Composite Likelihood Research Articles

Regularized maximum likelihood estimation for the random coefficients model

. The random coefficients model Y i = β 0 i + β 1 i X 1 i + β 2 i X 2 i + … + β d i X d i , with 𝐗 i , Y i , 𝜷 i i.i.d, and 𝜷 i independent of 𝐗 i is often used to capture unobserved heterogeneity in a population. We propose a quasi-maximum likelihood method to estimate the joint density distribution of the random coefficient model. This method implicitly involves the inversion of the Radon transformation in order to reconstruct the joint distribution, and hence is an inverse problem. To add stability to the solution, we apply Tikhonov-type regularization methods. Nonparametric estimation for the joint density of β i = ( β 0 i , … , β d i ) based on kernel methods or Fourier inversion have been proposed in recent years. Most of these methods assume a heavy tailed design density f 𝐗 . We analyze the convergence of the quasi maximum likelihood method without assuming heavy tails for f 𝐗 and illustrate performance by applying the method on simulated and real data.

Simultaneous Coefficient Clustering and Sparsity for Multivariate Mixed Models

In many applications of multivariate longitudinal mixed models, it is reasonable to assume that each response is informed by only a subset of covariates. Moreover, one or more responses may exhibit the same relationship to a particular covariate for example, if they are capturing the same underlying aspect of an individual physical, mental, and emotional health. To address the above challenges, we propose a method for simultaneous clustering and variable selection of fixed effect coefficients in multivariate mixed models. We achieve this in a computationally scalable manner via a composite likelihood approach: separate mixed models are first fitted to each response, after which the model estimates are combined into a single quadratic form resembling a multivariate Wald statistic. We then augment this with fusion- and sparsity-inducing penalties based on broken adaptive ridge regression. Simulation studies demonstrate that the proposed composite quadratic estimator is similar to or better than several existing techniques for fixed effects selection in (univariate) mixed models while being computationally much more efficient. We apply the proposed method to longitudinal panel data from Australia to quantify how an individual’s overall health, assessed via a set of eight composite scores, evolves as a function of various demographic and lifestyle variables.

Using generalized estimating equations to estimate nonlinear models with spatial data

. We study the estimation of nonlinear models with cross-sectional data using two-step generalized estimating equations within the quasi-maximum likelihood estimation framework. To improve efficiency, we propose a grouped estimator that accounts for potential spatial correlation in the underlying innovations of nonlinear models. Under mild weak dependence assumptions, we provide results on estimation consistency and asymptotic normality. Monte Carlo simulations demonstrate the efficiency gain of our approach compared to various estimation methods. Finally, we apply the proposed approach to examine the role of cultural distance in an extended gravity equation using international trade data from China. Compared to existing methods, our approach yields estimates with smaller standard errors and reinforces the hypothesis that both cultural and geographical distances significantly negatively influence international trade.

Matrix GARCH model: Inference and application*

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use of a univariate GARCH specification for the trace of conditional row or column covariance matrix, which allows for the model identification. Moreover, we introduce a quasi-maximum likelihood estimator (QMLE) for model estimation and develop a portmanteau test for model diagnostic checking. Simulation studies are conducted to assess the finite-sample performance of the QMLE and portmanteau test. To handle large dimensional matrix time series, we also propose a matrix factor GARCH model, and establish its theoretical properties. Finally, we demonstrate the superiority of the matrix GARCH and matrix factor GARCH models over existing multivariate GARCH-type models in volatility forecasting and portfolio allocations using three applications on credit default swap prices, global stock sector indices, and future prices.

Inference of Phylogenetic Networks from Sequence Data using Composite Likelihood.

