Pseudo-likelihood Research Articles

Methods for combining probability and nonprobability samples under unknown overlaps

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective sample size. Estimation of a population quantity derived from a convenience sample will typically result in bias since the distribution of variables of interest in the convenience sample is different from the population distribution. A recent set of approaches estimates inclusion probabilities for convenience sample units by specifying reference sample-weighted pseudo likelihoods. This paper introduces a novel approach that derives the propensity score for the observed sample as a function of inclusion probabilities for the reference and convenience samples as our main result. Our approach allows specification of a likelihood directly for the observed sample as opposed to the approximate or pseudo likelihood. We construct a Bayesian hierarchical formulation that simultaneously estimates sample propensity scores and the convenience sample inclusion probabilities. We use a Monte Carlo simulation study to compare our likelihood based results with the pseudo likelihood based approaches considered in the literature.

Evaluating the Efficiency of Restricted Pseudo Likelihood Estimation in Balanced and Unbalanced Clustered Binary Data Models

Clustered binary data analysis is a common task in various fields, such as social sciences and epidemiology. Restricted Pseudo Likelihood Estimation (PLE) is a widely used approach for analyzing clustered binary data, providing flexibility in handling complex dependencies within clusters. This study aims to evaluate the efficiency of Restricted Pseudo Likelihood Estimation in balanced and unbalanced clustered binary data models. Using simulated data, we compare the performance of PLE in balanced and unbalanced clustered binary data scenarios. We consider various factors such as the number of clusters, cluster sizes, and intra-cluster correlation. The preferred class of models for clustered binary data is the Hierarchical Generalized Linear Model (HGLM). This article compares the performance of a restricted pseudo-likelihood estimation method of the Hierarchical Generalized Linear Model (HGLM) with equal and unequal cluster sizes. Through comprehensive simulation experiments, we assess the accuracy and precision of PLE estimates in terms of parameter estimation, standard errors, and hypothesis testing. Our findings provide insights into the efficiency of Restricted Pseudo Likelihood Estimation (RPLE) in balanced and unbalanced clustered binary data models. The results highlight the advantages and limitations of PLE in different scenarios, aiding researchers in selecting appropriate modeling approaches for their specific data characteristics. The results can guide researchers in making informed decisions regarding the selection and application of PLE in their own studies, ultimately enhancing the validity and reliability of statistical analyses in the presence of clustered binary data.

Nested Pseudo likelihood estimation of continuous-time dynamic discrete games

We introduce a sequential estimator for continuous time dynamic discrete choice models (single-agent models and games) by adapting the nested pseudo likelihood (NPL) estimator of Aguirregabiria and Mira (2002, 2007), developed for discrete time models with discrete time data, to the continuous time case with data sampled either discretely (i.e., uniformly-spaced snapshot data) or continuously. We establish conditions for consistency and asymptotic normality of the estimator, a local convergence condition, and, for single agent models, a zero Jacobian property assuring local convergence. We carry out a series of Monte Carlo experiments using an entry-exit game with five heterogeneous firms to confirm the large-sample properties and demonstrate finite-sample bias reduction via iteration. In our simulations we show that the convergence issues documented for the NPL estimator in discrete time models are less likely to affect comparable continuous-time models. We also show that there can be large bias in economically-relevant parameters, such as the competitive effect and entry cost, from estimating a misspecified discrete time model when in fact the data generating process is a continuous time model.

Binary choice with misclassification and social interactions, with an application to peer effects in attitude

The interaction of economic agents is one of the most important elements in economic analyses. Social interactions on subjective outcomes, behavior, or decisions, are inherently difficult to identify and estimate because these variables are prone to misclassification errors. This paper puts forth a binary choice model with misclassification and social interactions to rectify the misclassification problems in social interactions studies. We achieve the identification of the conditional choice probability of the latent dependent variable by the technique of repeated measurements and a monotonicity condition. We construct the complete likelihood function from the two repeated measurements and propose a nested pseudo likelihood algorithm for estimation. Consistency and asymptotic normality results are shown for the proposed estimation method. We illustrate the finite sample performance of the model and the estimation method by three Monte Carlo experiments and an application to the study of peer effects among students in their attitudes towards learning.

