Conditional Likelihood Approach Research Articles

Reliability analysis based on doubly-truncated and interval-censored data

Field data provide important information on product reliability. Interval sampling is widely used for collection of field data, which typically report incident cases during a certain time period. Such sampling scheme induces doubly truncated (DT) data if the exact failure time is known. In many situations, the exact failure date is known only to fall within an interval, leading to doubly truncated and interval censored (DTIC) data. This article considers analysis of DTIC data under parametric failure time models. We consider a conditional likelihood approach and propose interval estimation for parameters and the cumulative distribution functions. Simulation studies show that the proposed method performs well for finite sample size.

Conditional likelihood inference in a heteroscedastic functional measurement error model

In this paper, we deal with inference about the structural parameters in a heteroscedastic functional measurement error models under the normal distribution assumption. Given a minimal sufficient statistic for the incidental parameters, the conditional maximum likelihood (CML) approach is used. We show that CML estimators have explicit expressions and their sampling distribution is exact. We also show that the classical test statistics to test hypotheses of interest coincide and have exact distributions. We apply the statistical inference tools developed to a data set on comparison of measurement methods.

Counting the Unseen: Estimation of Susceptibility Proportions in Zero-Inflated Models Using a Conditional Likelihood Approach

Zero-inflated count data models are widely used in various fields such as ecology, epidemiology, and transportation, where count data with a large proportion of zeros is prevalent. Despite their widespread use, their theoretical properties have not been extensively studied. This study aims to investigate the impact of ignoring heterogeneity in event count intensity and susceptibility probability on zero-inflated count data analysis within the zero-inflated Poisson framework. To address this issue, we propose a novel conditional likelihood approach that uses positive count data only to estimate event count intensity parameters and develop a consistent estimator for estimating the average susceptibility probability. Our approach is compared with the maximum likelihood approach, and we demonstrate our findings through a comprehensive simulation study and real data analysis. The results can also be extended to zero-inflated binomial and geometric models with similar conclusions. These findings contribute to the understanding of the theoretical properties of zero-inflated count data models and provide a practical approach to handling heterogeneity in such models.

Penalized Estimation of Sparse Markov Regime-Switching Vector Auto-Regressive Models

We consider sparse Markov regime-switching vector autoregressive (MSVAR) models in which the regimes are governed by a latent homogeneous Markov chain. In practice, even for moderate values of the number of Markovian regimes and data dimension, the associated MSVAR model has a large parameter dimension compared to a typical sample size. We provide a unified penalized conditional likelihood approach for estimating sparse MSVAR models. We show that our proposed estimators are consistent and recover the sparse structure of the model. We also show that, when the number of regimes is correctly or over-specified, our method provides consistent estimation of the predictive density. We develop an efficient implementation of the method based on a modified Expectation-Maximization (EM) algorithm. We discuss strategies for estimation of the number of regimes. We evaluate finite-sample performance of the method via simulations, and further demonstrate its utility by analyzing a real dataset.

E-ReMI: Extended Maximal Interaction Two-mode Clustering

In this paper, we present E-ReMI, a new method for studying two-way interaction in row by column (i.e., two-mode) data. E-ReMI is based on a probabilistic two-mode clustering model that yields a two-mode partition of the data with maximal interaction between row and column clusters. The proposed model extends REMAXINT by allowing for unequal cluster sizes for the row clusters, thus introducing more flexibility in the model. In the manuscript, we use a conditional classification likelihood approach to derive the maximum likelihood estimates of the model parameters. We further introduce a test statistic for testing the null hypothesis of no interaction, discuss its properties and propose an algorithm to obtain its distribution under this null hypothesis. Free software to apply the methods described in this paper is developed in the R language. We assess the performance of the new method and compare it with competing methodologies through a simulation study. Finally, we present an application of the methodology using data from a study of person by situation interaction.

Simultaneity in binary outcome models with an application to employment for couples

Two of Peter Schmidt’s many contributions to econometrics have been to introduce a simultaneous logit model for bivariate binary outcomes and to study estimation of dynamic linear fixed effects panel data models using short panels. In this paper, we study a dynamic panel data version of the bivariate model introduced in Schmidt and Strauss (Econometrica 43:745–755, 1975) that allows for lagged dependent variables and fixed effects as in Ahn and Schmidt (J Econom 68:5–27, 1995). We combine a conditional likelihood approach with a method of moments approach to obtain an estimation strategy for the resulting model. We apply this estimation strategy to a simple model for the intra-household relationship in employment. Our main conclusion is that the within-household dependence in employment differs significantly by the ethnicity composition of the couple even after one allows for unobserved household specific heterogeneity.

