Composite Likelihood Research Articles

Flexible Lévy-Based Models for Time Series of Count Data with Zero-Inflation, Overdispersion, and Heavy Tails

The explosion of time series count data with diverse characteristics and features in recent years has led to a proliferation of new analysis models and methods. Significant efforts have been devoted to achieving flexibility capable of handling complex dependence structures, capturing multiple distributional characteristics simultaneously, and addressing nonstationary patterns such as trends, seasonality, or change points. However, it remains a challenge when considering them in the context of long-range dependence. The Lévy-based modeling framework offers a promising tool to meet the requirements of modern data analysis. It enables the modeling of both short-range and long-range serial correlation structures by selecting the kernel set accordingly and accommodates various marginal distributions within the class of infinitely divisible laws. We propose an extension of the basic stationary framework to capture additional marginal properties, such as heavy-tailedness, in both short-term and long-term dependencies, as well as overdispersion and zero inflation in simultaneous modeling. Statistical inference is based on composite pairwise likelihood. The model’s flexibility is illustrated through applications to rainfall data in Guinea from 2008 to 2023, and the number of NSF funding awarded to academic institutions. The proposed model demonstrates remarkable flexibility and versatility, capable of simultaneously capturing overdispersion, zero inflation, and heavy-tailedness in count time series data.

Estimation of fixed effects partially linear varying coefficient spatial autoregressive model with disturbances correlated in space and time

In order to fully capture the substantive spatial effect, linear and varying coefficient effects of regressors, and space–time correlations of disturbances, this paper introduces a new fixed effects partially linear varying coefficient spatial autoregressive model (PLVCSARM) with disturbances correlated in space and time. Its profile quasi-maximum likelihood estimators (PQMLEs) are constructed. Under some mild conditions, the consistency and asymptotic normality of the PQMLEs are derived. Simulation results show that the proposed estimates perform well in finite sample cases.

Markov chain composite likelihood and its application in genetic recombination model

Phylogenetic Trees are critical in human genome research for investigating human evolution and identifying disease-associated genetic markers. New high-throughput genome sequencing technologies raise an urgent need to develop statistical methods that can construct phylogenetic trees from long genome sequences with quick computation speeds, while considering various biological complexities. Though an ancestral mixture model has been proposed [Chen SC, Lindsay BG. Building mixture trees from binary sequence data. Biometrika. 2006;93(4):843–860. doi: 10.1093/biomet/93.4.843] to this end by allowing genetic mutations over generations, another essential evolution factor, genetic recombination, is missed. Therefore, in this paper, we develop a novel genetic recombination model for tree construction and propose to use Markov chain composite likelihood (MCCL) to make model estimation computationally feasible. To further reduce computation complexity, a hierarchical estimator is constructed to estimate unknown ancestral distributions through MCCL. Simulation studies and real data example show that our proposed methods perform well and fast, so have the potential for implementation in long sequence genome data.

Propensity score-incorporated adaptive design approaches when incorporating real-world data.

The propensity score-integrated composite likelihood (PSCL) method is one method that can be utilized to design and analyze an application when real-world data (RWD) are leveraged to augment a prospectively designed clinical study. In the PSCL, strata are formed based on propensity scores (PS) such that similar subjects in terms of the baseline covariates from both the current study and RWD sources are placed in the same stratum, and then composite likelihood method is applied to down-weight the information from the RWD. While PSCL was originally proposed for a fixed design, it can be extended to be applied under an adaptive design framework with the purpose to either potentially claim an early success or to re-estimate the sample size. In this paper, a general strategy is proposed due to the feature of PSCL. For the possibility of claiming early success, Fisher's combination test is utilized. When the purpose is to re-estimate the sample size, the proposed procedure is based on the test proposed by Cui, Hung, and Wang. The implementation of these two procedures is demonstrated via an example.

Genetic diversity and positive signatures of selection in indigenous cattle breeds of Iran.

