Conditional Likelihood Research Articles

Estimating population size: The importance of model and estimator choice.

We consider estimator and model choice when estimating abundance from capture-recapture data. Our work is motivated by a mark-recapture distance sampling example, where model and estimator choice led to unexpectedly large disparities in the estimates. To understand these differences, we look at three estimation strategies (maximum likelihood estimation, conditional maximum likelihood estimation, and Bayesian estimation) for both binomial and Poisson models. We show that assuming the data have a binomial or multinomial distribution introduces implicit and unnoticed assumptions that are not addressed when fitting with maximum likelihood estimation. This can have an important effect in finite samples, particularly if our data arise from multiple populations. We relate these results to those of restricted maximum likelihood in linear mixed effectsmodels.

A Conway–Maxwell–Poisson-Binomial AR(1) Model for Bounded Time Series Data

Binomial autoregressive models are frequently used for modeling bounded time series counts. However, they are not well developed for more complex bounded time series counts of the occurrence of n exchangeable and dependent units, which are becoming increasingly common in practice. To fill this gap, this paper first constructs an exchangeable Conway-Maxwell-Poisson-binomial (CMPB) thinning operator and then establishes the Conway-Maxwell-Poisson-binomial AR (CMPBAR) model. We establish its stationarity and ergodicity, discuss the conditional maximum likelihood (CML) estimate of the model's parameters, and establish the asymptotic normality of the CML estimator. In a simulation study, the boxplots illustrate that the CML estimator is consistent and the qqplots show the asymptotic normality of the CML estimator. In the real data example, our model takes a smaller AIC and BIC than its main competitors.

Local likelihood of quantile difference under left-truncated, right-censored and dependent assumptions

We, in this paper, focus on the inference of conditional quantile difference (CQD) for left-truncated and right-censored model. Based on local conditional likelihood function of the observed data, local likelihood ratio function and smoothed local log-likelihood ratio (log-SLL) of the CQD are constructed, and the maximum local likelihood estimator of the CQD is further defined from the log-SLL. When the observations are assumed to be a sequence of stationary α-mixing random variables, we establish asymptotic normality of the defined estimator, and prove the Wilks' theorem of adjusted log-SLL. Besides, we define another estimator of the CQD based on product-limit estimator of conditional distribution function and give its asymptotic normality. Also, simulation study and real data analysis are conducted to investigate the finite sample behaviour of the proposed methods.

A trinomial difference autoregressive model and its applications

This paper considers the autoregressive modelling problem of ‐valued time series of counts, whose counting sequence consists of −1, 0 and 1. Most existing methods are based on the signed binomial thinning operator and its some extensions, in which the counting sequence consists of 0 and 1, that is, the cases of −1 is ignored. To fill this gap, we first construct the trinomial difference thinning operator and then propose the trinomial difference Z‐valued autoregressive (TDZAR) model and give some stochastic properties. An attractive merit of the TDZAR model is that the incorporated trinomial difference thinning operator makes the conditional maximum likelihood estimate more wieldy and easy. Second, we discuss the two‐step conditional least squares estimate and the conditional maximum likelihood estimate and establish their asymptotic properties of the estimators. Third, the performances of these estimators are compared via simulation study. Finally, we apply the proposed model to a real data set.

Improving estimation efficiency for two-phase, outcome-dependent sampling studies

Two-phase outcome dependent sampling (ODS) is widely used in many fields, especially when certain covariates are expensive and/or difficult to measure. For two-phase ODS, the conditional maximum likelihood (CML) method is very attractive because it can handle zero Phase 2 selection probabilities and avoids modeling the covariate distribution. However, most existing CML-based methods use only the Phase 2 sample and thus may be less efficient than other methods. We propose a general empirical likelihood method that uses CML augmented with additional information in the whole Phase 1 sample to improve estimation efficiency. The proposed method maintains the ability to handle zero selection probabilities and avoids modeling the covariate distribution, but can lead to substantial efficiency gains over CML in the inexpensive covariates, or in the influential covariate when a surrogate is available, because of an effective use of the Phase 1 data. Simulations and a real data illustration using NHANES data are presented.

