Pseudo-likelihood Method Research Articles

Fitting three-dimensional Laguerre tessellations by hierarchical marked point process models

We present a general statistical methodology for analysing a Laguerre tessellation data set viewed as a realization of a marked point process model. In the first step, for the points, we use a nested sequence of multiscale processes which constitute a flexible parametric class of pairwise interaction point process models. In the second step, for the marks/radii conditioned on the points, we consider various exponential family models where the canonical sufficient statistic is based on tessellation characteristics. For each step, parameter estimation based on maximum pseudolikelihood methods is tractable. For model selection, we consider maximized log pseudolikelihood functions for models of the radii conditioned on the points. Model checking is performed using global envelopes and corresponding tests in both steps and moreover by comparing observed and simulated tessellation characteristics in the second step. We apply our methodology for a 3D Laguerre tessellation data set representing the microstructure of a polycrystalline metallic material, where simulations under a fitted model may substitute expensive laboratory experiments.

A Small Area Estimation Method for Investigating the Relationship between Public Perception of Drug Problems with Neighborhood Prognostics: Trends in London between 2012 and 2019.

The correlation of the public’s perception of drug problems with neighborhood characteristics has rarely been studied. The aim of this study was to investigate factors that correlate with public perceptions in London boroughs using the Mayor’s Office for Policing and Crime (MOPAC) Public Attitude Survey between 2012 and 2019. A subject-specific random effect deploying a Generalized Linear Mixed Model (GLMM) using an Adaptive Gaussian Quadrature method with 10 integration points was applied. To obtain time trends across inner and outer London areas, the GLMM was fitted using a Restricted Marginal Pseudo Likelihood method. The perception of drug problems increased with statistical significance in 17 out of 32 London boroughs between 2012 and 2019. These boroughs were geographically clustered across the north of London. Levels of deprivation, as measured by the English Index of Multiple Deprivation, as well as the percentage of local population who were non-UK-born and recorded vehicle crime rates were shown to be positively associated with the public’s perception of drug problems. Conversely, recorded burglary rate was negatively associated with the public’s perception of drug problems in their area. The public are influenced in their perception of drug problems by neighborhood factors including deprivation and visible manifestations of antisocial behavior.

Pseudo-likelihood Methods for the Analysis of Longitudinal Binary Data Subject to Nonignorable Non-monotone Missingness

For longitudinal binary data with non-monotone non-ignorable missing outcomes over time, a full likelihood approach is complicated alge braically, and maximum likelihood estimation can be computationally pro hibitive with many times of follow-up. We propose pseudo-likelihoods to estimate the covariate effects on the marginal probabilities of the outcomes, in addition to the association parameters and missingness parameters. The pseudo-likelihood requires specification of the distribution for the data at all pairs of times on the same subject, but makes no assumptions about the joint distribution of the data at three or more times on the same sub ject, so the method can be considered semi-parametric. If using maximum likelihood, the full likelihood must be correctly specified in order to obtain consistent estimates. We show in simulations that our proposed pseudo likelihood produces a more efficient estimate of the regression parameters than the pseudo-likelihood for non-ignorable missingness proposed by Troxel et al. (1998). Application to data from the Six Cities study (Ware, et.al, 1984), a longitudinal study of the health effects of air pollution, is discussed.

Design and analysis of a 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria: Small sample considerations for cluster-randomized trials with count data.

Cluster-randomized trials allow for the evaluation of a community-level or group-/cluster-level intervention. For studies that require a cluster-randomized trial design to evaluate cluster-level interventions aimed at controlling vector-borne diseases, it may be difficult to assess a large number of clusters while performing the additional work needed to monitor participants, vectors, and environmental factors associated with the disease. One such example of a cluster-randomized trial with few clusters was the "efficacy and risk of harms of repeated ivermectin mass drug administrations for control of malaria" trial. Although previous work has provided recommendations for analyzing trials like repeated ivermectin mass drug administrations for control of malaria, additional evaluation of the multiple approaches for analysis is needed for study designs with count outcomes. Using a simulation study, we applied three analysis frameworks to three cluster-randomized trial designs (single-year, 2-year parallel, and 2-year crossover) in the context of a 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria. Mixed-effects models, generalized estimating equations, and cluster-level analyses were evaluated. Additional 2-year parallel designs with different numbers of clusters and different cluster correlations were also explored. Mixed-effects models with a small sample correction and unweighted cluster-level summaries yielded both high power and control of the Type I error rate. Generalized estimating equation approaches that utilized small sample corrections controlled the Type I error rate but did not confer greater power when compared to a mixed model approach with small sample correction. The crossover design generally yielded higher power relative to the parallel equivalent. Differences in power between analysis methods became less pronounced as the number of clusters increased. The strength of within-cluster correlation impacted the relative differences in power. Regardless of study design, cluster-level analyses as well as individual-level analyses like mixed-effects models or generalized estimating equations with small sample size corrections can both provide reliable results in small cluster settings. For 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria, we recommend a mixed-effects model with a pseudo-likelihood approximation method and Kenward-Roger correction. Similarly designed studies with small sample sizes and count outcomes should consider adjustments for small sample sizes when using a mixed-effects model or generalized estimating equation for analysis. Although the 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria is already underway as a parallel trial, applying the simulation parameters to a crossover design yielded improved power, suggesting that crossover designs may be valuable in settings where the number of available clusters is limited. Finally, the sensitivity of the analysis approach to the strength of within-cluster correlation should be carefully considered when selecting the primary analysis for a cluster-randomized trial.