While phylogenies have been essential in understanding how species evolve, they do not adequately describe some evolutionary processes. For instance, hybridization, a common phenomenon where interbreeding between two species leads to formation of a new species, must be depicted by a phylogenetic network, a structure that modifies a phylogenetic tree by allowing two branches to merge into one, resulting in reticulation. However, existing methods for estimating networks become computationally expensive as the dataset size and/or topological complexity increase. The lack of methods for scalable inference hampers phylogenetic networks from being widely used in practice, despite accumulating evidence that hybridization occurs frequently in nature. Here, we propose a novel method, PhyNEST (Phylogenetic Network Estimation using SiTe patterns), that estimates binary, level-1 phylogenetic networks with a fixed, user-specified number of reticulations directly from sequence data. By using the composite likelihood as the basis for inference, PhyNEST is able to use the full genomic data in a computationally tractable manner, eliminating the need to summarize the data as a set of gene trees prior to network estimation. To search network space, PhyNEST implements both hill climbing and simulated annealing algorithms. PhyNEST assumes that the data are composed of coalescent independent sites that evolve according to the Jukes-Cantor substitution model and that the network has a constant effective population size. Simulation studies demonstrate that PhyNEST is often more accurate than two existing composite likelihood summary methods (SNaQ and PhyloNet) and that it is robust to at least one form of model misspecification (assuming a less complex nucleotide substitution model than the true generating model). We applied PhyNEST to reconstruct the evolutionary relationships among Heliconius butterflies and Papionini primates, characterized by hybrid speciation and widespread introgression, respectively. PhyNEST is implemented in an open-source Julia package and is publicly available at https://github.com/sungsik-kong/PhyNEST.jl.

Composite dyadic models for spatio-temporal data.

Mechanistic statistical models are commonly used to study the flow of biological processes. For example, in landscape genetics, the aim is to infer spatial mechanisms that govern gene flow in populations. Existing statistical approaches in landscape genetics do not account for temporal dependence in the data and may be computationally prohibitive. We infer mechanisms with a Bayesian hierarchical dyadic model that scales well with large data sets and that accounts for spatial and temporal dependence. We construct a fully connected network comprising spatio-temporal data for the dyadic model and use normalized composite likelihoods to account for the dependence structure in space and time. We develop a dyadic model to account for physical mechanisms commonly found in physical-statistical models and apply our methods to ancient human DNA data to infer the mechanisms that affected human movement in Bronze Age Europe.

Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm

We study estimation of large Dynamic Factor models implemented through the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that as both n and T diverge to infinity: (i) the estimated loadings are \sqrt{T}-consistent and asymptotically normal and equivalent to their Quasi Maximum Likelihood estimates; (ii) the estimated factors are \sqrt{n}-consistent and asymptotically normal and equivalent to their Weighted Least Squares estimates. Moreover, the estimated loadings are asymptotically as efficient as those obtained by Principal Components analysis, while the estimated factors are more efficient if the idiosyncratic covariance is sparse enough.

Localized negative binomial quasi maximum likelihood estimation for time varying integer-valued processes

This paper aims to study the non parametric Negative Binomial Quasi-Maximum Likelihood Estimation (NBQMLE) for locally stationary integer valued processes. So, we have considered two locally stationary integer-valued models of negative binomial type, namely: INARCH ( p ) and INGARCH ( p , q ) models. Imposing some contraction arguments, we have extended the stationary negative-binomial QMLE to a localized one in our non-stationary environment. This estimation method is based on a kernel function that achieves the convergence rates of n h n order. Under some regularity assumptions, the consistency, as well as the asymptotic normality of the obtained estimator, are established. The performances of the established estimators are evaluated via a simulation study and an application to real data set.

A spatio-temporal model for temporal evolution of spatial extremal dependence

Few spatio-temporal models allow temporal non-stationarity. When modeling environmental data recorded over the last decades of the 20th century until now, it seems not reasonable to assume temporal stationarity, since it would not capture climate change effects. In this paper, we propose a space–time max-stable model for modeling some temporal non-stationarity of the spatial extremal dependence. Our model consists of a mixture of max-stable spatial processes, with a rate of mixing depending on time. We use maximum composite likelihood for estimation, model selection, and a non-stationarity test. The assessment of its performance is done through wide simulation experiments. The proposed model is used to investigate how the rainfall in the south of France evolves with time. The results demonstrate that the spatial extremal dependence is significantly non-stationary over time, with a decrease in the strength of dependence.

Quasi Maximum Likelihood Estimation for Large-Dimensional Matrix Factor Models

In this study, we introduce a novel approach, called the quasi maximum likelihood estimation (Q-MLE), for estimating large-dimensional matrix factor models. In contrast to the principal component analysis based approach, Q-MLE considers the heteroscedasticity of the idiosyncratic error term, the heteroscedasticity of which is simultaneously estimated with other parameters. Interestingly, under the homoscedasticity assumption of the idiosyncratic error, the Q-MLE estimator encompassed the projected estimator (PE) as a special case. We provide the convergence rates and asymptotic distributions of the Q-MLE estimators under mild conditions. Extensive numerical experiments demonstrate that the Q-MLE method performs better, especially when heteroscedasticity exists. Furthermore, two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincide with financial, economic, or geographical interpretations.