Capital social et pauvreté des ménages ruraux au Burkina Faso

L'objectif : Cet article analyse l'effet du capital social sur la pauvreté des ménages en milieu rural au Burkina Faso. Conception/méthodologie/approche : La présente recherche suppose une relation causale à double sens entre la pauvreté et l'accès au capital social. Cela suggère un problème d'endogénéité conduisant à l'utilisation de deux méthodes en deux étapes : l'approche Probit moindres carrés en deux étapes (2SPLS) et l'approche du maximum de vraisemblance conditionnelle en deux étapes (2SCML). Les analyses se sont basées sur des données d'enquêtes du Programme National de Gestion des Terroirs (PNGT 2) collectées en 2011 auprès des ménages en milieu rural. Résultats : Les investigations ont révélé que l'accès au capital social affecte positivement la consommation des ménages et réduit la pauvreté. Ces résultats montrent, en outre, que le revenu est négativement associé à l'accès au capital social. Les stratégies gouvernementales visant à réduire la pauvreté des ménages en milieu rural doivent encourager l'organisation des producteurs en groupements avec un accent mis sur les producteurs à faible revenu. Originalité/valeur : Le capital social joue un rôle important dans l'amélioration des conditions de vie des ménages indépendamment de l'espace géographique. Cependant, les réalités socioculturelles varient selon l'espace, ce qui affecte l'organisation et le contenu des associations et des groupements. Malgré les nombreux travaux sur le sujet, très peu ont concerné le Burkina Faso. Les quelques travaux n'ont pas examiné la double causalité entre le capital social et la pauvreté. Cette recherche qui utilise des données d'envergure nationale peut contribue à approfondir et élargir les connaissances sur la question.

Phosphorus and iron-oxide transport from a hydrologically isolated grassland hillslope

Dissolved reactive phosphorus (DRP) loss from agricultural soils can negatively affect water quality. Shallow subsurface pathways can dominate P losses in grassland soils, especially in wetter months when waterlogging is common. This study investigated the processes controlling intra- and inter-event and seasonal DRP losses from poorly drained permanent grassland hillslope plots. Temporal flow related water samples were taken from surface runoff and subsurface (in-field pipe) discharge, analysed, and related to the likelihood of anaerobic conditions and redoximorphic species including nitrate (NO3−) over time. Subsurface drainage accounted for 89% of total losses. Simple linear regression and correlation matrices showed positive relationships between DRP and iron and soil moisture deficit; and negative relationships between these three factors and NO3− concentrations in drainage. These data indicate that waterlogging and low NO3− concentrations control the release of P in drainage, potentially via reductive dissolution. The relationship between DRP and metal release was less obvious in surface runoff, as nutrients gathered from P-rich topsoil camoflaged redox reactions. The data suggest a threshold in NO3− concentrations that could exacerbate P losses, even in low P soils. Knowledge of how nutrients interact with soil drainage throughout the year can be used to better time soil N and P inputs via, for example, fertiliser or grazing to avoid to excessive P loss that could harm water quality.

A New Stochastic Order of Multivariate Distributions: Application in the Study of Reliability of Bridges Affected by Earthquakes

In this article, we introduce and study a new stochastic order of multivariate distributions, namely, the conditional likelihood ratio order. The proposed order and other stochastic orders are analyzed in the case of a bivariate exponential distributions family. The theoretical results obtained are applied for studying the reliability of bridges affected by earthquakes. The conditional likelihood ratio order involves the multivariate stochastic ordering; it resembles the likelihood ratio order in the univariate case but is much easier to verify than the likelihood ratio order in the multivariate case. Additionally, the likelihood ratio order in the multivariate case implies this ordering. However, the conditional likelihood ratio order does not imply the weak hard rate order, and it is not an order relation on the multivariate distributions set. The new conditional likelihood ratio order, together with the likelihood ratio order and the weak hazard rate order, were studied in the case of the bivariate Marshall–Olkin exponential distributions family, which has a lack of memory type property. At the end of the paper, we also presented an application of the analyzed orderings for this bivariate distributions family to the study of the effects of earthquakes on bridges.

