Likelihood Procedure Research Articles

Two consistent estimators for the skew Brownian motion

The skew Brownian motion (SBm) is of primary importance in modeling diffusion in media with interfaces which arise in many domains ranging from population ecology to geophysics and finance. We show that the maximum likelihood procedure estimates consistently the parameter of an SBm observed at discrete times. The difficulties arise because the observed process is only null recurrent and has a singular distribution with respect to the one of the Brownian motion. Finally, using the idea of the expectation–maximization algorithm, we show that the maximum likelihood estimator can be naturally interpreted as the expected total number of positive excursions divided by the expected number of excursions given the observations. The theoretical results are illustrated by numerical simulations.

Why fully efficient banks matter? A nonparametric stochastic frontier approach in the presence of fully efficient banks

A common assumption in the banking stochastic performance literature refers to the non-existence of fully efficient banks. This paper relaxes this strong assumption and proposes an alternative semiparametric zero-inefficiency stochastic frontier model. Specifically, we consider a nonparametric specification of the frontier whilst maintaining the parametric specification of the probability of fully efficient bank. We propose an iterative local maximum likelihood procedure that achieves the optimal convergence rates of both nonparametric frontier and the parameters contained in the probability of fully efficient bank. In an empirical application, we apply the proposed model and the estimation procedure to a global banking data set to derive new corrected measures of bank performance and productivity growth across the world. The results show that there is variability across regions, and the probability of fully efficient bank is mostly affected by bank-specific variables that are related to bank’s risk-taking attitude, whereas country-specific variables, such as inflation, also have an effect.

Forecasting of solar activity by alternative methods

The study is focused on the problem of forecasting nonstationary processes of solar activity using alternative procedures. The problem is urgent and it is considered by groups of researchers in many countries of the world. The processes under study belong to the class of nonlinear and nonstationary which requires selecting special methods for their modeling and forecasting. The study proposes an approach to forecasting based on three filters: the adaptive Kalman filter, optimal Kalman filter with parameter estimation using the maximum likelihood procedure and probabilistic particle filter. Selection of the filters is substantiated by the fact that they provide a possibility for taking into consideration stochastic external disturbances and measurement errors. The results of computational experiments showed the support for the idea that the methods selected are suitable for solving the problem stated. The best results of short-term forecasting of exponentially smoothed data were achieved using an adaptive filter. The analysis of results was performed by employing the known statistical quality characteristics including the mean absolute percentage error.

The impact of internalized stigma on the well-being of people with Schizophrenia

Previous research has shown that the internalization of schizophrenia-related stigma is associated with a worse prognosis and more suicidal tendencies. Empirical literature suggests that affective well-being -composed of positive affect (e.g. pride, enthusiasm, vitality, inspiration) and negative affect (e.g. shame, guilt, annoyance, worry)- seems to be the key component which, when being negatively affected by internalized stigma and the subsequent deterioration of self-concept, would lead to more severe symptomatology, lower recovery, and higher risk of suicide. Thus, our aim was to delve into the process by which affective well-being is impacted by the two main dimensions of internalized stigma (stereotype endorsement and alienation), with self-esteem and self-efficacy as mediators. The model was tested by path analysis -maximum likelihood procedure- in a sample of 216 patients. Our results indicate that alienation would entail more damage than stereotype endorsement both on affective well-being and on self-concept. Findings suggest that self-esteem mediates the impact of both internalized stigma dimensions on both types of affect, and that self-efficacy mediates the impact of alienation on positive affect. It is concluded that, in clinical practice, an important effort should be made to prevent internalized stigma (especially, alienation) and to promote positive self-concept of patients (especially, self-esteem).

The type II Topp-Leone generated family of distributions : Properties and applications

In this study, a new family of distributions called the type II Topp-Leone is introduced and three new special models are presented. Some mathematical properties of the type II Topp-Leone family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics, Rènyi and Shannon entropies are investigated. Parameter estimates of the family are obtained based on the maximum likelihood procedure for both uncensored and censored data. A simulation study is conducted to show the performance of the new family. Then, two real data sets based on censored and uncensored data sets are employed to show the usefulness of the new family.

