Pseudo-likelihood Approach Research Articles

Statistical Inference for Counting Processes Under Shape Heterogeneity.

Proportional rate models are among the most popular methods for analyzing recurrent event data. Although providing a straightforward rate-ratio interpretation of covariate effects, the proportional rate assumption implies that covariates do not modify the shape of the rate function. When the proportionality assumption fails to hold, we propose to characterize covariate effects on the rate function through two types of parameters: the shape parameters and the size parameters. The former allows the covariates to flexibly affect the shape of the rate function, and the latter retains the interpretability of covariate effects on the magnitude of the rate function. To overcome the challenges in simultaneously estimating the two sets of parameters, we propose a conditional pseudolikelihood approach to eliminate the size parameters in shape estimation, followed by an event count projection approach for size estimation. The proposed estimators are asymptotically normal with a root- convergence rate. Simulation studies and an analysis of recurrent hospitalizations using SEER-Medicare data are conducted to illustrate the proposed methods.

Derivation of outcome-dependent dietary patterns for low-income women obtained from survey data using a supervised weighted overfitted latent class analysis.

Poor diet quality is a key modifiable risk factor for hypertension and disproportionately impacts low-income women. Analyzing diet-driven hypertensive outcomes in this demographic is challenging due to the complexity of dietary data and selection bias when the data come from surveys, a main data source for understanding diet-disease relationships in understudied populations. Supervised Bayesian model-based clustering methods summarize dietary data into latent patterns that holistically capture relationships among foods and a known health outcome but do not sufficiently account for complex survey design. This leads to biased estimation and inference and lack of generalizability of the patterns. To address this, we propose a supervised weighted overfitted latent class analysis (SWOLCA) based on a Bayesian pseudo-likelihood approach that integrates sampling weights into an exposure-outcome model for discrete data. Our model adjusts for stratification, clustering, and informative sampling, and handles modifying effects via interaction terms within a Markov chain Monte Carlo Gibbs sampling algorithm. Simulation studies confirm that the SWOLCA model exhibits good performance in terms of bias, precision, and coverage. Using data from the National Health and Nutrition Examination Survey (2015-2018), we demonstrate the utility of our model by characterizing dietary patterns associated with hypertensive outcomes among low-income women in the United States.

A Note on Ising Network Analysis with Missing Data

The Ising model has become a popular psychometric model for analyzing item response data. The statistical inference of the Ising model is typically carried out via a pseudo-likelihood, as the standard likelihood approach suffers from a high computational cost when there are many variables (i.e., items). Unfortunately, the presence of missing values can hinder the use of pseudo-likelihood, and a listwise deletion approach for missing data treatment may introduce a substantial bias into the estimation and sometimes yield misleading interpretations. This paper proposes a conditional Bayesian framework for Ising network analysis with missing data, which integrates a pseudo-likelihood approach with iterative data imputation. An asymptotic theory is established for the method. Furthermore, a computationally efficient Pólya–Gamma data augmentation procedure is proposed to streamline the sampling of model parameters. The method’s performance is shown through simulations and a real-world application to data on major depressive and generalized anxiety disorders from the National Epidemiological Survey on Alcohol and Related Conditions (NESARC).

Grouped Heterogeneity in Linear Panel Data Models with Heterogeneous Error Variances

We develop a procedure to identify latent group structures in linear panel data models that exploits a grouping in the error variances of cross-sectional units. To accommodate such grouping, we introduce an objective function that avoids a singularity that arises in a pseudolikelihood approach. We provide theoretical and numerical evidence showing when allowing for variance groups improves classification. The developed procedure provides new evidence on the relation between firm-level research and development (R&D) investments and the business cycle. We find a well-defined group structure in the variances that ex-post can be related to firm size. Our estimates indicate stronger procyclical investment patterns at medium-size firms compared to large firms.

Improved semi-parametric inference for a mixture model of responses from a control versus treatment group trial.

The mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we introduce inference based on a pseudo-likelihood approach and compare it with an existing method of moment approach. An extensive simulation study is used to compare robust performance of the two approaches regarding point estimation, confidence regions, and confidence intervals. The methods are demonstrated on an illustrative blood pressure data set.

TEA: A Sequential Recommendation Framework via Temporally Evolving Aggregations.

Sequential recommendation aims to choose the most suitable items for a user at a specific timestamp given historical behaviors. Existing methods usually model the user behavior sequence based on transition-based methods such as Markov chain. However, these methods also implicitly assume that the users are independent of each other without considering the influence between users. In fact, this influence plays an important role in sequence recommendation since the behavior of a user is easily affected by others. Therefore, it is desirable to aggregate both user behaviors and the influence between users, which are evolved temporally and involved in the heterogeneous graph of users and items. In this article, we incorporate dynamic user-item heterogeneous graphs to propose a novel sequential recommendation framework. As a result, the historical behaviors as well as the influence between users can be taken into consideration. To achieve this, we first formalize sequential recommendation as a problem to estimate conditional probability given temporal dynamic heterogeneous graphs and user behavior sequences. After that, we exploit the conditional random field to aggregate the heterogeneous graphs and user behaviors for probability estimation and employ the pseudo-likelihood approach to derive a tractable objective function. Finally, we provide scalable and flexible implementations of the proposed framework. Experimental results on three real-world datasets not only demonstrate the effectiveness of our proposed method but also provide some insightful discoveries on the sequential recommendation.

Statistically Valid Variational Bayes Algorithm for Ising Model Parameter Estimation

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant in the likelihood. Here, we use a pseudo-likelihood instead, to study the Bayesian estimation of two-parameter, inverse temperature and magnetization, Ising model with a fully specified coupling matrix. We develop a computationally efficient variational Bayes procedure for model estimation. Under the Gaussian mean-field variational family, we derive posterior contraction rates of the variational posterior obtained under the pseudo-likelihood. We also discuss the loss incurred due to variational posterior over true posterior for the pseudo-likelihood approach. Extensive simulation studies validate the efficacy of mean-field Gaussian and bivariate Gaussian families as the possible choices of the variational family for inference of Ising model parameters. Supplementary materials for this article are available online.

Bayesian model selection for generalized linear mixed models.

We propose a Bayesian model selection approach for generalized linear mixed models (GLMMs). We consider covariance structures for the random effects that are widely used in areas such as longitudinal studies, genome-wide association studies, and spatial statistics. Since the random effects cannot be integrated out of GLMMs analytically, we approximate the integrated likelihood function using a pseudo-likelihood approach. Our Bayesian approach assumes a flat prior for the fixed effects and includes both approximate reference prior and half-Cauchy prior choices for the variances of random effects. Since the flat prior on the fixed effects is improper, we develop a fractional Bayes factor approach to obtain posterior probabilities of the several competing models. Simulation studies with Poisson GLMMs with spatial random effects and overdispersion random effects show that our approach performs favorably when compared to widely used competing Bayesian methods including deviance information criterion and Watanabe-Akaike information criterion. We illustrate the usefulness and flexibility of our approach with three case studies including a Poisson longitudinal model, a Poisson spatial model, and a logistic mixed model. Our proposed approach is implemented in the R package GLMMselect that is available onCRAN.

Parameter estimation of discretely observed interacting particle systems

In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean–Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general framework, as both coefficients depend on the solution and on the law of the solution itself. Starting from discrete observations of the interacting particle system over a fixed interval [0,T], we propose a contrast function based on a pseudo likelihood approach. We show that the associated estimator is consistent when the discretization step (Δn) and the number of particles ( N) satisfy Δn→0 and N→∞, and asymptotically normal when additionally the condition ΔnN→0 holds.

