Full Maximum Likelihood Research Articles

Towards efficient and optimal analysis of CMB anisotropies on a masked sky

Strong foreground contamination in high resolution CMB data requires masking which introduces statistical anisotropies and renders a full maximum likelihood analysis numerically intractable. Standard analysis methods like the pseudo-C_l framework lead to information loss due to estimator suboptimalities. We set out and validate a methodology for numerically efficient estimators for a masked sky that recover nearly as much information as a full maximum likelihood procedure. In addition to the standard pseudo-C_l statistic, the approach introduces an augmented basis designed to account for the mode coupling due to the masking of the sky. We motivate the choice of this basis by describing the basic structure of the covariance matrix. We demonstrate that the augmented estimator can achieve near-optimal results in the presence of a WMAP-realistic mask.

A combined gamma frailty and normal random-effects model for repeated, overdispersed time-to-event data

This paper presents, extends, and studies a model for repeated, overdispersed time-to-event outcomes, subject to censoring. Building upon work by Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs etal. (2010), gamma and normal random effects are included in a Weibull model, to account for overdispersion and between-subject effects, respectively. Unlike these authors, censoring is allowed for, and two estimation methods are presented. The partial marginalization approach to full maximum likelihood of Molenberghs etal. (2010) is contrasted with pseudo-likelihood estimation. A limited simulation study is conducted to examine the relative merits of these estimation methods. The modeling framework is employed to analyze data on recurrent asthma attacks in children on the one hand and on survival in cancer patients on the other.

Parametric likelihood inference for interval censored competing risks data

Parametric estimation of the cumulative incidence function (CIF) is considered for competing risks data subject to interval censoring. Existing parametric models of the CIF for right censored competing risks data are adapted to the general case of interval censoring. Maximum likelihood estimators for the CIF are considered under the assumed models, extending earlier work on nonparametric estimation. A simple naive likelihood estimator is also considered that utilizes only part of the observed data. The naive estimator enables separate estimation of models for each cause, unlike full maximum likelihood in which all models are fit simultaneously. The naive likelihood is shown to be valid under mixed case interval censoring, but not under an independent inspection process model, in contrast with full maximum likelihood which is valid under both interval censoring models. In simulations, the naive estimator is shown to perform well and yield comparable efficiency to the full likelihood estimator in some settings. The methods are applied to data from a large, recent randomized clinical trial for the prevention of mother-to-child transmission of HIV.

Principles of single-channel kinetic analysis.

Single-channel recording provides high resolution information on gating mechanisms of ion channels that are generally difficult to obtain from macroscopic measurements. Analysis of the data, however, has proven to be challenging. Early approaches rely on half-amplitude threshold detection to idealize the record into dwell-times, followed by fitting duration histograms to resolve kinetics. More recent analyses exploit explicit modeling of the data to improve the idealization accuracy. The dwell-time fitting has also evolved into direct fitting of dwell-time sequences using the maximum likelihood approach while taking account of effects of missed events. Finally, hidden Markov modeling provides an ultimate approach by which both single channel amplitudes and kinetics are analyzed simultaneously without the need of idealization. The progress in theory, along with the advance in computing power as well as the development of user-friendly software, has transformed single-channel analysis, once a specialty task, now readily accessible to a broader community of scientists.

Persistent and Transient Productive Inefficiency: A Maximum Simulated Likelihood Approach

The productive efficiency of a firm can be seen as composed of two parts, one persistent and one transient. The received empirical literature on the measurement of productive efficiency has paid relatively little attention to the difference between these two components. Ahn, Good and Sickles (2000) suggested some approaches that pointed in this direction. The possibility was also raised in Greene (2004), who expressed some pessimism over the possibility of distinguishing the two empirically. Recently, Colombi (2010) and Kumbhakar and Tsionas (2012), in a milestone extension of the stochastic frontier methodology have proposed a tractable model based on panel data the promises to provide separate estimates of the two components of efficiency. The approach developed in the original presentation proved very cumbersome actually to implement in practice. Colombi (2010) notes that FIML estimation of the model is ‘complex and time consuming.’ In the sequence of papers, Colombi (2010), Colombi et al. (2011, 2014), Kumbhakar, Lien and Hardaker (2012) and Kumbhakar and Tsionas (2012) have suggested other strategies, including a four step least squares method. The main point of this paper is that full maximum likelihood estimation of the model is neither complex nor time consuming. The extreme complexity of the log likelihood noted in Colombi (2010), Colombi et al. (2011, 2014) is reduced by using simulation and exploiting the Butler and Moffitt (1982) formulation. In this paper, we develop a practical full information maximum simulated likelihood estimator for the model. The approach is very effective and strikingly simple to apply, and uses all of the sample distributional information to obtain the estimates. We also implement the panel data counterpart of the JLMS (1982) estimator for technical or cost inefficiency. The technique is applied in a study of the cost efficiency of Swiss railways.

