Conditional Likelihood Approach Research Articles

Decomposing Quantile Wage Gaps: A Conditional Likelihood Approach

SummaryThe paper develops a parametric variant of the Machado–Mata simulation methodology to examine quantile wage differences between groups of workers, with an application to the wage gap between native and foreign workers in Luxembourg. Relying on conditional-likelihood-based ‘parametric quantile regression’ in place of the standard linear quantile regression is parsimonious and cuts computing time drastically with no loss in the accuracy of marginal quantile simulations in our application. We find that the native worker advantage is a concave function of quantile: the advantage is small (possibly negative) for both low and high quantiles, but it is large for the middle half of the quantile range (between the 20th and 70th native wage percentiles).

An Exponential Class of Dynamic Binary Choice Panel Data Models with Fixed Effects

This paper develops a model for dynamic binary choice panel data that allows for unobserved heterogeneity to be arbitrarily correlated with covariates. The model is of the exponential type. We derive moment conditions that enable us to eliminate the unobserved heterogeneity term and at the same time to identify the parameters of the model. We then propose GMM estimators that are consistent and asymptotically normally distributed at the root-N rate. We also study the conditional likelihood approach, which can only identify the effect of state dependence in our case. Monte Carlo experiments demonstrate the finite sample performance of our GMM estimators.

Testing for state dependence in binary panel data with individual covariates by a modified quadratic exponential model

ABSTRACTWe propose a test for state dependence in binary panel data with individual covariates. For this aim, we rely on a quadratic exponential model in which the association between the response variables is accounted for in a different way with respect to more standard formulations. The level of association is measured by a single parameter that may be estimated by a Conditional Maximum Likelihood (CML) approach. Under the dynamic logit model, the conditional estimator of this parameter converges to zero when the hypothesis of absence of state dependence is true. Therefore, it is possible to implement a t-test for this hypothesis which may be very simply performed and attains the nominal significance level under several structures of the individual covariates. Through an extensive simulation study, we find that our test has good finite sample properties and it is more robust to the presence of (autocorrelated) covariates in the model specification in comparison with other existing testing procedures for state dependence. The proposed approach is illustrated by two empirical applications: the first is based on data coming from the Panel Study of Income Dynamics and concerns employment and fertility; the second is based on the Health and Retirement Study and concerns the self reported health status.

Short Tree, Long Tree, Right Tree, Wrong Tree: New Acquisition Bias Corrections for Inferring SNP Phylogenies.

Single nucleotide polymorphisms (SNPs) are useful markers for phylogenetic studies owing in part to their ubiquity throughout the genome and ease of collection. Restriction site associated DNA sequencing (RADseq) methods are becoming increasingly popular for SNP data collection, but an assessment of the best practises for using these data in phylogenetics is lacking. We use computer simulations, and new double digest RADseq (ddRADseq) data for the lizard family Phrynosomatidae, to investigate the accuracy of RAD loci for phylogenetic inference. We compare the two primary ways RAD loci are used during phylogenetic analysis, including the analysis of full sequences (i.e., SNPs together with invariant sites), or the analysis of SNPs on their own after excluding invariant sites. We find that using full sequences rather than just SNPs is preferable from the perspectives of branch length and topological accuracy, but not of computational time. We introduce two new acquisition bias corrections for dealing with alignments composed exclusively of SNPs, a conditional likelihood method and a reconstituted DNA approach. The conditional likelihood method conditions on the presence of variable characters only (the number of invariant sites that are unsampled but known to exist is not considered), while the reconstituted DNA approach requires the user to specify the exact number of unsampled invariant sites prior to the analysis. Under simulation, branch length biases increase with the amount of missing data for both acquisition bias correction methods, but branch length accuracy is much improved in the reconstituted DNA approach compared to the conditional likelihood approach. Phylogenetic analyses of the empirical data using concatenation or a coalescent-based species tree approach provide strong support for many of the accepted relationships among phrynosomatid lizards, suggesting that RAD loci contain useful phylogenetic signal across a range of divergence times despite the presence of missing data. Phylogenetic analysis of RAD loci requires careful attention to model assumptions, especially if downstream analyses depend on branch lengths.

Estimation of the treatment effect under an incomplete block crossover design in binary data - A conditional likelihood approach.