Animal domestication, climate changes over time, and artificial selection have played significant roles in shaping the genome structure of various animal species, including cattle. These processes have led to the emergence of several indigenous cattle breeds with distinct genetic characteristics. This study focused on unraveling the genetic diversity and identifying candidate genomic regions in eight indigenous cattle breeds of Iran. The data consisted of ∼777 962 single nucleotide polymorphisms (SNPs) of 89 animals from Iranian indigenous cattle scattered throughout the country. We employed various methods, including integrated haplotype score, FST, and cross-population composite likelihood ratio, to conduct a genome scan for detecting selection signals within and between cattle populations. Average observed heterozygosity across the populations was 0.36, with a range of 0.32-0.40. In addition, negative and low rates of inbreeding (FIS) in the populations were observed. The genome-wide analysis revealed several genomic regions that harbored candidate genes associated with production traits (e.g., MFSD1, TYW5, ADRB2, BLK, and CRTC3), adaptation to local environmental constraints (CACNA2D1, CXCL3, and GRO1), and coat color (DYM). Finally, the study of the reported quantitative trait loci (QTL) regions in the cattle genome demonstrated that the identified regions were associated with QTL related to important traits such as milk composition, body weight, daily gain, feed conversion, and residual feed intake. Overall, this study contributes to a better understanding of the genetic diversity and potential candidate genes underlying important traits in Iranian indigenous cattle breeds, which can inform future breeding and conservation efforts.

A composite semiparametric homogeneity test for the distributions of multigroup interval-bounded longitudinal data

ABSTRACT Motivated by comparing the distribution of longitudinal quality of life (QoL) data among different treatment groups from a cancer clinical trial, we propose a semiparametric test statistic for the homogeneity of the distributions of multigroup longitudinal measurements, which are bounded in a closed interval with excess observations taking the boundary values. Our procedure is based on a three-component mixed density ratio model and a composite empirical likelihood for the longitudinal data taking values inside the interval. A nonparametric bootstrap method is applied to calculate the p-value of the proposed test. Simulation studies are conducted to evaluate the proposed procedure, which show that the proposed test is effective in controlling type I errors and more powerful than the procedure which ignores the values on the boundaries. It is also robust to the model mispecification than the parametric test. The proposed procedure is also applied to compare the distributions of the scores of Physical Function subscale and Global Heath Status between the patients randomized to two treatment groups in a cancer clinical trial.

Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation

A highly scalable method for (non-)Gaussian random fields estimation is proposed. In particular, a novel (a) symmetric weight function based on nearest neighbors for the method of maximum weighted composite likelihood based on pairs (WCLP) is studied.The new weight function allows estimating massive (up to millions) spatial datasets and improves the statistical efficiency of the WCLP method using symmetric weights based on distances, as shown in the numerical examples.As an application of the proposed method, the estimation of a novel non-Gaussian random field named Tukey-hh random field that has flexible marginal distributions (possibly skewed and/or heavy-tailed) is considered. In an extensive simulation study the statistical efficiency of the proposed nearest neighbors WCLP method with respect to the WCLP method using weights based on distances is explored when estimating the parameters of the Tukey-hh random field. In the Gaussian case the proposed method is compared with the Vecchia approximation from computational and statistical viewpoints. Finally, the effectiveness of the proposed methodology is illustrated by estimating a large dataset of mean temperatures in South-America. The proposed methodology has been implemented in an open-source package for the R statistical environment.

Conditional-mean multiplicative operator models for count time series

Multiplicative error models (MEMs) are commonly used for real-valued time series, but they cannot be applied to discrete-valued count time series as the involved multiplication would not preserve the integer nature of the data. Thus, the concept of a multiplicative operator for counts is proposed (as well as several specific instances thereof), which are then used to develop a kind of MEMs for count time series (CMEMs). If equipped with a linear conditional mean, the resulting CMEMs are closely related to the class of so-called integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models and might be used as a semi-parametric extension thereof. Important stochastic properties of different types of INGARCH-CMEM as well as relevant estimation approaches are derived, namely types of quasi-maximum likelihood and weighted least squares estimation. The performance and application are demonstrated with simulations as well as with two real-world data examples.