Testing Data Cloning as the Basis of an Estimator for the Stochastic Volatility in Mean Model

Developed as a refinement of stochastic volatility (SV) models, the stochastic volatility in mean (SVM) model incorporates the latent volatility as an explanatory variable in both the mean and variance equations. It, therefore, provides a way of assessing the relationship between returns and volatility, albeit at the expense of complicating the estimation process. This study introduces a Bayesian methodology that leverages data-cloning algorithms to obtain maximum likelihood estimates for SV and SVM model parameters. Adopting this Bayesian framework allows approximate maximum likelihood estimates to be attained without the need to maximize pseudo likelihood functions. The key contribution this paper makes is that it proposes an estimator for the SVM model, one that uses Bayesian algorithms to approximate the maximum likelihood estimate with great effect. Notably, the estimates it provides yield superior outcomes than those derived from the Markov chain Monte Carlo (MCMC) method in terms of standard errors, all while being unaffected by the selection of prior distributions.

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.

Semiparametric pseudo-score and pseudo-likelihood for evaluating correlate of protection in vaccine trials.

In vaccine clinical trials, vaccine efficacy endpoint analysis is usually associated with in high cost or extended study duration, due to the generally low infection rate. Correlate of protection (CoP), which refers to surrogate endpoint, usually immunological response, that can reliably predict the treatment effect, provides a more efficient and less costly approach to evaluate the vaccine. To handle the challenge of the missingness in the unobserved surrogate immune biomarker, the pseudo-score (PS) method, semiparametric method and pseudo-likelihood (PL) method demonstrated their advantages on different aspects. In this article, we propose new methodologies to combine the advantages of PS and PL with semiparametric methods respectively, to achieve higher estimate efficiency, allow continuous baseline predictor variable, and handle multiple surrogate markers. The advantage of our methodologies are demonstrated by a simulation study in different settings and applied to a case study, which eventually can improve the chance of a successful trial.

Breastfeeding and female labor force participation: the probability of survival of children in Nepal under 3 years old

BackgroundThe number of breastfeeding mothers participating in a labor force to generate income has been increasing in Nepal. In this regard, the study aims to assess the survival of Under 3 children in Nepal from the mother based on their labor force participation and breastfeeding status.MethodsData for the study were obtained from the Nepal Demographic and Health Survey 2016. The sample size of the study was 2,994 live births children, born in the last three years prior to the day of the interview. The robust hazard ratio and cox proportional hazard regression were conducted between dependent and independent variables with 95% confidence intervals (CIs) to conclude.ResultsFrom a total of 2,994 live births, 85 children died within 36 months of birth. More than 80% of the non-working mothers were breastfeeding their children. The findings shows that the survival of children under-3 is positively associated with the interaction with the mother’s work and breastfeeding status (Hazard Ratio 0.428, 95% CI 0.24, 0.75), family structure (Hazard Ratio 1.511; 95% CI 1.37, 1.655), relationship with the household head (Hazard Ratio 0.452; 95% CI 0.311, 0.65), wealth quintiles (Hazard Ratio 0.390; 95% CI 0.33, 0.46), caste (Hazard Ratio 0.652; 95% CI 0.60, 0.69), and religion (Hazard Ratio 2.015; 95% CI 1.09, 3.70) with model CI 95%, Log pseudo likelihood = -521.39236, prob. χ2 = 0.005 and time at risk = 52,748.ConclusionsThe highest rate of child survival was from the working mothers as well as continuing breastfeeding their children followed by mothers breastfeeding the child but not working, compared to mothers working but not breastfeeding the child, and mothers who were neither working nor breastfeeding their children respectively. This study provides clear evidence that breastfeeding is very important for the probability of survival of the child aged below 36 months and work of mother also have some positive impact on child survival. Employers should be encouraged to have a breastfeeding policy in the workplace through the establishment of a breastfeeding facility, and a flexible work schedule. At the same time government should also regulate the paid maternity leave and encourage societal support for the breastfeeding mothers.