A pairwise pseudo-likelihood approach for regression analysis of left-truncated failure time data with various types of censoring

BackgroundFailure time data frequently occur in many medical studies and often accompany with various types of censoring. In some applications, left truncation may occur and can induce biased sampling, which makes the practical data analysis become more complicated. The existing analysis methods for left-truncated data have some limitations in that they either focus only on a special type of censored data or fail to flexibly utilize the distribution information of the truncation times for inference. Therefore, it is essential to develop a reliable and efficient method for the analysis of left-truncated failure time data with various types of censoring.MethodThis paper concerns regression analysis of left-truncated failure time data with the proportional hazards model under various types of censoring mechanisms, including right censoring, interval censoring and a mixture of them. The proposed pairwise pseudo-likelihood estimation method is essentially built on a combination of the conditional likelihood and the pairwise likelihood that eliminates the nuisance truncation distribution function or avoids its estimation. To implement the presented method, a flexible EM algorithm is developed by utilizing the idea of self-consistent estimating equation. A main feature of the algorithm is that it involves closed-form estimators of the large-dimensional nuisance parameters and is thus computationally stable and reliable. In addition, an R package LTsurv is developed.ResultsThe numerical results obtained from extensive simulation studies suggest that the proposed pairwise pseudo-likelihood method performs reasonably well in practical situations and is obviously more efficient than the conditional likelihood approach as expected. The analysis results of the MHCPS data with the proposed pairwise pseudo-likelihood method indicate that males have significantly higher risk of losing active life than females. In contrast, the conditional likelihood method recognizes this effect as non-significant, which is because the conditional likelihood method often loses some estimation efficiency compared with the proposed method.ConclusionsThe proposed method provides a general and helpful tool to conduct the Cox’s regression analysis of left-truncated failure time data under various types of censoring.

Semiparametric regression analysis of length-biased and partly interval-censored data with application to an AIDS cohort study.

Length-biased data occur often in many scientific fields, including clinical trials, epidemiology surveys and genome-wide association studies, and many methods have been proposed for their analysis under various situations. In this article, we consider the situation where one faces length-biased and partly interval-censored failure time data under the proportional hazards model, for which it does not seem to exist an established method. For the estimation, we propose an efficient nonparametric maximum likelihood method by incorporating the distribution information of the observed truncation times. For the implementation of the method, a flexible and stable EM algorithm via two-stage data augmentation is developed. By employing the empirical process theory, we establish the asymptotic properties of the resulting estimators. A simulation study conducted to assess the finite-sample performance of the proposed method suggests that it works well and is more efficient than the conditional likelihood approach. An application to an AIDS cohort study is also provided.

Model misspecification and robust analysis foroutcome-dependent sampling designs under generalizedlinear models.

Outcome-dependent sampling (ODS) is a commonly used class of sampling designs to increase estimation efficiency in settings where response information (and possibly adjuster covariates) is available, but the exposure is expensive and/or cumbersome to collect. We focus on ODS within the context of a two-phase study, where in Phase One the response and adjuster covariate information is collected on a large cohort that is representative of the target population, but the expensive exposure variable is not yet measured. In Phase Two, using response information from Phase One, we selectively oversample a subset of informative subjects in whom we collect expensive exposure information. Importantly, the Phase Two sample is no longer representative, and we must use ascertainment-correcting analysis procedures for valid inferences. In this paper, we focus on likelihood-based analysis procedures, particularly a conditional-likelihood approach and a full-likelihood approach. Whereas the full-likelihood retains incomplete Phase One data for subjects not selected into Phase Two, the conditional-likelihood explicitly conditions on Phase Two sample selection (ie,it is a "complete case" analysis procedure). These designs and analysis procedures are typically implemented assuming a known, parametric model for the response distribution. However, in this paper, we approach analyses implementing a novel semi-parametric extension to generalized linear models (SPGLM) to develop likelihood-based procedures with improved robustness to misspecification of distributional assumptions. We specifically focus on the common setting where standard GLM distributional assumptions are not satisfied (eg,misspecified mean/variance relationship). We aim to provide practical design guidance and flexible tools for practitioners in these settings.

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.

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.