Balanced augmented empirical likelihood for regression models

This paper studies the problem of convex hull constraint in conventional empirical likelihood. Specifically, in the framework of regression, a balanced augmented empirical likelihood (BAEL) procedure through adding two synthetic data points is proposed. It can be used to resolve the under-coverage issue, especially in small-sample or high-dimension setting. Furthermore, some asymptotic properties for proposed BAEL ratio statistic are established under mild conditions. The proposed approach performs robust to different random errors by choosing a robust loss function. Extensive simulation studies and a real example are carried out to support our results.

Evolution of the bivariate tree diameter and height distributions via the stand age: von Bertalanffy bivariate diffusion process approach

ABSTRACTThis paper focuses on the tree diameter and height distribution modeling and prediction technique, which better reflects the tree size dynamics in a stand. The evolution of the tree diameter and height structure in a forest stand is modeled using the bivariate fixed- and mixed-effect parameters Bertalanffy-type stochastic differential equation, resulting in a new biologically plausible class of bivariate lognormal probability density functions of the tree size components for response to the average stand age. The newly developed bivariate lognormal shape probability density function of the tree diameter and height at a given stand age can be used to describe the evolution of the mean diameter, height, stem volume, and stand volume per hectare in a stand in the forward and backward directions. Fixed and random effects are estimated by the maximum likelihood procedure using the Scots pine trees dataset in Lithuania.

Examining Elementary Teachers’ Risk for Occupational Stress: Associations with Teacher, School, and State Policy Variables

Background/ContextIt is widely understood that teachers are plagued by a myriad of challenges that ultimately affect their stress levels, job satisfaction, and effectiveness at work. Teacher stress can lead to burnout, lowered occupational commitment, and an eventual decision to leave the field. An important question for the field is how best to understand which teachers are most vulnerable to stress. This study used Lazarus and Folkman's transactional theory, which is the dominant model within the stress literature, to examine teachers’ stress vulnerability.ObjectiveThis study examined how elementary teacher appraisals of their classroom environment contribute to their risk for stress in the context of individual, classroom, and school characteristics, as well as state-level policy factors. Further, this study looked at how these factors are associated with teachers’ occupational stress, burnout, and commitment to teaching.ParticipantsParticipants were 11,850 full-time public school elementary teachers (Grades 1–5) who responded to the National Center for Education Statistics 2007/2008 Schools and Staffing Survey (SASS).Research DesignSecondary data from the SASS were employed. The Rasch rating scale model was used to form scores on the Appraisal Index (teachers’ ratio of experiencing resources versus demands), as well as the Classroom Control and Burnout scales.Data Collection and AnalysisMultilevel modeling was used. Each model had two levels with teachers nested within the state where they work. Two types of models were estimated using hierarchical linear modeling (HLM) software and restricted maximum likelihood procedures. The SASS teacher final sampling weight was then normalized and applied to all analyses within the HLM software. All results were reported with robust standard errors.FindingsTeachers classified as at risk for stress based on SASS items about classroom demand and resources were found to be more likely to report lower job satisfaction and burnout symptoms, as well as reduced occupational commitment. Professional characteristics, school context, and the policy climate in which teachers work were also associated with teachers being at risk for stress.Conclusions/RecommendationsGiven these connections between occupational stressors, teacher appraisals of the classroom environment, and occupational outcomes, these results suggest that education stakeholders should be mindful of the climate and context in which public policies are enacted.

A flexible likelihood approach for predicting neural spiking activity from oscillatory phase

BackgroundThe synchronous ionic currents that give rise to neural oscillations have complex influences on neuronal spiking activity that are challenging to characterize. New methodHere we present a method to estimate probabilistic relationships between neural spiking activity and the phase of field oscillations using a generalized linear model (GLM) with an overcomplete basis of circular functions. We first use an L1-regularized maximum likelihood procedure to select an active set of regressors from the overcomplete set and perform model fitting using standard maximum likelihood estimation. An information theoretic model selection procedure is then used to identify an optimal subset of regressors and associated coefficients that minimize overfitting. To assess goodness of fit, we apply the time-rescaling theorem and compare model predictions to original data using quantile-quantile plots. ResultsSpike-phase relationships in synthetic data were robustly characterized. When applied to in vivo hippocampal data from an awake behaving rat, our method captured a multimodal relationship between the spiking activity of a CA1 interneuron, a theta (5–10 Hz) rhythm, and a nested high gamma (65–135 Hz) rhythm. Comparison with existing methodsPrevious methods for characterizing spike-phase relationships are often only suitable for unimodal relationships, impose specific relationship shapes, or have limited ability to assess the accuracy or fit of their characterizations. ConclusionsThis method advances the way spike-phase relationships are visualized and quantified, and captures multimodal spike-phase relationships, including relationships with multiple nested rhythms. Overall, our method is a powerful tool for revealing a wide range of neural circuit interactions.