CONSISTENT NON-GAUSSIAN PSEUDO MAXIMUM LIKELIHOOD ESTIMATORS OF SPATIAL AUTOREGRESSIVE MODELS

This paper studies the non-Gaussian pseudo maximum likelihood (PML) estimation of a spatial autoregressive (SAR) model with SAR disturbances. If the spatial weights matrix $M_{n}$ for the SAR disturbances is normalized to have row sums equal to 1 or the model reduces to a SAR model with no SAR process of disturbances, the non-Gaussian PML estimator (NGPMLE) for model parameters except the intercept term and the variance $\sigma _{0}^{2}$ of independent and identically distributed (i.i.d.) innovations in the model is consistent. Without row normalization of $M_{n}$ , the symmetry of i.i.d. innovations leads to consistent NGPMLE for model parameters except $\sigma _{0}^{2}$ . With neither row normalization of $M_{n}$ nor the symmetry of innovations, a location parameter can be added to the non-Gaussian pseudo likelihood function to achieve consistent estimation of model parameters except $\sigma _{0}^{2}$ . The NGPMLE with no added parameter can have a significant efficiency improvement upon the Gaussian PML estimator and the generalized method of moments estimator based on linear and quadratic moments. We also propose a non-Gaussian score test for spatial dependence, which can be locally more powerful than the Gaussian score test. Monte Carlo results show that our NGPMLE with no added parameter and the score test based on it perform well in finite samples.

Trade Continuity and Global Production Sharing in Emerging Economies: Evidence from Panel Gravity Analysis

ABSTRACT This article examines the effect of trade continuity, measured by the lagged imports of intermediate goods, on global production sharing in emerging economies. We estimate an augmented gravity model using the Poisson pseudo maximum likelihood method with a panel dataset of bilateral exports of 29 emerging economies from 2004 to 2017. Our results show that trade continuity positively affects global production sharing. We provide new empirical evidence that trade continuity is process-specific and may vary between parts and components and final assembly stages. Our findings have policy implications on the process-specific nature of global production sharing.

Marginal, conditional, and pseudo likelihood ratio approaches for biomarker combination to predict a binary disease outcome.

It is a common practice in public health research that multiple biomarkers are collected to diagnose or predict a disease outcome. A natural question is how to combine multiple biomarkers to improve the diagnostic accuracy. It has been shown by Neyman-Pearson lemma that the likelihood ratio statistic achieves the optimal AUC in theory. However, practical difficulty often lies in the estimation of the multivariate density functions. We propose three novel methods for the biomarker combination, with the idea of breaking down the joint densities to a series of univariate densities. The marginal likelihood ratio approach only assumes the marginal distribution of each biomarker. While the conditional likelihood ratio (CLR) and pseudo likelihood ratio (PLR) approaches assume the conditional distributions of a marker given others, and hence make use of the correlation structure to estimate the combination rules. The proposed methods make it much easier to assume and validate the univariate distributions of a biomarker than making multivariate distributional assumptions. Extensive simulation studies demonstrate that the CLR and the PLR approaches outperform many existing methods, and are therefore recommended for practical use. The proposed methods are motivated by and applied to a biomarker study to diagnose childhood autism/autism spectrum disorder.

Dynamic Score-Driven Independent Component Analysis

A model for dynamic independent component analysis is introduced where the dynamics are driven by the score of the pseudo likelihood with respect to the rotation angle of model innovations. While conditional second moments are invariant with respect to rotations, higher conditional moments are not, which may have important implications for applications. The pseudo maximum likelihood estimator of the model is shown to be consistent and asymptotically normally distributed. A simulation study reports good finite sample properties of the estimator, including the case of a misspecification of the innovation density. In an application to a bivariate exchange rate series of the Euro and the British Pound against the U.S. Dollar, it is shown that the model-implied conditional portfolio kurtosis largely aligns with narratives on financial stress as a result of the global financial crisis in 2008, the European sovereign debt crisis (2010–2013) and early rumors signalling the United Kingdom to leave the European Union (2017). These insights are consistent with a recently proposed model that associates portfolio kurtosis with a geopolitical risk factor.