Comparison of Methods for Handling Missing Covariate Data

Missing covariate data is a common problem in nonlinear mixed effects modelling of clinical data. The aim of this study was to implement and compare methods for handling missing covariate data in nonlinear mixed effects modelling under different missing data mechanisms. Simulations generated data for 200 individuals with a 50% difference in clearance between males and females. Three different types of missing data mechanisms were simulated and information about sex was missing for 50% of the individuals. Six methods for handling the missing covariate were compared in a stochastic simulations and estimations study where 200 data sets were simulated. The methods were compared according to bias and precision of parameter estimates. Multiple imputation based on weight and response, full maximum likelihood modelling using information on weight and full maximum likelihood modelling where the proportion of males among the individuals lacking information about sex was estimated (EST) gave precise and unbiased estimates in the presence of missing data when data were missing completely at random or missing at random. When data were missing not at random, the only method resulting in low bias and high parameter precision was EST.

Dynamic performance modelling and measuring for machine tools with continuous-state wear processes

In this paper, we consider the problem of using empirical continuous-state wear data of machine tools to estimate the dynamic lifetime distribution and to measure the performance of a machining process subject to stochastic tool-wear evolution. Machining systems are dynamic processes whose performance variable is usually characterised by the amount of tool wear that advances gradually with a continuous range of values. To accurately capture the performance of these continuous-state wear processes, neither traditional models such as the binary-state models nor multi-state models are suitable. In this paper, an exponential mixed-effects (EME) model is first developed. The EME model is subsequently transformed into a linear mixed-effects (LME) model to enhance the fit and predictability of the wear process data. The LME models take into consideration the correlations among repeated wear measurements collected at different time points within each subject. We then implement the expectation-maximisation (EM) algorithm to obtain the full maximum likelihood estimates (MLEs) of the parameters of the LME models whose asymptotic normal distributions can be used to acquire approximate confidence intervals and a testing hypothesis for the parameters. In addition, to measure the dynamic performance of tools, the amount of wear over time estimated from LME models is compared with a given tool-failure threshold. Consequently, we obtain the reliability of the tool and the estimation of its residual-lifetime distribution, which is critical information for the tool replacement or maintenance strategy. Finally, the lower and upper wear prediction limits of the 95% confidence level are presented. A practical application of the proposed methodology is illustrated throughout the paper.

Computational Issues in the Estima tion of the Spatial Probit Model: A Comparison of Various Estimators

In spatial discrete choice models the spatial dependent structure adds complexity in the estimation of parameters. Appropriate general method of moments (GMM) estimation needs inverses of n-by-n matrices and an optimization complexity of the moment conditions for moderate to large samples makes practical applications more difficult. Recently, Klier and McMillen (2008) have proposed a linearized version of the GMM estimator that avoids the infeasible problem of inverting n-by-n matrices when employing large samples. They show that standard GMM reduces to a nonlinear two-stage least squares problem. On the other hand, when we deal with full maximum likelihood (FML) estimation, a multidimensional integration problem arises and a viable computational solution needs to be found. Although it remains somewhat computationally burdensome, since the inverses of matrices dimensioned by the number of observations have to be computed, the ML estimator yields the potential advantage of efficiency. Therefore, through Monte Carlo experiments we compare GMM-based approaches with ML estimation in terms of their computation times and statistical properties. Furthermore, a comparison in terms of the marginal effects also is included. Finally, we recommend an algorithm based on sparse matrices that enables more efficient use of both ML and GMM estimators.