A random effects logistic regression model is proposed for an incomplete block crossover trial comparing three treatments when the underlying patient response is dichotomous. On the basis of the conditional distributions, the conditional maximum likelihood estimator for the relative effect between treatments and its estimated asymptotic standard error are derived. Asymptotic interval estimator and exact interval estimator are also developed. Monte Carlo simulation is used to evaluate the performance of these estimators. Both asymptotic and exact interval estimators are found to perform well in a variety of situations. When the number of patients is small, the exact interval estimator with assuring the coverage probability larger than or equal to the desired confidence level can be especially of use. The data taken from a crossover trial comparing the low and high doses of an analgesic with a placebo for the relief of pain in primary dysmenorrhea are used to illustrate the use of estimators and the potential usefulness of the incomplete block crossover design.

Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure

We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent latent process. The latent process accounts for unobserved heterogeneity and correlation between individuals in a dynamic fashion, and for dependence between the observed process and the missing data mechanism. Of particular interest is the case where the missing mechanism is non-ignorable. To deal with the topic we introduce a conditional to dropout model. A shape change in the random effects distribution is considered by directly modeling the effect of the missing data process on the evolution of the latent structure. To estimate the resulting model, we rely on the conditional maximum likelihood approach and for this aim we outline an EM algorithm. The proposal is illustrated via simulations and then applied on a dataset concerning skin cancers. Comparisons with other well-established methods are provided as well.

Rasch Mixture Models for DIF Detection: A Comparison of Old and New Score Specifications.

Rasch mixture models can be a useful tool when checking the assumption of measurement invariance for a single Rasch model. They provide advantages compared to manifest differential item functioning (DIF) tests when the DIF groups are only weakly correlated with the manifest covariates available. Unlike in single Rasch models, estimation of Rasch mixture models is sensitive to the specification of the ability distribution even when the conditional maximum likelihood approach is used. It is demonstrated in a simulation study how differences in ability can influence the latent classes of a Rasch mixture model. If the aim is only DIF detection, it is not of interest to uncover such ability differences as one is only interested in a latent group structure regarding the item difficulties. To avoid any confounding effect of ability differences (or impact), a new score distribution for the Rasch mixture model is introduced here. It ensures the estimation of the Rasch mixture model to be independent of the ability distribution and thus restricts the mixture to be sensitive to latent structure in the item difficulties only. Its usefulness is demonstrated in a simulation study, and its application is illustrated in a study of verbal aggression.

Likelihood approaches for proportional likelihood ratio model with right‐censored data

Regression methods for survival data with right censoring have been extensively studied under semiparametric transformation models such as the Cox regression model and the proportional odds model. However, their practical application could be limited because of possible violation of model assumption or lack of ready interpretation for the regression coefficients in some cases. As an alternative, in this paper, the proportional likelihood ratio model introduced by Luo and Tsai is extended to flexibly model the relationship between survival outcome and covariates. This model has a natural connection with many important semiparametric models such as generalized linear model and density ratio model and is closely related to biased sampling problems. Compared with the semiparametric transformation model, the proportional likelihood ratio model is appealing and practical in many ways because of its model flexibility and quite direct clinical interpretation. We present two likelihood approaches for the estimation and inference on the target regression parameters under independent and dependent censoring assumptions. Based on a conditional likelihood approach using uncensored failure times, a numerically simple estimation procedure is developed by maximizing a pairwise pseudo-likelihood. We also develop a full likelihood approach, and the most efficient maximum likelihood estimator is obtained by a profile likelihood. Simulation studies are conducted to assess the finite-sample properties of the proposed estimators and compare the efficiency of the two likelihood approaches. An application to survival data for bone marrow transplantation patients of acute leukemia is provided to illustrate the proposed method and other approaches for handling non-proportionality. The relative merits of these methods are discussed in concluding remarks.

A Novel Approach for Nonstationary Time Series Analysis with Time-Invariant Correlation Coefficient

We will concentrate on the modeling and analysis of a class of nonstationary time series, called correlation coefficient stationary series, which commonly exists in practical engineering. First, the concept and scope of correlation coefficient stationary series are discussed to get a better understanding. Second, a theorem is proposed to determine standard deviation function for correlation coefficient stationary series. Third, we propose a moving multiple-point average method to determine the function forms for mean and standard deviation, which can help to improve the analysis precision, especially in the context of limited sample size. Fourth, the conditional likelihood approach is utilized to estimate the model parameters. In addition, we discuss the correlation coefficient stationarity test method, which can contribute to the verification of modeling validity. Monte Carlo simulation study illustrates the authentication of the theorem and the validity of the established method. Empirical study shows that the approach can satisfactorily explain the nonstationary behavior of many practical data sets, including stock returns, maximum power load, China money supply, and foreign currency exchange rate. The effectiveness of these processes is addressed by forecasting performance.