Marginal models with individual-specific effects for the analysis of longitudinal bipartite networks

AbstractA new modeling framework for bipartite social networks arising from a sequence of partially time-ordered relational events is proposed. We directly model the joint distribution of the binary variables indicating if each single actor is involved or not in an event. The adopted parametrization is based on first- and second-order effects, formulated as in marginal models for categorical data and free higher order effects. In particular, second-order effects are log-odds ratios with meaningful interpretation from the social perspective in terms of tendency to cooperate, in contrast to first-order effects interpreted in terms of tendency of each single actor to participate in an event. These effects are parametrized on the basis of the event times, so that suitable latent trajectories of individual behaviors may be represented. Inference is based on a composite likelihood function, maximized by an algorithm with numerical complexity proportional to the square of the number of units in the network. A classification composite likelihood is used to cluster the actors, simplifying the interpretation of the data structure. The proposed approach is illustrated on simulated data and on a dataset of scientific articles published in four top statistical journals from 2003 to 2012.

Genetic Diversity, Selection Signatures, and Genome-Wide Association Study Identify Candidate Genes Related to Litter Size in Hu Sheep.

Hu sheep is a renowned prolific local sheep breed in China, widely distributed across the country due to its excellent reproductive performance. Deciphering the molecular mechanisms underlying the high fecundity of Hu sheep is crucial for improving the litter size of ewes. In this study, we genotyped 830 female Hu sheep using the Illumina OvineSNP50 BeadChip and performed genetic diversity analysis, selection signature detection, and a genome-wide association study (GWAS) for litter size. Our results revealed that the Hu sheep population exhibits relatively high genetic diversity. A total of 4927 runs of homozygosity (ROH) segments were detected, with the majority (74.73%) being short in length. Different genomic inbreeding coefficients (FROH, FHOM, FGRM, and FUNI) ranged from -0.0060 to 0.0126, showing low levels of inbreeding in this population. Additionally, we identified 91 candidate genomic regions through three complementary selection signature methods, including ROH, composite likelihood ratio (CLR), and integrated haplotype score (iHS), and annotated 189 protein-coding genes. Moreover, we observed two significant SNPs related to the litter size of Hu sheep using GWAS analysis based on a repeatability model. Integrating the selection signatures and the GWAS results, we identified 15 candidate genes associated with litter size, among which BMPR1B and UNC5C were particularly noteworthy. These findings provide valuable insights for improving the reproductive performance and breeding of high-fecundity lines of Hu sheep.

A general framework for regression with mismatched data based on mixture modelling

Abstract The advent of the information age has revolutionized data collection and has led to a rapid expansion of available data sources. Methods of data integration are indispensable when a question of interest cannot be addressed using a single data source. Record linkage (RL) is at the forefront of such data integration efforts. Incentives for sharing linked data for secondary analysis have prompted the need for methodology accounting for possible errors at the RL stage. Mismatch error is a common consequence resulting from the use of nonunique or noisy identifiers at that stage. In this paper, we present a framework to enable valid postlinkage inference in the secondary analysis setting in which only the linked file is given. The proposed framework covers a variety of statistical models and can flexibly incorporate information about the underlying RL process. We propose a mixture model for linked records whose two components reflect distributions conditional on match status, i.e. correct or false match. Regarding inference, we develop a method based on composite likelihood and the expectation-maximization algorithm that is implemented in the R package pldamixture. Extensive simulations and case studies involving contemporary RL applications corroborate the effectiveness of our framework.

Community influence analysis in social networks

Heterogeneous influence detection across network nodes is an important task in network analysis. A community influence model (CIM) is proposed to allow nodes to be classified into different communities (i.e., clusters or groups) such that the nodes within the same community share the common influence parameter. Employing the quasi-maximum likelihood approach, together with the fused lasso-type penalty, both the number of communities and the influence parameters can be estimated without imposing any specific distribution assumption on the error terms. The resulting estimators are shown to enjoy the oracle property; namely, they perform as well as if the true underlying network structure were known in advance. The proposed approach is also applicable for identifying influential nodes in a homogeneous setting. The performance of our method is illustrated via simulation studies and two empirical examples using stock data and coauthor citation data, respectively.