Estimating Intertemporal Elasticity of Substitution in a Sticky Price Model

Cancellation of income and substitution effect implied by King-Plosser-Rebelo (1988) preferences breaks tight coefficient restriction between the slope of the Phillips curve and the elasticity of consumption with respect to real interest rate in a sticky price macro model. This facilitates the estimation of intertemporal elasticity of substitution using full information Bayesian Maximum Likelihood techniques within a structural model. The US data from the period 1984 - 2007 supports low intertemporal elasticity of substitution and strongly rejects a logarithmic and an additively separable utility specification commonly applied in the New Keynesian literature. Keywords: Monetary policy, Bayesian estimation, Non-separable utility. JEL: E32, E52, E21

Joint Timing and Channel Estimation for Bandlimited Long-Code-Based MC-DS-CDMA: A Low-Complexity Near-Optimal Algorithm and the CRLB

Joint Timing and Channel Estimation (JTCE) for bandlimited long-code-aided Multi-Carrier Direct-Sequence Code Division Multiple Access (MC-DS-CDMA) systems is investigated. We establish the optimal multiuser timing and channel estimates for the uplink MC-DS-CDMA receiver by minimising a weighted least squares cost function with respect to K independent parameters, where K is the number of active users. A guided random search procedure known as Repeated Weighted Boosting Search (RWBS) is invoked for numerically solving this challenging multivariate optimisation problem, and thereby for producing near-optimal timing and channel estimates. The Cramer-Rao Lower Bound (CRLB) for the JTCE problem of interest is derived to benchmark the performance of the proposed RWBS based estimator. Quantitatively, for the scenario of K=10 users, E_b/N_0≥3 dB where E_b is the energy per bit and N_0 the single-sided noise power spectral density, and for a near-far ratio of 10 dB, the RWBS based estimator using an observation window of 20 symbols is shown to approach the CRLB at a complexity 10 orders of magnitude lower in comparison to its full maximum likelihood search based counterpart. The proposed algorithm does not require the transmission of known pilots, yet it is capable of handling time-variant channel states.

Dual criteria decisions

The most popular models of decision making use a single criterion to evaluate projects or lotteries. However, decision makers may actually consider multiple criteria when evaluating projects. We consider a dual criteria model from psychology. This model integrates the familiar tradeoffs between risk and utility that economists traditionally assume, allowance for rank-dependent decision weights, and consideration of income thresholds. We examine the issues involved in full maximum likelihood estimation of the model using observed choice data. We propose a general method for integrating the multiple criteria, using the logic of mixture models, which we believe is attractive from a decision-theoretic and statistical perspective. The model is applied to observed choices from a major natural experiment involving intrinsically dynamic choices over highly skewed outcomes. The evidence points to the clear role that income thresholds play in such decision making, but does not rule out a role for tradeoffs between risk and utility or probability weighting.

A Comparison of Factor Score Estimation Methods in the Presence of Missing Data: Reliability and an Application to Nicotine Dependence

Factor score estimation is a controversial topic in psychometrics, and the estimation of factor scores from exploratory factor models has historically received a great deal of attention. However, both confirmatory factor models and the existence of missing data have generally been ignored in this debate. This article presents a simulation study that compares the reliability of sum scores, regression-based and expected posterior methods for factor score estimation for confirmatory factor models in the presence of missing data. Although all methods perform reasonably well with complete data, expected posterior-weighted (full) maximum likelihood methods are significantly more reliable than sum scores and regression estimators in the presence of missing data. Factor score reliability for complete data can be predicted by Guttman's 1955 formula for factor communality. Furthermore, factor score reliability for incomplete data can be reasonably approximated by communality raised to the power. An empirical demonstration shows that the full maximum likelihood method best preserves the relationship between nicotine dependence and a genetic predictor under missing data. Implications and recommendations for applied research are discussed.