Consistent and robust inference in hazard probability and odds models with discrete-time survival data.

For discrete-time survival data, conditional likelihood inference in Cox's hazard odds model is theoretically desirable but exact calculation is numerical intractable with a moderate to large number of tied events. Unconditional maximum likelihood estimation over both regression coefficients and baseline hazard probabilities can be problematic with a large number of time intervals. We develop new methods and theory using numerically simple estimating functions, along with model-based and model-robust variance estimation, in hazard probability and odds models. For the probability hazard model, we derive as a consistent estimator the Breslow-Peto estimator, previously known as an approximation to the conditional likelihood estimator in the hazard odds model. For the hazard odds model, we propose a weighted Mantel-Haenszel estimator, which satisfies conditional unbiasedness given the numbers of events in addition to the risk sets and covariates, similarly to the conditional likelihood estimator. Our methods are expected to perform satisfactorily in a broad range of settings, with small or large numbers of tied events corresponding to a large or small number of time intervals. The methods are implemented in the R package dSurvival.

The role of score and information bias in panel data likelihoods

We show why reducing information bias can improve the performance of likelihood based estimators and confidence regions in small samples, and why it seems to matter more for inference than for estimation. The insights in this paper are helpful in explaining several simulation findings in the panel data literature. E.g., we can explain the well documented phenomenon that reducing the score bias alone often reduces the finite sample variance of estimators and improves the coverage of confidence regions in small samples, and why confidence regions based on conditional (on sufficient statistics) likelihoods can have excellent coverage even in very short panels. We can also explain the simulation results in Schumann, Severini, and Tripathi (2021), who find that, in short panels, estimators and confidence regions based on pseudolikelihoods that are simultaneously first-order score and information unbiased perform much better than those based on pseudolikelihoods that are only first-order score unbiased.

Evaluation of the Revised Versus Original Ryan White Part A HIV Care Coordination Program in a Cluster-Randomized, Stepped-Wedge Trial.

To address challenges with delivery of an evidence-based HIV care coordination program (CCP), the New York City Health Department initiated a CCP redesign. We conducted a site-randomized stepped-wedge trial to evaluate effectiveness of the revised versus the original model. The CCP is delivered in New York City hospitals, community health centers, and community-based organizations to people experiencing or at risk for poor HIV outcomes. The outcome, timely viral suppression (TVS), was defined as achievement of viral load <200 copies/mL within 4 months among enrollees with unsuppressed viral load (≥200 copies/mL). Seventeen original-CCP provider agencies were randomized within matched pairs to early (August 2018) or delayed (May 2019) starts of revised-model implementation. Data from 3 periods were examined to compare revised versus original CCP effects on TVS. The primary analysis of the intervention effect applied fully conditional maximum likelihood estimation together with an exact, conditional P -value and an exact test-based 95% CI. We assigned each trial enrollee the implementation level of their site (based on a three-component measure) and tested for association with TVS, adjusting for period and study arm. Over 3 nine-month periods, 960 individuals were eligible for trial inclusion (intention to treat). The odds ratio of TVS versus no TVS comparing revised with original CCP was 0.88 (95% CI: 0.45, 1.7). Thus, the revised program yielded slightly lower TVS, although the effect was statistically nonsignificant. TVS was not significantly associated with revised-CCP implementation level. Program revisions did not increase TVS, irrespective of the implementation level.

A mixed generalized Poisson INAR model with applications

ABSTRACT A very attractive property of the mixed integer-valued autoregressive model is that it can capture structural changes. Inspired by this, we propose a mixed generalized Poisson integer-valued autoregressive model with a mixture of the quasi-binomial and generalized Poisson thinning operators. The first-order and higher-order mixed models are introduced, respectively. Some properties of the mixed models are presented. Conditional maximum likelihood estimation is considered for the parameters of the proposed model. The mean, median and mode of the conditional distribution are used to predict the one-step-ahead values. Furthermore, an approximate Bayesian model averaging prediction with the Bayesian information criterion is introduced to the higher-order models in the application to real data. Some Monte Carlo simulation results are presented for assessing the performance of parameter estimation and forecasting methods. At last, the applications of proposed models to real data are given for illustrating purposes.