Explanatory power of behavioral models in the newsvendor problem: a simulation study

Experience weighted attraction (EWA) combines reinforcement learning with fictious play models and has proven to perform well as an explanatory model in economic experiments on individual decision making. Yet, EWA is a relatively complex model with a rather large number of free parameters and includes characteristics of simpler decision models, which might explain its good performance on laboratory data in the past. We present a simulation study which uses different models (including EWA) to generate order decisions in a newsvendor setting. Next, maximum likelihood estimations of these models are executed on the generated data and the fit of the models is evaluated using information criteria. Attention is focused on the performance of EWA. Furthermore, we present analyses on the parameter mix of EWA if more parsimonious models or a mix of these simpler models are used. Our results indicate that decision makers in newsvendor problems do not follow unique and simple decision rules. The results indicate that (1) the maximum likelihood procedure combined with the use of information criteria generally is suited to identify the true model; (2) EWA does not perform well when static models are given; yet, (3) in a mix of static and dynamic models EWA once again performs best. Given the past success of EWA on experimental data on both aggregate and individual level, these results may indicate that decision makers in newsvendor problems do not follow unique and simple decision rules.

Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects

For the partially linear errors-in-variables panel data models with fixed effects, we, in this paper, study asymptotic distributions of a corrected empirical log-likelihood ratio and maximum empirical likelihood estimator of the regression parameter. In addition, we propose penalized empirical likelihood (PEL) and variable selection procedure for the parameter with diverging numbers of parameters. By using an appropriate penalty function, we show that PEL estimators have the oracle property. Also, the PEL ratio for the vector of regression coefficients is defined and its limiting distribution is asymptotically chi-square under the null hypothesis. Moreover, empirical log-likelihood ratio for the nonparametric part is also investigated. Monte Carlo simulations are conducted to illustrate the finite sample performance of the proposed estimators.

Robust likelihood inference for diagnostic accuracy measures for paired organs.

Paired data arise naturally in Ophthalmology where pairs of eyes undergo diagnostic tests to predict the presence of certain diseases. The common correlation model is popular for modeling the joint probabilities of responses from fellow eyes for inference about accuracy measures. One of the assumptions underlying the model is exchangeability of fellow eyes that stipulates the accuracy measures such as sensitivities/specificities of fellow eyes be equal. We propose a parametric robust likelihood approach to testing the equality of accuracy measures of fellow eyes without modeling correlation. The robust likelihood procedure is applicable for inference about diagnostic accuracy measures in general paired designs. We provide simulations and analyses of a data set in Ophthalmology to demonstrate the effectiveness of the parametric robust procedure.

Structural Equation Modeling of Social Networks: Specification, Estimation, and Application

Psychologists are interested in whether friends and couples share similar personalities or not. However, no statistical models are readily available to test the association between personalities and social relations in the literature. In this study, we develop a statistical model for analyzing social network data with the latent personality traits as covariates. Because the model contains a measurement model for the latent traits and a structural model for the relationship between the network and latent traits, we discuss it under the general framework of structural equation modeling (SEM). In our model, the structural relation between the latent variable(s) and the outcome variable is no longer linear or generalized linear. To obtain model parameter estimates, we propose to use a two-stage maximum likelihood (ML) procedure. This modeling framework is evaluated through a simulation study under representative conditions that would be found in social network data. Its usefulness is then demonstrated through an empirical application to a college friendship network.