Improved inference on capture recapture models with behavioural effects

In the context of capture-recapture modeling for estimating the unknown size of a finite population it is often required a flexible framework for dealing with a behavioural response to trapping. Many alternative settings have been proposed in the literature to account for the variation of capture probability at each occasion depending on the previous capture history. Inference is typically carried out relying on the so-called conditional likelihood approach. We highlight that such approach may, with positive probability, lead to inferential pathologies such as unbounded estimates for the finite size of the population. The occurrence of such likelihood failures is characterized within a very general class of behavioural effect models. It is also pointed out that a fully Bayesian analysis overcomes the likelihood failure phenomenon. The overall improved performance of alternative Bayesian estimators is investigated under different non-informative prior distributions verifying their comparative merits with both simulated and real data.

A conditional likelihood approach for regression analysis using biomarkers measured with batch‐specific error

Measurement error is common in epidemiological and biomedical studies. When biomarkers are measured in batches or groups, measurement error is potentially correlated within each batch or group. In regression analysis, most existing methods are not applicable in the presence of batch-specific measurement error in predictors. We propose a robust conditional likelihood approach to account for batch-specific error in predictors when batch effect is additive and the predominant source of error, which requires no assumptions on the distribution of measurement error. Although a regression model with batch as a categorical covariable yields the same parameter estimates as the proposed conditional likelihood approach for linear regression, this result does not hold in general for all generalized linear models, in particular, logistic regression. Our simulation studies show that the conditional likelihood approach achieves better finite sample performance than the regression calibration approach or a naive approach without adjustment for measurement error. In the case of logistic regression, our proposed approach is shown to also outperform the regression approach with batch as a categorical covariate. In addition, we also examine a 'hybrid' approach combining the conditional likelihood method and the regression calibration method, which is shown in simulations to achieve good performance in the presence of both batch-specific and measurement-specific errors. We illustrate our method by using data from a colorectal adenoma study.

Parameter Estimation for Exponentially Tempered Power Law Distributions

Tail estimates are developed for power law probability distributions with exponential tempering, using a conditional maximum likelihood approach based on the upper-order statistics. Tempered power law distributions are intermediate between heavy power-law tails and Laplace or exponential tails, and are sometimes called “semi-heavy” tailed distributions. The estimation method is demonstrated on simulated data from a tempered stable distribution, and for several data sets from geophysics and finance that show a power law probability tail with some tempering.

Regression analysis based on conditional likelihood approach under semi-competing risks data

Medical studies often involve semi-competing risks data, which consist of two types of events, namely terminal event and non-terminal event. Because the non-terminal event may be dependently censored by the terminal event, it is not possible to make inference on the non-terminal event without extra assumptions. Therefore, this study assumes that the dependence structure on the non-terminal event and the terminal event follows a copula model, and lets the marginal regression models of the non-terminal event and the terminal event both follow time-varying effect models. This study uses a conditional likelihood approach to estimate the time-varying coefficient of the non-terminal event, and proves the large sample properties of the proposed estimator. Simulation studies show that the proposed estimator performs well. This study also uses the proposed method to analyze AIDS Clinical Trial Group (ACTG 320).

Maximum Margin Bayesian Network Classifiers

We present a maximum margin parameter learning algorithm for Bayesian network classifiers using a conjugate gradient (CG) method for optimization. In contrast to previous approaches, we maintain the normalization constraints on the parameters of the Bayesian network during optimization, i.e., the probabilistic interpretation of the model is not lost. This enables us to handle missing features in discriminatively optimized Bayesian networks. In experiments, we compare the classification performance of maximum margin parameter learning to conditional likelihood and maximum likelihood learning approaches. Discriminative parameter learning significantly outperforms generative maximum likelihood estimation for naive Bayes and tree augmented naive Bayes structures on all considered data sets. Furthermore, maximizing the margin dominates the conditional likelihood approach in terms of classification performance in most cases. We provide results for a recently proposed maximum margin optimization approach based on convex relaxation. While the classification results are highly similar, our CG-based optimization is computationally up to orders of magnitude faster. Margin-optimized Bayesian network classifiers achieve classification performance comparable to support vector machines (SVMs) using fewer parameters. Moreover, we show that unanticipated missing feature values during classification can be easily processed by discriminatively optimized Bayesian network classifiers, a case where discriminative classifiers usually require mechanisms to complete unknown feature values in the data first.