On Periodic Generalized Poisson INAR(p) Models

This paper deals with some probabilistic and statistical properties of periodic generalized Poisson integer-valued autoregressive processes of order p, Necessary and sufficient conditions for the periodic stationarity, both in mean and second order, are established. The closed-forms of the mean and the second moment are, under these conditions, obtained. Moreover, the Wold–Cramér expression of the underlying second-order periodically stationary process is then established. The autocovariance structure is studied, while providing the closed-form of the periodic autocorrelation function. The Yule–Walker (YW), the two-stage conditional least squares (CLS) and the conditional maximum likelihood (CML) estimation methods of the underlying parameters are obtained. An intensive simulation study and an application on a real count data consisting of the daily number of daytime road accidents in Schiphol area, in Netherlands are provided.

Cross-section asymptotic for random-effects panel data models with autoregressive errors

A useful strategy to examine serial correlation in panel regression models is to adopt serially correlated error terms. The random effect is also present to address the individual-specific heterogeneity. Familiar transformations can restructure the AR(1) process into a serially uncorrelated dynamic model. It may result in unfitting estimation results once the statistical inference is carried on the conditional likelihood. We discuss in the article the consequence of this action. In particular, in the case of large cross-section units and short time-sequences, we provide analytical expressions for the asymptotic bias of maximum likelihood estimates when the analyst naïvely neglects the initial conditions problem. Under several conditions, we compute the size of biases and measure the mean squared errors to illustrate this violation. We also construct a joint regression model of the initial and subsequent responses to handle the initial conditions. Then, we conduct simulation studies to determine the asymptotic behavior.

A new minification integer‐valued autoregressive process driven by explanatory variables

SummaryThe discrete minification model based on the modified negative binomial operator, as an extension to the continuous minification model, can be used to describe an extreme value after few increasing values. To make this model more practical and flexible, a new minification integer‐valued autoregressive process driven by explanatory variables is proposed. Ergodicity of the new process is discussed. The estimators of the unknown parameters are obtained via the conditional least squares and conditional maximum likelihood methods, and the asymptotic properties are also established. A testing procedure for checking existence of the explanatory variables is developed. Some Monte Carlo simulations are given to illustrate the finite‐sample performances of the estimators under specification and misspecification and the test, respectively. A real example is applied to illustrate the performance of our model.

The balanced discrete triplet Lindley model and its INAR(1) extension: properties and COVID-19 applications.

This paper proposes a new flexible discrete triplet Lindley model that is constructed from the balanced discretization principle of the extended Lindley distribution. This model has several appealing statistical properties in terms of providing exact and closed form moment expressions and handling all forms of dispersion. Due to these, this paper explores further the usage of the discrete triplet Lindley as an innovation distribution in the simple integer-valued autoregressive process (INAR(1)). This subsequently allows for the modeling of count time series observations. In this context, a novel INAR(1) process is developed under mixed Binomial and the Pegram thinning operators. The model parameters of the INAR(1) process are estimated using the conditional maximum likelihood and Yule-Walker approaches. Some Monte Carlo simulation experiments are executed to assess the consistency of the estimators under the two estimation approaches. Interestingly, the proposed INAR(1) process is applied to analyze the COVID-19 cases and death series of different countries where it yields reliable parameter estimates and suitable forecasts via the modified Sieve bootstrap technique. On the other side, the new INAR(1) with discrete triplet Lindley innovations competes comfortably with other established INAR(1)s in the literature.

Point estimation following a two-stage group sequential trial.

