bayesian information criterion (EBIC) for best subset selection. Our proposed method can successfully select predictors when the variables are highly correlated, and it can also identify variables that make a contribution to the conditional quantiles but are marginally uncorrelated or weakly correlated with the response. Theoretical results show that the proposed algorithm can yield the sure screening set. By controlling the false selection rate, model selection consistency can be achieved theoretically. In practice, we proposed using EBIC for best subset selection so that the resulting model is screening consistent. Simulation studies demonstrate that the proposed algorithm performs well, and an empirical example is presented. Supplementary materials for this article are available online.

Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models

In this paper, we consider semiparametric varying coefficient partially linear models when the predictor variables of the linear part are ultra-high dimensional where the dimensionality grows exponentially with the sample size. We propose a profile forward regression (PFR) method to perform variable screening for ultra-high dimensional linear predictor variables. The proposed PFR algorithm can not only identify all relevant predictors consistently even for ultra-high semiparametric models including both nonparametric and parametric parts, but also possesses the screening consistency property. To determine whether or not to include the candidate predictor in the model of selected ones, we adopt an extended Bayesian information criterion (EBIC) to select the “best” candidate model. Simulation studies and a real data example are also carried out to assess the performance of the proposed method and to compare it with existing screening methods.

Forward Variable Selection for Sparse Ultra-High Dimensional Varying Coefficient Models

ABSTRACTVarying coefficient models have numerous applications in a wide scope of scientific areas. While enjoying nice interpretability, they also allow for flexibility in modeling dynamic impacts of the covariates. But, in the new era of big data, it is challenging to select the relevant variables when the dimensionality is very large. Recently, several works are focused on this important problem based on sparsity assumptions; they are subject to some limitations, however. We introduce an appealing forward selection procedure. It selects important variables sequentially according to a reduction in sum of squares criterion and it employs a Bayesian information criterion (BIC)-based stopping rule. Clearly, it is simple to implement and fast to compute, and possesses many other desirable properties from theoretical and numerical viewpoints. The BIC is a special case of the extended BIC (EBIC) when an extra tuning parameter in the latter vanishes. We establish rigorous screening consistency results when either BIC or EBIC is used as the stopping criterion. The theoretical results depend on some conditions on the eigenvalues related to the design matrices, which can be relaxed in some situations. Results of an extensive simulation study and a real data example are also presented to show the efficacy and usefulness of our procedure. Supplementary materials for this article are available online.

Extended Bayesian information criterion in the Cox model with a high-dimensional feature space

Variable selection in the Cox proportional hazards model (the Cox model) has manifested its importance in many microarray genetic studies. However, theoretical results on the procedures of variable selection in the Cox model with a high-dimensional feature space are rare because of its complicated data structure. In this paper, we consider the extended Bayesian information criterion (EBIC) for variable selection in the Cox model and establish its selection consistency in the situation of high-dimensional feature space. The EBIC is adopted to select the best model from a model sequence generated from the SIS-ALasso procedure. Simulation studies and real data analysis are carried out to demonstrate the merits of the EBIC.

Edge detection in sparse Gaussian graphical models

In this paper, we consider the problem of detecting edges in a Gaussian graphical model. The problem is equivalent to the identification of non-zero entries of the concentration matrix of a normally distributed random vector. Following the methodology initiated in Meinshausen and Bühlmann (2006), we tackle the problem through regression models where each component of the random vector is regressed on the remaining components. We adapt a method called SLasso cum EBIC (sequential LASSO cum extended Bayesian information criterion) recently developed in Luo and Chen (2011) for feature selection in sparse regression models to suit the special nature of the concentration matrix, and propose two approaches, dubbed SR-SLasso and JR-SLasso, for the identification of non-zero entries of the concentration matrix. Comprehensive numerical studies are conducted to compare the proposed approaches with other available competing methods. The numerical studies demonstrate that the proposed approaches are more accurate than the other methods for the identification of non-zero entries of the concentration matrix.