Nonignorable Consequences of (Partially) Ignoring Missing Item Responses: Students Omit (Constructed Response) Items Due to a Lack of Knowledge

In recent literature, alternative models for handling missing item responses in large-scale assessments have been proposed. Based on simulations and arguments based on psychometric test theory, it is argued in this literature that missing item responses should never be scored as incorrect in scaling models but rather treated as ignorable or handled based on a model. The present article shows that these arguments have limited validity and illustrates the consequences in a country comparison using the PIRLS 2011 study. It is argued that students omit (constructed response) items because they do not know the correct item answer. A different treatment of missing item responses than scoring them as incorrect leads to significant changes in country rankings, which induces nonignorable consequences regarding the validity of the results. Additionally, two alternative item response models are proposed based on different assumptions for missing item responses. In the first pseudo-likelihood approach, missing item responses for a particular student are replaced by a score that ranges between zero and a model-implied probability computed based on the non-missing items. In the second approach, the probability of a missing item response is predicted by a latent response propensity variable and the item response itself. The models were applied to the PIRLS 2011 study, demonstrating that country comparisons change under different modeling assumptions for missing item responses.

A multivariate pseudo-likelihood approach to estimating directional ocean wave models

Abstract Buoy data in the form of multivariate time series are routinely recorded at many locations in the world’s oceans. Such data can help characterise the ocean wavefield by modelling the frequency-direction spectrum. State-of-the-art methods for estimating the parameters of such models do not make use of the full spatiotemporal content of the buoy observations due to unnecessary assumptions and smoothing. We explain how the multivariate debiased Whittle likelihood can be used to jointly estimate all parameters of such frequency-direction spectra directly from recorded time series. We apply the method to North Sea buoy data and discuss challenging practical issues.

A pairwise pseudo-likelihood approach for regression analysis of left-truncated failure time data with various types of censoring

BackgroundFailure time data frequently occur in many medical studies and often accompany with various types of censoring. In some applications, left truncation may occur and can induce biased sampling, which makes the practical data analysis become more complicated. The existing analysis methods for left-truncated data have some limitations in that they either focus only on a special type of censored data or fail to flexibly utilize the distribution information of the truncation times for inference. Therefore, it is essential to develop a reliable and efficient method for the analysis of left-truncated failure time data with various types of censoring.MethodThis paper concerns regression analysis of left-truncated failure time data with the proportional hazards model under various types of censoring mechanisms, including right censoring, interval censoring and a mixture of them. The proposed pairwise pseudo-likelihood estimation method is essentially built on a combination of the conditional likelihood and the pairwise likelihood that eliminates the nuisance truncation distribution function or avoids its estimation. To implement the presented method, a flexible EM algorithm is developed by utilizing the idea of self-consistent estimating equation. A main feature of the algorithm is that it involves closed-form estimators of the large-dimensional nuisance parameters and is thus computationally stable and reliable. In addition, an R package LTsurv is developed.ResultsThe numerical results obtained from extensive simulation studies suggest that the proposed pairwise pseudo-likelihood method performs reasonably well in practical situations and is obviously more efficient than the conditional likelihood approach as expected. The analysis results of the MHCPS data with the proposed pairwise pseudo-likelihood method indicate that males have significantly higher risk of losing active life than females. In contrast, the conditional likelihood method recognizes this effect as non-significant, which is because the conditional likelihood method often loses some estimation efficiency compared with the proposed method.ConclusionsThe proposed method provides a general and helpful tool to conduct the Cox’s regression analysis of left-truncated failure time data under various types of censoring.

A pairwise pseudo-likelihood approach for the additive hazards model with left-truncated and interval-censored data

A pairwise pseudo-likelihood approach for the additive hazards model with left-truncated and interval-censored data

Close-kin mark-recapture methods to estimate demographic parameters of mosquitoes.