Do Institutional Characteristics of Microfinance Institutions Matter for External Sources of Funds? Evidence from Bangladesh

This study mainly aims to examine whether the institutional characteristics matter for external sources of funds of microfinance institutions (MFIs) in Bangladesh considering unbalanced panel data of 258 MFIs for the period of 2009-2014. The study considers four institutional characteristics of MFIs, namely, the number of branches, profitability measured by return on assets, location, and age of MFIs as well as several macroeconomic variables such as interest rate cap, economic growth, and inflation. The external sources of funds are decomposed into five sub-panels, that is, government funds, loans from commercial banks, loans from Palli Karma Sahayak Foundation, donors' funds, and loans from other MFIs in order to draw more conclusive evidence. It also helps provide a comparative analysis on the effects of each institutional characteristic of MFIs on different types of external sources of funds. The study employs the Poisson pseudo maximum likelihood method which is supposed to be more appropriate in the present case for avoiding the problem associated with zero value of dependent variable. The estimation results suggest that institutional characteristics of the MFIs contribute considerably in supporting the growth and development of the industry by drawing funds from external financial sources albeit some indicators of institutional characteristics refer to adverse impact on a few external sources of funds. In the case of macroeconomic factors, market intervention through the interest rate cap limits the operation of microfinance institutions making funds scarce for them. Additionally, the comparative analysis of alternative funding both from the debt and equity sources will help policymakers and managers to adopt an appropriate policy to attain the cost-effectiveness of MFIs of Bangladesh which is one of the important policy implications of the study.

Structure learning in inverse Ising problems using ℓ 2-regularized linear estimator

The inference performance of the pseudolikelihood method is discussed in the framework of the inverse Ising problem when the ℓ 2-regularized (ridge) linear regression is adopted. This setup is introduced for theoretically investigating the situation where the data generation model is different from the inference one, namely the model mismatch situation. In the teacher-student scenario under the assumption that the teacher couplings are sparse, the analysis is conducted using the replica and cavity methods, with a special focus on whether the presence/absence of teacher couplings is correctly inferred or not. The result indicates that despite the model mismatch, one can perfectly identify the network structure using naive linear regression without regularization when the number of spins N is smaller than the dataset size M, in the thermodynamic limit N → ∞. Further, to access the underdetermined region M < N, we examine the effect of the ℓ 2 regularization, and find that biases appear in all the coupling estimates, preventing the perfect identification of the network structure. We, however, find that the biases are shown to decay exponentially fast as the distance from the center spin chosen in the pseudolikelihood method grows. Based on this finding, we propose a two-stage estimator: in the first stage, the ridge regression is used and the estimates are pruned by a relatively small threshold; in the second stage the naive linear regression is conducted only on the remaining couplings, and the resultant estimates are again pruned by another relatively large threshold. This estimator with the appropriate regularization coefficient and thresholds is shown to achieve the perfect identification of the network structure even in 0 < M/N < 1. Results of extensive numerical experiments support these findings.

Full-Scale Distribution System Topology Identification Using Markov Random Field

The identification of the distribution system topology is the key concern in distribution system state estimation and the precondition for its energy management. However, lacking sufficient measurement devices, full-scale identification of entire distribution grid can hardly be achievable in practice. The frequent topology changes in distribution systems impose challenges for topology identification. This paper proposes a novel topology identification method by deeply mining the data obtained from gird terminals and smart meters at end-users premises. The proposed method starts with data processing, followed by nodal correlation analysis and topology modeling based on the Markov Random Field (MRF) method, where the pseudo-likelihood method and L2 regularization theory are introduced to improve the computation efficiency while preventing the over-fitting problem. Then the iterative screening method is developed to generate the distribution system topology of medium/low-voltage distribution systems. Finally, the incremental learning and parallel programming models are proposed to implement the algorithms on single/multi-terminal. The effectiveness of the proposed model is validated on IEEE 33-node, IEEE 123-node and actual distribution systems.