Carbon Dioxide Emissions, Energy Consumption in Agriculture: A Causality Analysis for India

This article utilises the vector error correction model (VECM) and Granger causality tests to explore short-run and long-run relationships, in India, across carbon dioxide (CO2) emissions, energy consumption, agriculture value added (AV), trade liberalisation and financial development over the time period 1971–2013. The study adopts the autoregressive distributed lag (ARDL)-bound testing approach and Johansen–Juselius maximum likelihood procedure to find out the cointegrating relation among the variables. Both ARDL approach and Johansen–Juselius cointegration approach show that the concerned variables under study are cointegrated. Short-run Granger causality results indicate the existence of bidirectional causality between AV and CO2 emissions, and energy used and CO2 emissions. In the long-run trade, financial development, energy consumption and AV affect CO2 emissions. The results put thrust on the need to utilise energy-efficient technologies in agriculture to save the damage of the environment. JEL: C32, O53, Q43

Provisional heritability estimates of four distraction index traits in a breeding population of German Shepherd dogs

AIMTo obtain provisional estimates of the heritability (h2) of passive laxity of the coxofemoral joints of a breeding colony of German Shepherd dogs, measured using the PennHIP distraction index (DI).METHODSRecords were obtained of the PennHIP DI of right and left hips of 195 German Shepherd dogs (377 DI records) from the dog breeding colony of the New Zealand Police Dog Breeding Centre between 2003 and 2016, as well as pedigree records of 884 animals over four generations. Estimates of h2 and variance components for the log transformed DI data were obtained using restricted maximum likelihood procedures with a single trait sire model. Four DI traits for each dog were analysed: left hip, right hip, mean and worse-hip DI. The model included the fixed effects of sex and year of birth, with the age at scoring as a covariable, the random sire effect and residual error for each observation.RESULTSThe h2 of the DI of the left hip (0.81, SE 0.40) was higher than the h2 of the DI of the right hip (0.35, SE 0.36). The h2 for the worse-hip DI (0.15, SE 0.28) in each dog was lower than the h2 of the individual hip DI, or the h2 for the mean of the two hips (0.53, SE 0.36) in each dog. The low number of generations prevented a meaningful analysis of the genetic trend.CONCLUSIONS AND CLINICAL RELEVANCEThe h2 estimates for the left, right and mean DI traits were moderate to high, whereas the h2 estimates for the worse-hip DI (as used by the PennHIP programme for ranking of dogs) was low, but all estimates had large SE due to the small sample size. This provisional estimate of the h2 of four distraction index traits suggests that the mean DI could be useful as a selection tool against canine hip dysplasia in German Shepherd dogs, whereas the worse-hip DI may be less effective. Heritability estimates from a population with a greater number of DI measures is needed to validate this finding given the large SE in our study.

Bayesian estimator for Logit Mixtures with inter- and intra-consumer heterogeneity

Estimating discrete choice models on panel data allows for the estimation of preference heterogeneity in the sample. While the Logit Mixture model with random parameters is mostly used to account for variation across individuals, preferences may also vary across different choice situations of the same individual. Up to this point, Logit Mixtures incorporating both inter- and intra-consumer heterogeneity are estimated with the classical Maximum Simulated Likelihood (MSL) procedure. The MSL procedure becomes computationally expensive with an increasing sample size and can be burdensome in the presence of a multi-modal likelihood function. We therefore propose a Hierarchical Bayes estimator for Logit Mixtures with both levels of heterogeneity. It builds on the Allenby-Train procedure, which considers only inter-consumer heterogeneity. To test the proposed procedures, we analyze how well the true patterns of heterogeneity are recovered in a simulation environment. Results from the Monte Carlo simulation suggest that falsely ignoring intra-consumer heterogeneity despite its presence in the data leads to biased estimates and a decreased goodness of fit. The latter is confirmed by a real-world example of explaining mode choices for GPS traces. We further show that the runtime of the proposed estimator is substantially faster than for the corresponding MSL estimator.