Close-kin mark-recapture (CKMR) methods have recently been used to infer demographic parameters such as census population size and survival for fish of interest to fisheries and conservation. These methods have advantages over traditional mark-recapture methods as the mark is genetic, removing the need for physical marking and recapturing that may interfere with parameter estimation. For mosquitoes, the spatial distribution of close-kin pairs has been used to estimate mean dispersal distance, of relevance to vector-borne disease transmission and novel biocontrol strategies. Here, we extend CKMR methods to the life history of mosquitoes and comparable insects. We derive kinship probabilities for mother-offspring, father-offspring, full-sibling and half-sibling pairs, where an individual in each pair may be a larva, pupa or adult. A pseudo-likelihood approach is used to combine the marginal probabilities of all kinship pairs. To test the effectiveness of this approach at estimating mosquito demographic parameters, we develop an individual-based model of mosquito life history incorporating egg, larva, pupa and adult life stages. The simulation labels each individual with a unique identification number, enabling close-kin relationships to be inferred for sampled individuals. Using the dengue vector Aedes aegypti as a case study, we find the CKMR approach provides unbiased estimates of adult census population size, adult and larval mortality rates, and larval life stage duration for logistically feasible sampling schemes. Considering a simulated population of 3,000 adult mosquitoes, estimation of adult parameters is accurate when ca. 40 adult females are sampled biweekly over a three month period. Estimation of larval parameters is accurate when adult sampling is supplemented with ca. 120 larvae sampled biweekly over the same period. The methods are also effective at detecting intervention-induced increases in adult mortality and decreases in population size. As the cost of genome sequencing declines, CKMR holds great promise for characterizing the demography of mosquitoes and comparable insects of epidemiological and agricultural significance.

Worldwide bilateral geopolitical interactions network inferred from national disciplinary profiles

A disciplinary profile of a country is defined as the versor whose components are the number of papers produced in a given discipline divided by the overall production of the country. Starting from the Essential Science Indicators (ESI) schema of classification of subject areas, we obtained the yearly disciplinary profiles of a worldwide graph, where on each node sits a country, in the two time intervals 1988--1988 and 1992--2017, the fall of the Berlin Wall being the watershed. We analyze the empirical pairwise cross-correlation matrices of the time series of disciplinary profiles. The contrast with random matrix theory proves that, beyond measurement noise, the empirical cross-correlation matrices bring genuine information. Arising from the Shannon theorem as the least-structured model consistent with the measured pairwise correlations, the stationary probability distribution of disciplinary profiles can be described by a Boltzmann distribution related to a generalized ${n}_{d}$-dimensional Heisenberg model. The set of network interactions of the Heisenberg model has been inferred and to it, two clusterization methods, hierarchical clustering, and principal component analysis have been applied. This allows obtaining a characterization of the worldwide bilateral interactions based on physical modeling. A simple geopolitical analysis reveals the consistency of the results obtained and gives a boost to a deeper historical analysis. In order to obtain the optimal set of pairwise interactions, we used a pseudolikelihood approach. We analytically computed the pseudolikelihood and its gradient. The analytical computations deserve interest in whatever inference Bayesian problem involving an ${n}_{d}$-dimensional Heisenberg model.

Fast Network Community Detection With Profile-Pseudo Likelihood Methods

The stochastic block model is one of the most studied network models for community detection, and fitting its likelihood function on large-scale networks is known to be challenging. One prominent work that overcomes this computational challenge is the fast pseudo-likelihood approach proposed by Amini et al. for fitting stochastic block models to large sparse networks. However, this approach does not have convergence guarantee, and may not be well suited for small and medium scale networks. In this article, we propose a novel likelihood based approach that decouples row and column labels in the likelihood function, enabling a fast alternating maximization. This new method is computationally efficient, performs well for both small- and large-scale networks, and has provable convergence guarantee. We show that our method provides strongly consistent estimates of communities in a stochastic block model. We further consider extensions of our proposed method to handle networks with degree heterogeneity and bipartite properties. Supplementary materials for this article are available online.