Modified Maximum Pseudo Likelihood Method of Copula Parameter Estimation for Skewed Hydrometeorological Data

For multivariate frequency analysis of hydrometeorological data, the copula model is commonly used to construct joint probability distribution due to its flexibility and simplicity. The Maximum Pseudo-Likelihood (MPL) method is one of the most widely used methods for fitting a copula model. The MPL method was derived from the Weibull plotting position formula assuming a uniform distribution. Because extreme hydrometeorological data are often positively skewed, capacity of the MPL method may not be fully utilized. This study proposes the modified MPL (MMPL) method to improve the MPL method by taking into consideration the skewness of the data. In the MMPL method, the Weibull plotting position formula in the original MPL method is replaced with the formulas which can consider the skewness of the data. The Monte-Carlo simulation has been performed under various conditions in order to assess the performance of the proposed method with the Gumbel copula model. The proposed MMPL method provides more precise parameter estimates than does the MPL method for positively skewed hydrometeorological data based on the simulation results. The MMPL method would be a better alternative for fitting the copula model to the skewed data sets. Additionally, applications of the MMPL methods were performed on the two weather stations (Seosan and Yeongwol) in South Korea.

Proportional Mean Residual Life Model with Varying Coefficients for Length-Biased and Right-Censored Data

Length-biased data are encountered in many fields, including economics, engineering and epidemiological cohort studies. There are two main challenges in the analysis of such data: the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed data. In this paper, a proportional mean residual life varying-coefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the model. Asymptotic properties are investigated for the proposed estimators. The finite sample performance of the proposed methodology is demonstrated by simulation studies. Finally, the method is applied to a real data set concerning the Academy Awards.

An errors-in-variables model based on the Birnbaum–Saunders distribution and its diagnostics with an application to earthquake data

Regression modelling where explanatory variables are measured with error is a common problem in applied sciences. However, if inappropriate analysis methods are applied, then unreliable conclusions can be made. This work deals with estimation and diagnostic analytics in regression modelling based on the Birnbaum–Saunders distribution using additive measurement errors. The maximum pseudo-likelihood and regression calibration methods are used for parameter estimation. We also carry out a residual analysis and apply global and local diagnostic techniques in order to detect anomalous and potentially influential observations. Simulations are conducted to validate the proposed approach and to evaluate performance. A real-world data set, related to earthquakes, is used to illustrate the new approach.

Foreign Direct Investment and International Trade: Empirical Analysis of Mutual Influence

Foreign direct investment and international movement of commodities are interrelated in the world economy. At the same time, the nature of this relationship and the causality issues are ambiguous and need to be studied from both theoretical and empirical sides. The aim of this paper is to estimate empirically the mutual influence of foreign direct investment and international trade in the modern economy. The econometric model is based on the gravity approach, the estimation is made using the Poisson pseudo maximum likelihood method on the data for 67 host and 109 home FDI countries for the period of 2001–2016. The hypotheses on the positive mutual influence of foreign direct investment and international trade are tested. A positive and significant influence of export and import flows on inward foreign direct investment is observed. The largest impact of export and import on foreign direct investment is observed when a two-year lag is considered. We could not reveal a significant influence of foreign direct investment on export and import flows either within one year, or for the lagged FDI values. The authors argue that pro-trade government policy, aimed at the integration of the country into global value chains is an important factor stimulating the inflow of foreign direct investment to the country. From the practical point of view, understanding the causal linkages between export, import and foreign direct investment helps state authorities better forecast the direct and indirect effects of various trade policy incentives.

Novel two-phase sampling designs for studying binary outcomes.

In biomedical cohort studies for assessing the association between an outcome variable and a set of covariates, usually, some covariates can only be measured on a subgroup of study subjects. An important design question is-which subjects to select into the subgroup to increase statistical efficiency. When the outcome is binary, one may adopt a case-control sampling design or a balanced case-control design where cases and controls are further matched on a small number of complete discrete covariates. While the latter achieves success in estimating odds ratio (OR) parameters for the matching covariates, similar two-phase design options have not been explored for the remaining covariates, especially the incompletely collected ones. This is of great importance in studies where the covariates of interest cannot be completely collected. To this end, assuming that an external model is available to relate the outcome and complete covariates, we propose a novel sampling scheme that oversamples cases and controls with worse goodness-of-fit based on the external model and further matches them on complete covariates similarly to the balanced design. We develop a pseudolikelihood method for estimating OR parameters. Through simulation studies and explorations in a real-cohort study, we find that our design generally leads to reduced asymptotic variances of the OR estimates and the reduction for the matching covariates is comparable to that of the balanced design.