Quantifying and correcting bias due to outcome dependent self-reported weights in longitudinal study of weight loss interventions

In response to the escalating global obesity crisis and its associated health and financial burdens, this paper presents a novel methodology for analyzing longitudinal weight loss data and assessing the effectiveness of financial incentives. Drawing from the Keep It Off trial—a three-arm randomized controlled study with 189 participants—we examined the potential impact of financial incentives on weight loss maintenance. Given that some participants choose not to weigh themselves because of small weight change or weight gains, which is a common phenomenon in many weight-loss studies, traditional methods, for example, the Generalized Estimating Equations (GEE) method tends to overestimate the effect size due to the assumption that data are missing completely at random. To address this challenge, we proposed a framework which can identify evidence of missing not at random and conduct bias correction using the estimating equation derived from pairwise composite likelihood. By analyzing the Keep It Off data, we found that the data in this trial are most likely characterized by non-random missingness. Notably, we also found that the enrollment time (i.e., duration time) would be positively associated with the weight loss maintenance after adjusting for the baseline participant characteristics (e.g., age, sex). Moreover, the lottery-based intervention was found to be more effective in weight loss maintenance compared with the direct payment intervention, though the difference was non-statistically significant. This framework's significance extends beyond weight loss research, offering a semi-parametric approach to assess missing data mechanisms and robustly explore associations between exposures (e.g., financial incentives) and key outcomes (e.g., weight loss maintenance). In essence, the proposed methodology provides a powerful toolkit for analyzing real-world longitudinal data, particularly in scenarios with data missing not at random, enriching comprehension of intricate dataset dynamics.

Whole Genome Resequencing Revealed the Genetic Relationship and Selected Regions among Baicheng-You, Beijing-You, and European-Origin Broilers.

As the only two You-chicken breeds in China, Baicheng-You (BCY) and Beijing-You (BJY) chickens are famous for their good meat quality. However, so far, the molecular basis of germplasm of the two You-chicken breeds is not yet clear. The genetic relationship among BCY, BJY, and European-origin broilers (BRs) was analyzed using whole genome resequencing data to contribute to this issue. A total of 18,852,372 single nucleotide polymorphisms (SNPs) were obtained in this study. After quality control, 8,207,242 SNPs were applied to subsequent analysis. The data indicated that BJY chickens possessed distant distance with BRs (genetic differentiation coefficient (FST) = 0.1681) and BCY (FST = 0.1231), respectively, while BCY and BRs had a closer relationship (FST = 0.0946). In addition, by using FST, cross-population extended haplotype homozygosity (XP-EHH), and cross-population composite likelihood ratio (XP-CLR) methods, we found 374 selected genes between BJY and BRs chickens and 279 selected genes between BCY and BJY chickens, respectively, which contained a number of important candidates or genetic variations associated with feather growth and fat deposition of BJY chickens and potential disease resistance of BCY chickens. Our study demonstrates a genome-wide view of genetic diversity and differentiation among BCY, BJY, and BRs. These results may provide useful information on a molecular basis related to the special characteristics of these broiler breeds, thus enabling us to better understand the formation mechanism of Chinese-You chickens.

Indexing and partitioning the spatial linear model for large data sets.

We consider four main goals when fitting spatial linear models: 1) estimating covariance parameters, 2) estimating fixed effects, 3) kriging (making point predictions), and 4) block-kriging (predicting the average value over a region). Each of these goals can present different challenges when analyzing large spatial data sets. Current research uses a variety of methods, including spatial basis functions (reduced rank), covariance tapering, etc, to achieve these goals. However, spatial indexing, which is very similar to composite likelihood, offers some advantages. We develop a simple framework for all four goals listed above by using indexing to create a block covariance structure and nearest-neighbor predictions while maintaining a coherent linear model. We show exact inference for fixed effects under this block covariance construction. Spatial indexing is very fast, and simulations are used to validate methods and compare to another popular method. We study various sample designs for indexing and our simulations showed that indexing leading to spatially compact partitions are best over a range of sample sizes, autocorrelation values, and generating processes. Partitions can be kept small, on the order of 50 samples per partition. We use nearest-neighbors for kriging and block kriging, finding that 50 nearest-neighbors is sufficient. In all cases, confidence intervals for fixed effects, and prediction intervals for (block) kriging, have appropriate coverage. Some advantages of spatial indexing are that it is available for any valid covariance matrix, can take advantage of parallel computing, and easily extends to non-Euclidean topologies, such as stream networks. We use stream networks to show how spatial indexing can achieve all four goals, listed above, for very large data sets, in a matter of minutes, rather than days, for an example data set.