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.

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.

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.

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.

Robust nonlinear structural equation modeling with interaction between exogenous and endogenous latent variables

ABSTRACT A handful of studies have been devoted to nonlinear structural equation modeling (SEM) in the literature. However, they generally overlooked the interactions among exogenous and endogenous latent variables and the interactions among endogenous latent variables. In this study, we propose a maximum likelihood approach for a nonlinear SEM model that incorporates such overlooked interactions. We also propose a two-stage pseudo maximum likelihood approach under the assumption of normal mixture, being computational efficient and robust against distributional misspecification. The simulation study shows that both approaches accurately estimate the unknown parameters if the distribution is correctly specified. However, only the pseudo maximum likelihood approach is robust against distributional misspecification.

Weighted Empirical and Euclidean Likelihood Covariate Adjustment

Abstract Covariate adjustment is often used in statistical analysis of randomized experiments to increase efficiency of estimators of treatment effects. In this paper, we study covariate adjustment based on the empirical and Euclidean likelihoods, and propose weighted versions that arise as natural alternatives. The weighted methods incorporate the auxiliary information that the covariates have equal means among the treatment groups due to randomization. We show that the empirical and the Euclidean likelihoods and their weighted versions are first order equivalent to Koch’s nonparametric covariance adjustment. Allowing the weights to be negative, the resulting pseudo Euclidean likelihood is equivalent to Koch’s method, and its weighted version can be viewed as a weighted version of Koch’s method. In a simulation study, we assess the finite sample properties of the proposed methods. The analysis of a clinical trial data set illustrates an application of these methods to a practical situation.

Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE

The analysis of sample-based studies involving sampling designs for small sample size, is challenging because the sample selection probabilities (as well as the sample weights) is dependent on the response variable and covariates. The study has focused on using systems of weighted regression estimating equations, using different modified weights, to estimate the coefficients of Weighted Likelihood Estimators. Usually, the design-consistent (Weighted) estimators are obtained by solving (sample) weighted estimating equations. They are then used to construct estimates which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A. The purpose of our study is to compare derived Estimators of the weighted regression estimating equations for estimating the coefficients of Weighted Likelihood Estimators, the Semi-Parametric Weighted Likelihood Estimator, SPW and the Weighted Conditional Pseudo Likelihood Estimator, WCPE with the conventional Horvitz-Thompson Weighted Likelihood Estimator, using relative efficiency, sample bias and Standard Error for small sample size. The constructed estimates from the system of weighted regression estimating equations, using different modified weights, are actually the Weighted Likelihood Estimators. The study compared the two new estimators, the Semi-parametric weighted estimator, SPW and the Weighted Conditional Pseudo Likelihood estimator, WCPE, for both the unmodified and modified Weights, which were found to have better relative efficiency and smaller finite small sample bias than the estimates from conventional Horvitz-Thompson Weighted Estimator, for both generated and for real data. The outcome of the tests show strong similarity in performance to those obtained using the simulated data. Estimates were constructed which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A.

Synthetic Microdata for Establishment Surveys Under Informative Sampling

AbstractMany agencies are investigating whether releasing synthetic microdata could be a viable dissemination strategy for highly sensitive data, such as business data, for which disclosure avoidance regulations otherwise prohibit the release of public use microdata. However, existing methods assume that the original data either cover the entire population or comprise a simple random sample, which limits the application of these methods in the context of survey data with unequal weights. This paper discusses synthetic data generation under informative sampling. To utilise design information in survey weights, we rely on the pseudo likelihood approach when building a hierarchical Bayesian model to estimate the distribution of the finite population. Then, synthetic populations are randomly drawn from the estimated finite population density. We present the full conditional distributions of the Markov chain Monte Carlo algorithm for posterior inference with the pseudo likelihood function. Using simulation studies, we show that the suggested synthetic data approach offers high utility for design-based and model-based analyses while offering a high level of disclosure protection. We apply the proposed method to a subset of the 2012 U.S. Economic Census and evaluate results with utility metrics and disclosure avoidance metrics under data attacker scenarios commonly used for business data.