Loneliness in Europe: Personal and Societal Individualism-Collectivism and Their Connection to Social Isolation

This article explains perceived loneliness among people in Europe by accounting for cultural factors as well as social isolation. Culturally, it measures the impact of both personal and societal individualism-collectivism on loneliness. It accounts for social isolation by looking at the separate effects of living alone, emotional isolation, and relational isolation. Using a 2014 European Social Survey sample comprising 36,760 individuals in 21 countries, the study predicts loneliness using multilevel logistic regression modeling using both maximum likelihood and Bayesian estimation procedures. Results indicate that societal individualism may strongly reduce loneliness, even after taking into account that social isolation partially mediates this relationship. Further, the effects of living alone and relational isolation depend upon whether one is personally an individualist or collectivist. Living alone and relational isolation greatly increase loneliness, and such negative effects are somewhat reduced for individualists. However, individualists are not protected from the negative impacts of emotional isolation at all, and the above moderation effects do not hold for the most severe forms of loneliness. Based on this analysis, the best case for reduced loneliness for individualists and collectivists alike is that they maintain a strong degree of multiple forms of social integration and live in an individualist society. (Less)

Generalized prediction intervals for treatment effects in random-effects models.

This article derives generalized prediction intervals for random effects in linear random-effects models. For balanced and unbalanced data in two-way layouts, models are considered with and without interaction. Coverage of the proposed generalized prediction intervals was estimated in a simulation study based on an agricultural field experiment. Generalized prediction intervals were compared with prediction intervals based on the restricted maximum likelihood (REML) procedure and the approximate methods of Satterthwaite and Kenward and Roger. The simulation study showed that coverage of generalized prediction intervals was closer to the nominal level 0.95 than coverage of prediction intervals based on the REML procedure.

Direct and maternal variance components and genetic parameters for average daily body weight gain and Kleiber ratios in Nellore sheep.

The objective of the present study was to estimate variance components and genetic parameters for average daily gain from birth to weaning (ADGa), birth to 6months (ADGb) and 3 to 6months (ADGc) and corresponding Kleiber ratios (Ka, Kb, and Kc) in Nellore sheep. Data were collected from the records maintained at Livestock Research Station, Palamaner, for analysis and the data spread from 1993 to 2016 (23years). Lambing year, sex of lamb, season of lambing, and parity of dam were included in the model as fixed effects, and ewe weight was kept as a covariate. Six animal models were fitted with various combinations of direct and maternal genetic effects using restricted maximum likelihood procedure. The Akaike's information criterion was employed to determine the best model for each trait. Direct heritability estimates obtained in the study for ADGa, ADGb, ADGc, Ka, Kb, and Kc were 0.37, 0.41, 0.34, 0.48, 0.46, and 0.37, respectively, and their corresponding maternal heritabilities ranged from 0.11, 0.21, 0.11, 0.24, 0.22, and 0.11, respectively. (Co)variance among the direct and maternal effects were found to be negative in all the traits. Direct genetic correlations among the studied traits were positive with few exceptions, and they ranged from - 0.03 (Ka-Kc) to 0.99 (ADGa-Ka); similarly, the phenotypic correlations ranged from low to high - 0.18 (ADGa-Kc and Ka-Kc) to 0.95 (ADGa-Ka). These results indicated the importance of maternal effects in affecting the growth rate and efficiency of feed utilization traits and also suggested the possibility of moderate genetic progress for these traits through selection.

A bivariate count model with discrete Weibull margins

Multivariate discrete data arise in many fields (statistical quality control, epidemiology, failure and reliability analysis, etc.) and modelling such data is a relevant task. Here we consider the construction of a bivariate model with discrete Weibull margins, based on Farlie–Gumbel–Morgenstern copula, analyse its properties especially in terms of attainable correlation, and propose several methods for the point estimation of its parameters. Two of them are the standard one-step and two-step maximum likelihood procedures; the other two are based on an approximate method of moments and on the method of proportion, which represent intuitive alternatives for estimating the dependence parameter. A Monte Carlo simulation study is presented, comprising more than one hundred artificial settings, which empirically assesses the performance of the different estimation techniques in terms of statistical properties and computational cost. For illustrative purposes, the model and related inferential procedures are fitted and applied to two datasets taken from the literature, concerning failure data, presenting either positive or negative correlation between the two observed variables. The applications show that the proposed bivariate discrete Weibull distribution can model correlated counts even better than existing and well-established joint distributions.