High-dimensional structure learning of binary pairwise Markov networks: A comparative numerical study

Learning the undirected graph structure of a Markov network from data is a problem that has received a lot of attention during the last few decades. As a result of the general applicability of the model class, a myriad of methods have been developed in parallel in several research fields. Recently, as the size of the considered systems has increased, the focus of new methods has been shifted towards the high-dimensional domain. In particular, introduction of the pseudo-likelihood function has pushed the limits of score-based methods which were originally based on the likelihood function. At the same time, methods based on simple pairwise tests have been developed to meet the challenges arising from increasingly large data sets in computational biology. Apart from being applicable to high-dimensional problems, methods based on the pseudo-likelihood and pairwise tests are fundamentally very different. To compare the accuracy of the different types of methods, an extensive numerical study is performed on data generated by binary pairwise Markov networks. A parallelizable Gibbs sampler, based on restricted Boltzmann machines, is proposed as a tool to efficiently sample from sparse high-dimensional networks. The results of the study show that pairwise methods can be more accurate than pseudo-likelihood methods in settings often encountered in high-dimensional structure learning applications.

Doubly robust pseudo-likelihood for incomplete hierarchical binary data

Missing data is almost inevitable in correlated-data studies. For non-Gaussian outcomes with moderate to large sequences, direct-likelihood methods can involve complex, hard-to-manipulate likelihoods. Popular alternative approaches, like generalized estimating equations, that are frequently used to circumvent the computational complexity of full likelihood, are less suitable when scientific interest, at least in part, is placed on the association structure; pseudo-likelihood (PL) methods are then a viable alternative. When the missing data are missing at random, Molenberghs et al. (2011, Statistica Sinica, 21,187–206) proposed a suite of corrections to the standard form of PL, taking the form of singly and doubly robust estimators. They provided the basis and exemplified it in insightful yet primarily illustrative examples. We here consider the important case of marginal models for hierarchical binary data, provide an effective implementation and illustrate it using data from an analgesic trial. Our doubly robust estimator is more convenient than the classical doubly robust estimators. The ideas are illustrated using a marginal model for a binary response, more specifically a Bahadur model.

Resistance to Phytophthora cinnamomi in Castanea spp. is under moderately high genetic control mainly because of additive genetic variance

Susceptibility to Phytophthora cinnamomi is one of the main traits in Castanea sativa breeding programs. An inoculation experiment using 25 control pollinated families, with seedlings of these families cloned by cuttings, was conducted by soil infestation with one P. cinnamomi isolate. Forty-seven days after inoculation, foliar and root collar symptoms and root necrosis were recorded. The data were analyzed using a model based on restricted maximum pseudolikelihood methods of the GLIMMIX procedure to estimate the additive, dominance and epistatic components of the genetic variance, as well as the narrow sense heritability and the breeding values. At the end of the experiment, the percentages of dead plants ranged from 4% to 56% in C. sativa, and 18% to 20% in backcrosses to C. sativa, with much lower percentages in the F1 hybrids (C. crenata × C. sativa). Foliar symptoms were proportional to mortality, affecting 28% of the plants, but root collar lesions and root necrosis were more prevalent, affecting 65% and 84% of the plants, respectively. The proportions of genetic to phenotypic variance, 0.50–0.63, and the estimated values of narrow-sense heritability, 0.30–0.46, indicate that resistance to P. cinnamomi is under moderate to moderately high genetic control caused mainly by additive genetic variance. A high number of backcrosses to C. sativa showed good breeding values for resistance to P. cinnamomi.

Parameter inference in a probabilistic model using clustered data

We propose a method to infer the parameters of a probabilistic model from given data samples. Our method is based on the pseudolikelihood and composite likelihood methods. We cluster the given data samples and apply the clustered data samples to the pseudolikelihood and composite likelihood methods. From an expansion of the pseudolikelihood method around the mean of a cluster, the mean-field and Thouless–Anderson–Palmer equations are derived. Likewise, from an expansion of the composite likelihood method around the mean of a cluster, a method that is similar to the Bethe approximation is derived. We then perform numerical simulations using our method. We find that our method gives an accurate estimate in the range of weak coupling parameters but has an inferior accuracy compared to the pseudolikelihood and composite likelihood methods in the range of strong coupling parameters. In the range of strong coupling parameters, as the number of clusters increases, the inference accuracy of our method improves. Compared to the pseudolikelihood and composite likelihood methods, our method reduces the number of computational tasks for the estimation, therefore, sacrificing the inference accuracy.