Repeated testing in a group sequential trial can result in bias in the maximum likelihood estimate of the unknown parameter of interest. Many authors have therefore proposed adjusted point estimation procedures, which attempt to reduce such bias. Here, we describe nine possible point estimators within a common general framework for a two-stage group sequential trial. We then contrast their performance in five example trial settings, examining their conditional and marginal biases and residual mean square error. By focusing on the case of a trial with a single interim analysis, additional new results aiding the determination of the estimators are given. Our findings demonstrate that the uniform minimum variance unbiased estimator, whilst being marginally unbiased, often has large conditional bias and residual mean square error. If one is concerned solely about inference on progression to the second trial stage, the conditional uniform minimum variance unbiased estimator may be preferred. Two estimators, termed mean adjusted estimators, which attempt to reduce the marginal bias, arguably perform best in terms of the marginal residual mean square error. In all, one should choose an estimator accounting for its conditional and marginal biases and residual mean square error; the most suitable estimator will depend on relative desires to minimise each of these factors. If one cares solely about the conditional and marginal biases, the conditional maximum likelihood estimate may be preferred provided lower and upper stopping boundaries are included. If the conditional and marginal residual mean square error are also of concern, two mean adjusted estimators perform well.

First-order binomial autoregressive processes with Markov-switching coefficients

In this article, a new autoregressive process for finite-range time series of counts is proposed to analyse the finite-range integer-valued data based on an invisible Markov chain. We derive the probabilistic and statistical properties of the model. Conditional least squares (CLS) method and conditional maximum likelihood (CML) method are employed to estimate the parameters of interest. Furthermore, the forecasting problem is addressed. In addition, multiple simulation studies are performed to investigate the finite sample performance of parameter estimators and to compare the proposed estimation methods. The proposed model is applied to a finite-range data series of measles infections in Germany in 2004–2005.

A multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP): Modelling framework for episode-level activity participation and time-use analysis

This paper formulates a novel, multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP) to analyze multiple discrete-continuous (MDC) choices at a disaggregate level, including the number of instances different alternatives are chosen and the amount of consumption at each instance of choice. In doing so, the proposed model ensures a logically consistent prediction of multiple choice instances of an alternative. Specifically, the model prevents the prediction of positive allocation to the jth instance (i.e., a frequency of j episodes) of a good while predicting zero allocation to the (j-1)th or lower-numbered instances of that alternative. This is achieved by imposing a non-increasing order on the baseline-preference parameters of different choice instances of an alternative. The model results in a conditional likelihood function, where the likelihood arising from the optimality conditions of the utility maximization problem is conditioned on the ordering of baseline marginal utilities. Combining this strategy with independent and identically distributed (IID) Gumbel stochastic terms in the utility functions results in a closed-form likelihood expression that is not much more difficult than that of the MDCEV model. The proposed framework is applied for an empirical analysis of disaggregate, episode-level activity participation and time allocation behavior of non-working adults in Los Angeles, California. The empirical MDCEV-OP model provided better fit and predictive accuracy (in both estimation and validation datasets) for analyzing episode-level activity participation than a disaggregate MDCEV model that does not recognize the logical ordering of episodes. At the same time, the activity-level predictions aggregated from the episode-level predictions of the MDCEV-OP model do not deviate significantly from the predictions of an aggregate MDCEV model. These results highlight the efficacy of the proposed model for analyzing episode-level activity generation and time allocation.

Maximum likelihood estimation of the SDMINAR(p) model to analyze some COVID-19 data

Motivated by a certain type of infinite-patch metapopulation model, this current work proposes a new mixed INAR(p) model (SDMINAR(p)) based on binomial thinning and negative binomial thinning operators, where the innovations are assumed to be serially dependent in such a way that their mean is increased if the population at time { t − 1 , t − 2 , … , t − p } are large. Strict stationarity ergodicity property is proved. Conditional maximum likelihood estimation are adopted to estimate the model parameters. Asymptotic normality property of the estimators are displayed. The performances of the estimators are investigated in simulation, which manifests that the maximum likelihood estimation performs better when sample size increases. Finally, the practical relevance of the model is demonstrated by the COVID-19 data of suspected cases and severe cases imported from outside China with a comparison with relevant models that exist so far in the literature.