Pseudo-Likelihood Estimation for Parameters of Stochastic Time-Fractional Diffusion Equations

Although stochastic fractional partial differential equations have received increasing attention in the last decade, the parameter estimation of these equations has been seldom reported in literature. In this paper, we propose a pseudo-likelihood approach to estimating the parameters of stochastic time-fractional diffusion equations, whose forward solver has been investigated very recently by Gunzburger, Li, and Wang (2019). Our approach can accurately recover the fractional order, diffusion coefficient, as well as noise magnitude given the discrete observation data corresponding to only one realization of driving noise. When only partial data is available, our approach can also attain acceptable results for intermediate sparsity of observation.

Unveiling the Patterns of Reticulated Evolutionary Processes with Phylogenomics: Hybridization and Polyploidy in the Genus Rosa.

Reticulation, caused by hybridization and allopolyploidization, is considered an important and frequent phenomenon in the evolution of numerous plant lineages. Although both processes represent important driving forces of evolution, they are mostly ignored in phylogenetic studies involving a large number of species. Indeed only a scattering of methods exists to recover a comprehensive reticulated evolutionary history for a broad taxon sampling. Among these methods, comparisons of topologies obtained from plastid markers with those from a few nuclear sequences are favored, even though they restrict in-depth studies of hybridization and polyploidization. The genus Rosa encompasses c. 150 species widely distributed throughout the northern hemisphere and represents a challenging taxonomic group in which hybridization and polyploidization are prominent. Our main objective was to develop a general framework that would take patterns of reticulation into account in the study of the phylogenetic relationships among Rosa species. Using amplicon sequencing, we targeted allele variation in the nuclear genome as well as haploid sequences in the chloroplast genome. We successfully recovered robust plastid and nuclear phylogenies and performed in-depth tests for several scenarios of hybridization using a maximum pseudo-likelihood approach on taxon subsets. Our diploid-first approach followed by hybrid and polyploid grafting resolved most of the evolutionary relationships among Rosa subgenera, sections, and selected species. Based on these results, we provide new directions for a future revision of the infrageneric classification in Rosa. The stepwise strategy proposed here can be used to reconstruct the phylogenetic relationships of other challenging taxonomic groups with large numbers of hybrid and polyploid taxa. [Amplicon sequencing; interspecific hybridization; polyploid detection; reticulate evolution.].

A bias-adjusted estimator in quantile regression for clustered data

Quantile regression models with random effects are useful for studying associations between covariates and quantiles of the response distribution for clustered data. Parameter estimation is examined for a class of mixed-effects quantile regression models, with focus on settings with many but small clusters. The main contributions are the following: (i) documenting that existing methods may lead to severely biased estimators for fixed effects parameters; (ii) proposing a new two-step estimation methodology where predictions of the random effects are first computed by a pseudo likelihood approach (the LQMM method) and then used as offsets in standard quantile regression; (iii) proposing a novel bootstrap sampling procedure in order to reduce bias of the two-step estimator and compute confidence intervals. The proposed estimation and associated inference is assessed numerically through rigorous simulation studies and applied to an AIDS Clinical Trial Group (ACTG) study.

Strong selection consistency of Bayesian vector autoregressive models based on a pseudo-likelihood approach

Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macroeconomics and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which will provide novel insights into the role of temporal dependence for regularized estimates of the models parameters. However, hardly anything is known regarding posterior model selection consistency for Bayesian VAR models in such regimes. In this work, we develop a pseudo-likelihood based Bayesian approach for consistent variable selection in high-dimensional VAR models by considering hierarchical normal priors on the autoregressive coefficients, as well as on the model space. We establish strong selection consistency of the proposed method, namely that the posterior probability assigned to the true underlying VAR model converges to one under high-dimensional scaling where the dimension p of the VAR system grows nearly exponentially with the sample size n. Further, the result is established under mild regularity conditions on the problem parameters. Finally, as a by-product of these results, we also establish strong selection consistency for the sparse high-dimensional linear regression model with serially correlated regressors and errors.