On the frequency domain composite likelihood methods for estimating space-time covariance functions for large datasets

Covariance function plays very important roles in modeling and in prediction of spatial data. For instance, many statistical inferences such as maximum likelihood estimation and best linear unbiased prediction involve covariance matrices which must be inverted and this evaluation is slow when the number of observations is large, and the complexity increases even further in a space-time context. In this paper, we propose approximation methods based on three types of frequency domain composite likelihoods for the estimation of spatial-temporal covariance functions: paired, differenced, and conditional composite likelihoods to overcome this problem. The proposed likelihoods involve computationally efficient and matrix-free Gaussian likelihood approximations that have been successful in fitting parametric space-time covariance functions for massive datasets. We conduct a simulation study to evaluate the performance of the proposed estimation methods from statistical and computational viewpoints. The frequency domain spectral composite likelihood estimates demonstrate better performance compared to the observation domain composite likelihoods. Furthermore, our numerical examples show that paired and conditional frequency domain composite likelihoods work better than differenced frequency domain composite likelihood from statistical point of view.

Demographically explicit scans for barriers to gene flow using gIMble.

Identifying regions of the genome that act as barriers to gene flow between recently diverged taxa has remained challenging given the many evolutionary forces that generate variation in genetic diversity and divergence along the genome, and the stochastic nature of this variation. Progress has been impeded by a conceptual and methodological divide between analyses that infer the demographic history of speciation and genome scans aimed at identifying locally maladaptive alleles i.e. genomic barriers to gene flow. Here we implement genomewide IM blockwise likelihood estimation (gIMble), a composite likelihood approach for the quantification of barriers, that bridges this divide. This analytic framework captures background selection and selection against barriers in a model of isolation with migration (IM) as heterogeneity in effective population size (Ne) and effective migration rate (me), respectively. Variation in both effective demographic parameters is estimated in sliding windows via pre-computed likelihood grids. gIMble includes modules for pre-processing/filtering of genomic data and performing parametric bootstraps using coalescent simulations. To demonstrate the new approach, we analyse data from a well-studied pair of sister species of tropical butterflies with a known history of post-divergence gene flow: Heliconius melpomene and H. cydno. Our analyses uncover both large-effect barrier loci (including well-known wing-pattern genes) and a genome-wide signal of a polygenic barrier architecture.

A - 139 Neurobehavioral Symptoms Are Not Associated with Objective Neuropsychological Test Performance in a Group of Veterans and First Responders Seeking Care for Post-Concussive Symptoms.

Subjective post-concussive neurobehavioral symptoms do not often relate to objective cognitive assessment. This archival analysis aimed to characterize the relationship of subjective neurobehavioral symptoms to neuropsychological tests among military veterans and retired first responders with previous mild TBI (mTBI) presenting to an outpatient multidisciplinary program. 51 patients (88% male; 82% White; 94% veteran), ages 25-68 (M = 43.9, SD = 10.1) underwent neuropsychological evaluation with a flexible battery (M subtests = 29.6; SD = 5.2), through the Transforming Health and Resilience in Veterans (THRIVE) Program at UNC-Chapel Hill. The proportion of below average neuropsychological scores (i.e., ≤ 8th percentile on published norms) was modeled as a function of three subscales (Affective, Cognitive, Somatosensory) on the Neurobehavioral Symptom Inventory (NSI) and estimated premorbid IQ (PIQ) using fractional logit regression with quasi-maximum likelihood estimation and heteroskedasticity consistent "HC1" standard errors. Model diagnostics and sensitivity analyses for overly influential cases (|DFBETAS| ≥ 2/√n) were conducted. Thirty-eight individuals were included in analyses after removing those with invalid test performance (n = 4) and missing data (n = 9). The mean (median) observed below average scores was 10.9% (5.7%), with the predicted proportion at 8%. No NSI subscale was related to neuropsychological performance. However, upon removal of two overly influential cases, PIQ was inversely associated with rate of low scores - OR: 0.61 (95% CI: 0.36-0.97), SE: 0.14, p = 0.035. Subjective neurobehavioral symptoms were unrelated to objective neuropsychological tests in veterans and first responders seeking care for TBI-related symptoms.