Semiparametric inference for estimating equations with nonignorably missing covariates

ABSTRACTWe consider statistical inference of unknown parameters in estimating equations (EEs) when some covariates have nonignorably missing values, which is quite common in practice but has rarely been discussed in the literature. When an instrument, a fully observed covariate vector that helps identifying parameters under nonignorable missingness, is available, the conditional distribution of the missing covariates given other covariates can be estimated by the pseudolikelihood method of Zhao and Shao [(2015), ‘Semiparametric pseudo likelihoods in generalised linear models with nonignorable missing data’, Journal of the American Statistical Association, 110, 1577–1590)] and be used to construct unbiased EEs. These modified EEs then constitute a basis for valid inference by empirical likelihood. Our method is applicable to a wide range of EEs used in practice. It is semiparametric since no parametric model for the propensity of missing covariate data is assumed. Asymptotic properties of the proposed estimator and the empirical likelihood ratio test statistic are derived. Some simulation results and a real data analysis are presented for illustration.

Bayesian Inference for Gaussian Graphical Models Beyond Decomposable Graphs

SummaryBayesian inference for graphical models has received much attention in the literature in recent years. It is well known that, when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general non-decomposable setting. Penalized likelihood inference in contrast has made tremendous gains in the past few years in terms of scalability and tractability. Bayesian inference, however, has not had the same level of success, though a scalable Bayesian approach has its strengths, especially in terms of quantifying uncertainty. To address this gap, we propose a scalable and flexible novel Bayesian approach for estimation and model selection in Gaussian undirected graphical models. We first develop a class of generalized G-Wishart distributions with multiple shape parameters for an arbitrary underlying graph. This class contains the G-Wishart distribution as a special case. We then introduce the class of generalized Bartlett graphs and derive an efficient Gibbs sampling algorithm to obtain posterior draws from generalized G-Wishart distributions corresponding to a generalized Bartlett graph. The class of generalized Bartlett graphs contains the class of decomposable graphs as a special case but is substantially larger than the class of decomposable graphs. We proceed to derive theoretical properties of the proposed Gibbs sampler. We then demonstrate that the proposed Gibbs sampler is scalable to significantly higher dimensional problems compared with using an accept–reject or a Metropolis–Hasting algorithm. Finally, we show the efficacy of the proposed approach on simulated and real data. In particular, we demonstrate that our generalized Bartlett methodology can be used for efficient model selection by reducing the graph search space by using penalized likelihood and pseudolikelihood methods.

A nonparametric time-varying coefficient model for panel count data

ABSTRACTIn this research, we describe a nonparametric time-varying coefficient model for the analysis of panel count data. We extend the traditional panel count data models by incorporating B-splines estimates of time-varying coefficients. We show that the proposed model can be implemented using a nonparametric maximum pseudo-likelihood method. We further examine the theoretical properties of the estimators of model parameters. The operational characteristics of the proposed method are evaluated through a simulation study. For illustration, we analyse data from a study of childhood wheezing, and describe the time-varying effect of an inflammatory marker on the risk of wheezing.

The Effect of Corruption on International Trade: A Case Study of Indonesian Trade to Nine Countries

Corruption is a form of abuse of ethical authority by public officials, which is divided into two parts: bribery and forced collection. The effect of corruption like bribes and illegal levies is widespread in the public sector. One interesting investigation is the effect of corruption on international trade. Corruption becomes a barrier in international trade, where corruption plays a role in the access of trade goods and services from within and abroad. Using the gravity model, the focus of this research was the effect of corruption on international trade by taking a case study of Indonesia’s bilateral trade with its nine largest export destination countries. Using panel data, analysis tools used in this research were common effect, fixed effect, random effect and poisson pseudo maximum likelihood (PPML). In this research, it was found that geographical distance variable in its fixed units caused the omitted variable so that the error term correlated with independent variables. In order to overcome the problem, poisson pseudo maximum likelihood method was used in performing regression gravity model with linear log form, so the omitted variable issue on the geographical distance can be eliminated. The results of this research concluded that corruption played a role in international trade through bureaucratic mechanisms of trade and investment licensing and the effect of corruption was more detrimental to exporters.Keywords: Gravity Model, Corruption, International Trade, Poisson Pseudo Maximum Likelihood (PPML).