Maximum Likelihood Estimation for Semiparametric Density Ratio Model

In the statistical literature, the conditional density model specification is commonly used to study regression effects. One attractive model is the semiparametric density ratio model, under which the conditional density function is the product of an unknown baseline density function and a known parametric function containing the covariate information. This model has a natural connection with generalized linear models and is closely related to biased sampling problems. Despite the attractive features and importance of this model, most existing methods are too restrictive since they are based on multi-sample data or conditional likelihood functions. The conditional likelihood approach can eliminate the unknown baseline density but cannot estimate it. We propose efficient estimation procedures based on the nonparametric likelihood. The nonparametric likelihood approach allows for general forms of covariates and estimates the regression parameters and the baseline density simultaneously. Therefore, the nonparametric likelihood approach is more versatile than the conditional likelihood approach especially when estimation of the conditional mean or other quantities of the outcome is of interest. We show that the nonparametric maximum likelihood estimators are consistent, asymptotically normal, and asymptotically efficient. Simulation studies demonstrate that the proposed methods perform well in practical settings. A real example is used for illustration.

Conditional likelihood approach for analyzing single visit abundance survey data in the presence of zero inflation and detection error

Current methods to correct for detection error require multiple visits to the same survey location. Many historical datasets exist that were collected using only a single visit, and logistical/cost considerations prevent many current research programs from collecting multiple visit data. In this paper, we explore what can be done with single visit count data when there is detection error. We show that when appropriate covariates that affect both detection and abundance are available, conditional likelihood can be used to estimate the regression parameters of a binomial–zero‐inflated Poisson (ZIP) mixture model and correct for detection error. We use observed counts of Ovenbirds (Seiurus aurocapilla) to illustrate the estimation of the parameters for the binomial–zero‐inflated Poisson mixture model using a subset of data from one of the largest and longest ecological time series datasets that only has single visits. Our single visit method has the following characteristics: (i) it does not require the assumptions of a closed population or adjustments caused by movement or migration; (ii) it is cost effective, enabling ecologists to cover a larger geographical region than possible when having to return to sites; and (iii) its resultant estimators appear to be statistically and computationally highly efficient. Copyright © 2012 John Wiley & Sons, Ltd.

An Exponential Class of Dynamic Binary Choice Panel Data Models with Fixed Effects

This paper develops a model for dynamic binary choice panel data that allows for unobserved heterogeneity to be arbitrarily correlated with covariates. The model is of the exponential type. We derive moment conditions that enable us to eliminate the unobserved heterogeneity term and at the same time to identify the parameters of the model. We then propose GMM estimators that are consistent and asymptotically normally distributed at the root-N rate. We also study the conditional likelihood approach, which can only identify the effect of state dependence in our case. Monte Carlo experiments demonstrate the finite sample performance of our GMM estimators.

Secondary Analysis under Cohort Sampling Designs Using Conditional Likelihood

Under cohort sampling designs, additional covariate data are collected on cases of a specific type and a randomly selected subset of noncases, primarily for the purpose of studying associations with a time-to-event response of interest. With such data available, an interest may arise to reuse them for studying associations between the additional covariate data and a secondary non-time-to-event response variable, usually collected for the whole study cohort at the outset of the study. Following earlier literature, we refer to such a situation as secondary analysis. We outline a general conditional likelihood approach for secondary analysis under cohort sampling designs and discuss the specific situations of case-cohort and nested case-control designs. We also review alternative methods based on full likelihood and inverse probability weighting. We compare the alternative methods for secondary analysis in two simulated settings and apply them in a real-data example.

A robust P-spline approach to closed population capture–recapture models with time dependence and heterogeneity

We extend the conditional likelihood approach to the analysis of capture–recapture experiments for closed populations by nonparametrically modeling the relationship between capture probabilities and individual covariates using P-splines. The model allows nonparametric functions of multivariate continuous covariates as well as categorical covariates and time effects, greatly enhancing the techniques available to an analyst. To implement this approach in practice, we found it necessary to develop a robust modification of the Horvitz–Thompson estimator. The method is illustrated on several data sets and a small simulation study is conducted.

The effect of misspecification of random effects distributions in clustered data settings with outcome‐dependent sampling

Genetic epidemiologists often gather outcome-dependent samples of family data to measure within-family associations of genetic factors with disease outcomes. Generalized linear mixed models provide effective methods to estimate within-family associations but typically require parametric specification of the random effects distribution. Although misspecification of the random effects distribution often leads to little bias in estimated regression coefficients in standard, prospective clustered data settings, some recent studies suggest that such misspecification will impact parameter estimates from outcome-dependent cluster sampling designs. Using analytic results, simulation studies and fits to example data, this study examines the effect of misspecification of random effects distributions on parameter estimates in clustered data settings with outcome-dependent sampling. We show that the effects are consistent with results from prospective cluster sampling settings. In particular, ascertainment corrected mixed model methods that assume normally distributed random intercepts and conditional likelihood approaches provide accurate estimates of within-family covariate effects even under a misspecified random effects distribution.