Detection of genomic variations and selection signatures in Wagyu using whole-genome sequencing data.

Wagyu is recognized for producing marbled beef with high nutritional value and flavor. Reportedly, Wagyu has been widely used to improve the meat quality of local breeds around the world. However, studies on the genetic mechanism of meat quality in Wagyu at the whole-genome level are rarely reported. Here, whole-genome sequencing data of 11 Wagyu and 115 other individuals were used to explore the genomic variations and genes under selection pressure in Wagyu. A total of 31 349 non-synonymous variants and 53 102 synonymous variants were identified in Wagyu. The population structure analysis showed that Wagyu had the closest genetic relationship with Mishima-Ushi cattle and was apparently separated from other cattle breeds. Then, composite likelihood ratio (CLR), integrated haplotype score, fixation index and cross-population composite likelihood ratio (XP-CLR) tests were performed to identify the candidate genes under positive selection in Wagyu. In total, 770 regions containing 312 genes were identified by at least three methods. Among them, 97 regions containing 27 genes were detected by all four methods. We specifically illustrate a list of interesting genes, including LRP2BP, GAA, CACNG6, CXADR, GPCPD1, KLF2, KLF13, SOX5, MYBPC1, SLC25A10, ATP8A1 and MYH15, which are associated with lipid metabolism, fat deposition, muscle development, bone development, feed intake and growth traits in Wagyu. This is the first study to explore the genomic variations and selection signatures of Wagyu at the whole-genome level. These results will provide significant help to beef cattle improvement and breeding.

Comprehensive evaluation of germplasm resources of nine Macrobrachium rosenbergii strains in China

Macrobrachium rosenbergii, as an introduced species, is extensively cultured in China. In this study, 176 individuals from nine domestic strains in China, i.e., Florida (FD), Guangxi (GX), Hefu (HF), Myanmar (MD), “Nantaihu No. 2″ (NT), Thailand (TG), Taiwan (TW), “Shufeng No. 1″ (SF), and Zhengda (ZD), were collectedfor genome resequencing. We evaluated the genetic diversity, population structure and population history of nine cultured strains using SNP markers. We found that genetic diversity of the M. rosenbergii strains was at a low level, among which FD and TG strains showed relatively higher genetic diversity, inferring that the genetic diversity of domestic populations decreased after artificial selection. Population genetic structure analysis showed that the individuals GX, HF, SF and NT strains were irregularly clustered together, and the ZD and TW strains exhibited the specific ancestors compared with other strains. The phylogenetic tree revealed that the individuals from TW, MD, ZD strains grouped into population-specific clusters. The principal components analysis (PCA) also showed that the nine strains were mixed together except the individuals from ZD and TW strains which were separated into specific subgroups. The Fst analysis showed that the Fst values detected from nine strains were less than 0.05, with the lowest Fst observed between SF and NT strains. In addition, two positively selected genes involved in metal transport and stress response were identified in the nine domestic strains by using selective sweep analyses with composite likelihood ratio (CLR), Fst, Pi, and Tajima’ D methods. The TreeMix phylogeny inferred four gene flow events among the nine strains, which occurred in the following directions: (1) from the common ancestor of ZD and TG to SF, (2) from SF to MD, (3) from SF to NT, and (4) from HF to GX. This study contributes to the better understanding genetic background and germplasm status of domestic M. rosenbergii strains in China.