Regularization in dynamic random‐intercepts models for analysis of longitudinal data

AbstractThis paper addresses the problem of simultaneous variable selection and estimation in the random‐intercepts model with the first‐order lag response. This type of model is commonly used for analyzing longitudinal data obtained through repeated measurements on individuals over time. This model uses random effects to cover the intra‐class correlation, and the first lagged response to address the serial correlation, which are two common sources of dependency in longitudinal data. We demonstrate that the conditional likelihood approach by ignoring correlation among random effects and initial responses can lead to biased regularized estimates. Furthermore, we demonstrate that joint modeling of initial responses and subsequent observations in the structure of dynamic random‐intercepts models leads to both consistency and Oracle properties of regularized estimators. We present theoretical results in both low‐ and high‐dimensional settings and evaluate regularized estimators' performances by conducting simulation studies and analyzing a real dataset. Supporting information is available online.

Land Rights and Improvement Investments Among Crop Farmers in Southwest, Nigeria

This study examined the effects of land rights on investment decisions of farmers and determinants of land rights as well as the impact of land rights on farm productivity in Southwest Nigeria. Multistage sampling process was used in the selection of 320 respondents for the study. Two-stage conditional maximum likelihood (2SCML) approach of multivariate probit regression model and Endogenous switching regression (ESR) model were used for the analysis of the collected data. The results of Average Treatment Effect on the Treated (ATT) estimates from ESR revealed that land rights increase farm productivity. This study further confirmed the importance of land rights in facilitating investment in soil-improving measures which subsequently leads to higher productivity. One of the policy implications emanating from this study suggests that having use and transfer rights as against use only rights goes a long way in enhancing investment in soil-improving or conservation measures.
 Keywords: Crop, Investment, Land, Multivariate Probit Regression Model, Rights, Two-stage Conditional Maximum Likelihood.

Effects of Clustering COVID-19 Data Series and Its Implications

The outbreak of the highly infectious SARS-CoV-2 has been declared by the WHO as a public health emergency of international concern, since early 2020. The virus has led to a huge number of deaths and has caused major damage to the worldwide economy. In particular, countries with high reliance on the tourism sector such as the Small Island Developing States (SIDS) are continuously suffering from the COVID-19 phenomenon. Currently, there is the surfacing of vaccines to fight against the virus but the SARS-Cov 2 is passing through several mutation stages, making it more infectious and virulent. This necessitates the proper management to control the virus and in this context, Zarikas et al (2020) argued that, by clustering the countries with similar COVID-19 trend, the spread of the SARS-CoV-2 can be better managed as this can provide better guidance to some harmonised sanitary measures and policies and in monitoring the vaccination programme. In addition, this paper proposes a clustered longitudinal regression model that accommodates for some physical explanatory variables and normally distributed latent contributory effects. For this study, 18 Small Island Developing States (SIDs) were clustered in 4 groups, based on the United Nations income group classification. A clustered longitudinal autoregressive process is proposed to model the data. The Conditional Maximum likelihood approach is used to estimate the model parameters. Interestingly, different variations of the proposed process were fitted to obtain a superior fitting with lower Akaike Information Criteria.

A Nuisance-Free Inference Procedure Accounting for the Unknown Missingness with Application to Electronic Health Records.

We study how to conduct statistical inference in a regression model where the outcome variable is prone to missing values and the missingness mechanism is unknown. The model we consider might be a traditional setting or a modern high-dimensional setting where the sparsity assumption is usually imposed and the regularization technique is popularly used. Motivated by the fact that the missingness mechanism, albeit usually treated as a nuisance, is difficult to specify correctly, we adopt the conditional likelihood approach so that the nuisance can be completely ignored throughout our procedure. We establish the asymptotic theory of the proposed estimator and develop an easy-to-implement algorithm via some data manipulation strategy. In particular, under the high-dimensional setting where regularization is needed, we propose a data perturbation method for the post-selection inference. The proposed methodology is especially appealing when the true missingness mechanism tends to be missing not at random, e.g., patient reported outcomes or real world data such as electronic health records. The performance of the proposed method is evaluated by comprehensive simulation experiments as well as a study of the albumin level in the MIMIC-III database.

Sufficient statistics for unobserved heterogeneity in structural dynamic logit models

We study the identification and estimation of structural parameters in dynamic panel data logit models where decisions are forward-looking and the joint distribution of unobserved heterogeneity and observable state variables is nonparametric, i.e., fixed-effects model. We consider models with two endogenous state variables: the lagged decision variable, and the time duration in the last choice. This class of models includes as particular cases important economic applications such as models of market entry–exit, occupational choice, machine replacement, inventory and investment decisions, or dynamic demand of differentiated products. We prove the identification of the structural parameters using a conditional likelihood approach. The structure of the model implies that there is a sufficient statistic such that the likelihood function conditional on this statistic no longer depends on the unobserved heterogeneity – neither through the current utility nor through the continuation value of the forward-looking decision problem – but still depends on the structural parameters. We apply this estimator to a machine replacement model.