Penalized composite likelihood estimation for hidden Markov models with unknown number of states

Estimating hidden Markov models (HMMs) with unknown number of states is a challenging task. In this paper, we propose a new penalized composite likelihood approach for simultaneously estimating both the number of states and the parameters in an overfitted HMM. We prove the order selection consistency and asymptotic normality of the resultant estimator. Simulation studies and an application demonstrate the finite sample performance of the proposed method.

Threshold spatial autoregressive model

In this paper, we consider the estimation and inferential issues of the threshold spatial autoregressive (TSAR) model, which is a hybrid of the threshold and spatial autoregressive models. We use the quasi maximum likelihood (QML) method to estimate the model. In addition, we prove the tightness and the Hájek–Rényi type inequality for a quadratic form and establish a full inferential theory of the QML estimator under the setup that threshold effect shrinks to zero as the sample size increases. We conduct hypothesis testing on the presence of the threshold effect, using three super-type statistics. Their asymptotic behaviors are studied under the Pitman local alternatives. A bootstrap procedure is applied to obtain the asymptotically correct critical value. We also consider hypothesis testing on the threshold value set equal to a prespecified one. We run Monte Carlo simulations to investigate the finite sample performance of the QML estimators and find that the estimators perform well. In an empirical application, we apply the proposed TSAR model to study the relationship between financial development and economic growth, and we find firm evidence to support the TSAR model.

Joint value-at-risk and expected shortfall regression for location-scale time series models

. This article studies the joint value-at-risk (VaR) and expected shortfall (ES) regression for a wide class of location-scale time series models including autoregressive and moving average models with generalized autoregressive conditional heteroscedasticity errors. In contrast to the quasi-maximum likelihood estimation, we estimate the model parameters with the aim of more accurate VaR and ES estimation. Then, we show consistency and asymptotic normality for parameter estimators under weak regularity conditions. Finally, a simulation study and a real data analysis are shown to illustrate our results.

Effects of probability model misspecification on the number of ground motions required for seismic performance assessment

The number of ground motions used in nonlinear response history analysis (NRHA) determines the precision of the parameter estimates obtained in seismic performance assessments. While this issue has been extensively studied in the earthquake engineering literature, the relationship of probability model misspecification to parameter estimation uncertainty, and the implication to the required number of ground motions needed for NRHA, has not been examined. Probability model misspecification has the potential to increase estimation uncertainty and hence requires a greater number of ground motions to achieve the same precision compared to when misspecification is disregarded. This study develops a procedure to determine the required number of ground motions in seismic code-prescriptive and risk-based assessments with possible probability model misspecification. Specifically, we employ the quasi-maximum likelihood estimation (QMLE), which is robust to probability model misspecification, to evaluate estimation uncertainty. The QMLE approach is applied to an archetype California bridge under the two seismic assessment scenarios. In the code-prescriptive assessment, misspecification errors are identified for dispersion estimates of the bridge column ductility demand. In the most extreme case of the risk-based evaluation, misspecification increases the estimation uncertainty of the mean annual frequency of exceeding a limit state by as much as three times, which substantially increases the required number of ground motions. Based on the findings from this study, we advocate for the use of QMLE to detect and rectify the implications of model misspecification to estimation uncertainty and the number of ground motions used in probabilistic seismic performance assessments.

Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects

Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects

PQMLE and Generalized F-Test of Random Effects Semiparametric Model with Serially and Spatially Correlated Nonseparable Error

Semiparametric panel data models are powerful tools for analyzing data with complex characteristics such as linearity and nonlinearity of covariates. This study aims to investigate the estimation and testing of a random effects semiparametric model (RESPM) with serially and spatially correlated nonseparable error, utilizing a combination of profile quasi-maximum likelihood estimation and local linear approximation. Profile quasi-maximum likelihood estimators (PQMLEs) for unknowns and a generalized F-test statistic FNT are built to determine the beingness of nonlinear relationships. The asymptotic properties of PQMLEs and FNT are proven under regular assumptions. The Monte Carlo results imply that the PQMLEs and FNT performances are excellent on finite samples; however, missing the spatially and serially correlated error leads to estimator inefficiency and bias. Indonesian rice-farming data is used to illustrate the proposed approach, and indicates that landarea exhibits a significant nonlinear relationship with riceyield, in addition, high-yieldvarieties, mixed-yieldvarieties, and seedweight have significant positive impacts on rice yield.