Cumulative logit model in the analysis of endometrial cancer under a matched pair case-control design

Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our previous studies, we have shown that the use of a polytomous logistic model for estimating cumulative odds ratios when the outcome (response) variable is ordinal (in addition to being polytomous) under matched pairs case-control design. The cumulative odds ratios were estimated based on separate fitting of the model at each of the cutpoint level as compared to less than equal to that level. In this paper we propose an alternative method of estimating the cumulative odds ratios and reanalyze the Los Angeles Endometrial Cancer data in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer under the matched pair case-control design. Methods: In the present study, the cumulative logit model is fitted using a single multinomial logit model for the data. For this, the full maximum likelihood estimation procedure is adopted. A test for equality of the cumulative odds ratios across the exposure levels is proposed. Results: The analysis revealed that there is a strong evidence of risk for developing endometrial cancer due to oestrogen exposure above each of the three dose level as compared to less than equal to that level. The estimated values at the three cutpoint levels were found to be 6.17, 3.60 and 5.16 respectively. Conclusions: The odds of developing endometrial cancer are very high for the users of any amount of oestrogen, even if it is the least dose, as compared to the non-users.

Roles of extension and ethno-religious networks in acceptance of resource-conserving agriculture among Ethiopian farmers

This article analyses roles of social and extension networks in adoption of resource-conserving practices among Ethiopian farmers. We gathered data from 297 randomly sampled households on their agricultural practices, social networks, access to the extension, and geographical location. After examining general determinants of practising resource-conserving agriculture, we employ a two-stage regression with full-maximum likelihood correction for selection bias to establish the roles of general social networks and external professionals in acceptance of conservation techniques. In accordance with previous research, probit regression in the first stage shows that the access to extension increases with farmers’ wealth and the size of their personal networks, and decreases with the distance of their households from village centres. However, after accounting for this unequal access to extension, the second-stage linear regression shows that regardless of education, wealth or geographical location, those whose religion and ethnicity match with their agent, report learning more about conservation from extension sources. Furthermore, farmers who are socially well connected within the community tend to be less receptive to agents’ recommendations regarding resource conservation. Dissemination policy of conservation agriculture should consider the ethnic and religious affinity between farmers and their extension agents. It also needs to pay more attention to socially and geographically isolated individuals.

124

Introduction: Thirst is a common and distressing symptom for ICU patients, yet under-recognized and undertreated by clinicians. Thirst distress (TD) is the emotional response engendered by this symptom. We conducted a single-blinded, randomized clinical trial testing a non-pharmacologic, nurse-delivered intervention for TD. Hypothesis: We hypothesized that, compared to usual care, this intervention would relieve TD over time. Methods: Cognitively clear patients from several ICUs (77 beds) who rated TI > 3 on 0-10 scale were consented and randomized to usual care (“UC”) or intervention (“I”) groups. All patients rated pre TD. Then “UC” patients were observed for 15 minutes by Research Nurse (RN) #1. For “I” patients, RN#1 administered a theoretically based “thirst bundle:” 3 oral swab wipes and 3-6 sterile ice cold water sprays 3 times in 15 minutes, with a lip moisturizer at the end. After each session, RN#2, blinded to the procedure, obtained the post TD score. This session was repeated 2 more times on Day 1 and 3 times on Day 2. Mean session duration: 15.6 ± 2.7 minutes.We performed a multilevel regression analysis to determine if the decrease over time in TD was greater in “I” versus “UC” patients. We used full maximum likelihood, which allows for missing data on the dependent variable. Results: Sample characteristics: Average ICU day: 5.2 ± 5.8. The 125 “UC” and 127 “I” patients had no significant difference in mean age: (55.4 vs 54), % male: (56% vs 54%), APACHE II score: (20.2 vs 20.5) Patients on mechanical ventilation (MV) were similar: (“UC” 4.8%, “I” 7.1%.) On Days 1 (average 5.2 ± 5.8 days after ICU admission) and 2, “I” patients had a significantly greater decrease in TD than did UC patients. Day 1: “UC” mean TD scores: pre = 4.2 (SE = 0.3); post = 3.6 (0.3); “I” mean TD scores: pre = 4.9 (0.3); post = 3.2 (0.3).”I” decreased 1.12 points more than “UC” (p = 0.012). Day 2: “UC” mean TD scores: pre = 3.3 (0.4); post = 3.4(0.4). “I” mean TD scores: pre = 4.5(0.4); post = 2.5(0.4). “I” decreased 2.6 points more than “UC” (p = 0.001). Conclusions: A simple bundle of thirst relief measures significantly decreased ICU patients’ thirst distress and should be considered as a practice intervention.