A weak‐signal‐assisted procedure for variable selection and statistical inference with an informative subsample

AbstractThis paper is motivated from an HIV‐1 drug resistance study where we encounter three analytical challenges: to analyze data with an informative subsample, to take into account the weak signals, and to detect important signals and also conduct statistical inference. We start with an initial estimation method, which adopts a penalized pairwise conditional likelihood approach for variable selection. This initial estimator incorporates the informative subsample issue. To accounting for the effect of weak signals, we use a key idea of partial ridge regression. We also propose a one‐step estimation method for each of the signal coefficients and then construct confidence intervals accordingly. We apply the proposed method to the Stanford HIV‐1 drug resistance study and compare the results with existing approaches. We also conduct comprehensive simulation studies to demonstrate the superior performance of our proposed method.

A spatiotemporal Richards–Schnute growth model and its estimation when data are collected through length-stratified sampling

We propose a spatiotemporal generalized von Bertalanffy (vonB) growth model that also includes between-individual (BI) variation and male/female correlation. The generalized vonB model includes the effect of maturation on growth. The model and the methodology are applied to a long time-series of survey observations of age and length for American plaice on the Grand Bank off the northeast coast of Canada. The bias in age-length data due to size selectivity of the survey gear is accounted for. The survey design includes length-stratified age sampling which is a type of response selective sampling design for growth model estimation. We propose and implement a conditional empirical proportion likelihood approach for these data. Neglecting this sampling scheme can lead to seriously biased estimation results. We found that a 6-parameter growth model is necessary for capturing the biphasic growth patterns of the American plaice on the Grand Bank, and the survey gear selectivity and BI variation are important for a good model fit. We proposed an empirically optimal BI variation model for this data. Our estimation results indicate that there are substantial differences in size-at-age for male and female American plaice, and this changes over time and between regions.

The assessment of procedural skills in physiotherapy education: a measurement study using the Rasch model

BackgroundProcedural skills are a key element in the training of future physiotherapists. Procedural skills relate to the acquisition of appropriate motor skills, which allow the safe application of clinical procedures to patients. In order to evaluate procedural skills in physiotherapy education validated assessment instruments are required. Recently the assessment of procedural skills in physiotherapy education (APSPT) tool was developed. The overall aim of this study was to establish the structural validity of the APSPT. In order to do this the following objectives were examined: i) the fit of the items of APSPT to the Rasch-model, ii) the fit of the overall score to the Rasch model, iii) the difficulty of each test item and iv) whether the difficulty levels of the individual test items cover the whole capacity spectrum of students in pre-registration physiotherapy education.MethodsFor this observational cross-sectional measurement properties study a convenience sample of 69 undergraduate pre-registration physiotherapy students of the HES-SO Valais-Wallis was recruited. Participants were instructed to perform a task procedure on a simulated patient. The performance was evaluated with the APSPT. A conditional maximum likelihood approach was used to estimate the parameters of a partial credit model for polytomous item responses. Item fit, ordering of thresholds, targeting and goodness of fit to the Rasch model was assessed.ResultsItem fit statistics showed that 25 items of the APSPT showed adequate fit to the Rasch model. Disordering of item thresholds did not occur and the targeting of the APSPT was adequate to measure the abilities of the included participants. Undimensionality and subgroup homogeneity were confirmed.ConclusionThis study presented evidence for the structural validity of the APSPT. Undimensionality of the APSPT was confirmed and therefore presents evidence that the latent dimension of procedural skills in physiotherapy education consists of several subcategories. However, the results should be interpreted with caution given the small sample size.

A Bayesian semiparametric method for analyzing length-biased data

Survival data obtained from prevalent cohort study designs are often subject to length-biased sampling. Frequentist methods including estimating equation approaches, as well as full likelihood methods, are available for assessing covariate effects on survival from such data. Bayesian methods allow a perspective of probability interpretation for the parameters of interest, and may easily provide the predictive distribution for future observations while incorporating weak prior knowledge on the baseline hazard function. There is lack of Bayesian methods for analyzing length-biased data. In this paper, we propose Bayesian methods for analyzing length-biased data under a proportional hazards model. The prior distribution for the cumulative hazard function is specified semiparametrically using I-Splines. Bayesian conditional and full likelihood approaches are developed for analyzing simulated and real data.