Nonlinear effects of socio-economic factors on urban haze in China: Evidence from spatial econometric smooth transition autoregressive regression approach

In recent years, China has achieved numerous economic miracles but it has also been plagued by severe air pollution. The frequent hazy weather has severely restricted China's sustainable development. To investigate the nonlinear threshold effect of socio-economic factors on urban haze in China, this study constructs a spatial econometric Smooth Transition Autoregressive Regression (STAR) model based on the STIRPAT theory by using the remote sensing inversion PM2.5 data of 223 prefecture-level and above cities in China mainland during 2004–2016. In this study, the ARAR-STAR model is estimated by quasi-maximum likelihood estimation, and the accuracy of parameter estimation is verified by Monte Carlo simulation, which proves that the ARAR-STAR model constructed in this study is robust. It is concluded that: there is a complex spatial nonlinear relationship between socio-economic factors such as economic development level, population density, advanced industrial structure, energy consumption, opening-up, and haze pollution. The effect of socio-economic factors on haze emission reduction under the spatial influence has complex heterogeneity with the smooth transition between high and low regimes with economic development. The ARAR-STAR model constructed in this paper, which has both individual fixed effects and time fixed effects, expands the form of existing spatial panel nonlinear models and enriches and implements the application of spatial panel smooth transfer threshold models in the environmental field. Not only can it provide policy recommendations for China to achieve "coordinated efficiency in pollution reduction and carbon reduction" as soon as possible, but it also contributes to China's plan to address global climate change and promote global sustainable development.

A composite Bayesian approach for quantile curve fitting with non-crossing constraints

To fit a set of quantile curves, Bayesian simultaneous quantile curve fitting methods face some challenges in properly specifying a feasible formulation and efficiently accommodating the non-crossing constraints. In this article, we propose a new minimization problem and develop its corresponding Bayesian analysis. The new minimization problem imposes two penalties to control not only the smoothness of fitted quantile curves but also the differences between quantile curves. This enables a direct inference on differences of quantile curves and facilitates improved information sharing among quantiles. After adopting B-spline approximation for the positive smoothing functions in the minimization problem, we specify the pseudo composite asymmetric Laplace likelihood and derive its priors. The computation algorithm, including partially collapsed Gibbs sampling for model parameters and Monte Carlo Expectation-Maximization algorithm for penalty parameters, are provided to carry out the proposed approach. The extensive simulation studies show that, compared with other candidate methods, the proposed approach yields more robust estimation. More advantages of the proposed approach are observed for the extreme quantiles, heavy-tailed random errors, and inference on the differences of quantiles. We also demonstrate the relative performances of the proposed approach and other competing methods through two real data analyses.

Genomic inference of a severe human bottleneck during the Early to Middle Pleistocene transition.

Population size history is essential for studying human evolution. However, ancient population size history during the Pleistocene is notoriously difficult to unravel. In this study, we developed a fast infinitesimal time coalescent process (FitCoal) to circumvent this difficulty and calculated the composite likelihood for present-day human genomic sequences of 3154 individuals. Results showed that human ancestors went through a severe population bottleneck with about 1280 breeding individuals between around 930,000 and 813,000 years ago. The bottleneck lasted for about 117,000 years and brought human ancestors close to extinction. This bottleneck is congruent with a substantial chronological gap in the available African and Eurasian fossil record. Our results provide new insights into our ancestry and suggest a coincident speciation event.

Analysis of secondary failure time responses in studies with response-dependent sampling schemes.

Response-dependent sampling is routinely used as an enrichment strategy in the design of family studies investigating the heritable nature of disease. In addition to the response of primary interest, investigators often wish to investigate the association between biomarkers and secondary responses related to possible comorbidities. Statistical analysis regarding genetic biomarkers and their association with the secondary outcome must address the biased sampling scheme involving the primary response. In this article, we develop composite likelihoods and two-stage estimation procedures for such secondary analyses in which the within-family dependence structure for the primary and secondary outcomes is modeled via a Gaussian copula. The dependence among responses within family members is modeled based on kinship coefficients. Auxiliary data from independent individuals are exploited by augmenting the composite likelihoods to increase precision of marginal parameter estimates and enhance the efficiency of estimators of the dependence parameters. Simulation studies are carried out to evaluate the finite sample performance of the proposed method, and an application to a motivating family study in psoriatic arthritis is given for illustration.