Smoothed nonparametric estimation for current status competing risks data

We study the nonparametric estimation of the cumulative incidence function and the cause-specific hazard function for current status data with competing risks via kernel smoothing. A smoothed naive nonparametric maximum likelihood estimator and a smoothed full nonparametric maximum likelihood estimator are shown to have pointwise asymptotic normality and faster convergence rates than the corresponding unsmoothed nonparametric likelihood estimators. Using the smoothed estimators and the plug-in principle, we can estimate the cause-specific hazard function, which has not been studied previously. We also propose semi-smoothed estimators of the cause-specific hazard as an alternative to the smoothed estimator and demonstrate that neither is uniformly more efficient than the other. Numerical studies show that a smoothed bootstrap method works well for selecting the bandwidths in the smoothed nonparametric estimation. The use of the estimators is exemplified by an application to cumulative incidence and hazard of subtype-specific HIV infection from a sero-prevalence study in injecting drug users in Thailand. Copyright 2013, Oxford University Press.

Approximate and Pseudo-Likelihood Analysis for Logistic Regression Using External Validation Data to Model Log Exposure

A common goal in environmental epidemiologic studies is to undertake logistic regression modeling to associate a continuous measure of exposure with binary disease status, adjusting for covariates. A frequent complication is that exposure may only be measurable indirectly, through a collection of subject-specific variables assumed associated with it. Motivated by a specific study to investigate the association between lung function and exposure to metal working fluids, we focus on a multiplicative-lognormal structural measurement error scenario and approaches to address it when external validation data are available. Conceptually, we emphasize the case in which true untransformed exposure is of interest in modeling disease status, but measurement error is additive on the log scale and thus multiplicative on the raw scale. Methodologically, we favor a pseudo-likelihood (PL) approach that exhibits fewer computational problems than direct full maximum likelihood (ML) yet maintains consistency under the assumed models without necessitating small exposure effects and/or small measurement error assumptions. Such assumptions are required by computationally convenient alternative methods like regression calibration (RC) and ML based on probit approximations. We summarize simulations demonstrating considerable potential for bias in the latter two approaches, while supporting the use of PL across a variety of scenarios. We also provide accessible strategies for obtaining adjusted standard errors to accompany RC and PL estimates.

Multivariate Latent Growth Models for Mixed Data with Covariate Effects

The paper presents an extension of a new class of multivariate latent growth models (Bianconcini and Cagnone, 2012) to allow for covariate effects on manifest, latent variables and random effects. The new class of models combines: (i) multivariate latent curves that describe the temporal behavior of the responses, and (ii) a factor model that specifies the relationship between manifest and latent variables. Based on the Generalized Linear and Latent Variable Model framework (Bartholomew and Knott, 1999), the response variables are assumed to follow different distributions of the exponential family, with item-specific linear predictors depending on both latent variables and measurement errors. A full maximum likelihood method is used to estimate all the model parameters simultaneously. Data coming from the Data WareHouse of the University of Bologna are used to illustrate the methodology.

First‐order integer valued AR processes with zero inflated poisson innovations

The first‐order nonnegative integer valued autoregressive process has been applied to model the counts of events in consecutive points of time. It is known that, if the innovations are assumed to follow a Poisson distribution then the marginal model is also Poisson. This model may however not be suitable for overdispersed count data. One frequent manifestation of overdispersion is that the incidence of zero counts is greater than expected from a Poisson model. In this paper, we introduce a new stationary first‐order integer valued autoregressive process with zero inflated Poisson innovations. We derive some structural properties such as the mean, variance, marginal and joint distribution functions of the process. We consider estimation of the unknown parameters by conditional or approximate full maximum likelihood. We use simulation to study the limiting marginal distribution of the process and the performance of our fitting algorithms. Finally, we demonstrate the usefulness of the proposed model by analyzing some real time series on animal health laboratory submissions.

A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses.

The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate ordinal items. Time-dependent latent variables are linked with an autoregressive model. Simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood. Model selection criteria developed for composite likelihood estimation are used in the applications. Furthermore, lower-order residuals are used as measures-of-fit for the selected models.