8. Permutation Models for Relational Data

2007 ◽  
Vol 37 (1) ◽  
pp. 257-281 ◽  
Author(s):  
Carter T. Butts
Keyword(s):  
Linear Time ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Spatial Proximity ◽  
High Tech ◽  
Modeling Framework ◽  
Relational Structures ◽  
Strongly Connected ◽  
Permutation Models ◽  
Pseudo Likelihood Estimation

A common problem in sociology, psychology, biology, geography, and management science is the comparison of dyadic relational structures (i.e., graphs). Where these structures are formed on a common set of elements, a natural question that arises is whether there is a tendency for elements that are strongly connected in one set of structures to be more—or less—strongly connected within another set. We may ask, for instance, whether there is a correspondence between golf games and business deals, trade and warfare, or spatial proximity and genetic similarity. In each case, the data for such comparisons may be continuous or discrete, and multiple relations may be involved simultaneously (e.g., when comparing multiple measures of international trade volume with multiple types of political interactions). We propose here an exponential family of permutation models that is suitable for inferring the direction and strength of association among dyadic relational structures. A linear-time algorithm is shown for MCMC simulation of model draws, as is the use of simulated draws for maximum likelihood estimation (MCMC-MLE) and/or estimation of Monte Carlo standard errors. We also provide an easily performed maximum pseudo-likelihood estimation procedure for the permutation model family, which provides a reasonable means of generating seed models for the MCMC-MLE procedure. Use of the modeling framework is demonstrated via an application involving relationships among managers in a high-tech firm.

A review of multistate modelling approaches in monitoring disease progression: Bayesian estimation using the Kolmogorov-Chapman forward equations

2021 ◽  
pp. 096228022199750
Author(s):  
Zvifadzo Matsena Zingoni ◽  
Tobias F Chirwa ◽  
Jim Todd ◽  
Eustasius Musenge
Keyword(s):  
Bayesian Estimation ◽  
Transition Probabilities ◽  
Markov Property ◽  
Likelihood Estimation ◽  
Single Individual ◽  
Transition Rates ◽  
Multistate Models ◽  
Time To Event ◽  
Modeling Framework ◽  
Forward Equations

There are numerous fields of science in which multistate models are used, including biomedical research and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time-to-event life history of an individual through a flexible framework for longitudinal data. The multistate framework can describe more than one possible time-to-event outcome for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations from the Bayesian estimation perspective. Most multistate models assume the Markov property and time homogeneity; however, if these assumptions are violated, an extension to non-Markovian and time-varying transition rates is possible. This manuscript extends reviews in various types of multistate models, assumptions, methods of estimation and data features compatible with fitting multistate models. We highlight the contrast between the frequentist (maximum likelihood estimation) and the Bayesian estimation approaches in the multistate modeling framework and point out where the latter is advantageous. A partially observed and aggregated dataset from the Zimbabwe national ART program was used to illustrate the use of Kolmogorov-Chapman forward equations. The transition rates from a three-stage reversible multistate model based on viral load measurements in WinBUGS were reported.

scholarly journals An autoregressive model for irregular time series of variable stars

2016 ◽  
Vol 12 (S325) ◽  
pp. 259-262
Author(s):  
Susana Eyheramendy ◽  
Felipe Elorrieta ◽  
Wilfredo Palma
Keyword(s):  
Time Series ◽  
Gravitational Lensing ◽  
Autoregressive Model ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Variable Stars ◽  
Light Curves ◽  
Finite Sample ◽  
Harmonic Model ◽  
Dependency Structure

AbstractThis paper discusses an autoregressive model for the analysis of irregularly observed time series. The properties of this model are studied and a maximum likelihood estimation procedure is proposed. The finite sample performance of this estimator is assessed by Monte Carlo simulations, showing accurate estimators. We implement this model to the residuals after fitting an harmonic model to light-curves from periodic variable stars from the Optical Gravitational Lensing Experiment (OGLE) and Hipparcos surveys, showing that the model can identify time dependency structure that remains in the residuals when, for example, the period of the light-curves was not properly estimated.

scholarly journals Technical Efficiency and Small Scale Maize Producers in Mwanza Region: A Stochastic Frontier Analysis

2021 ◽  
Vol 9 (3) ◽  
Author(s):  
Mukole Kongolo
Keyword(s):  
Technical Efficiency ◽  
Best Practice ◽  
Stochastic Frontier Analysis ◽  
Stochastic Frontier ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Farm Size ◽  
Small Scale ◽  
Maize Production ◽  
Frontier Analysis

This study measured technical efficiency and its determinants in maize production by small-scale producers in Mwanza region, using a stochastic frontier production function approach. A randomly selected sample of participants in the two districts was used. The Maximum Likelihood estimation procedure was followed to obtain the determinants of technical efficiency and technical efficiency levels of small-scale maize producers. The minimum and maximum values of technical efficiency were between 20% and 91%, indicating that the least practices of specific producer operates at a minimum level of 20%, while the best practice producers  operate  at 91% technical efficiency  level respectively. The summary results of the mean technical efficiency was 63%. The main determinants of technical efficiency were labour, farm size, producer’s experience, producer’s age, family size which were all positive and statistically significant. The findings suggest that the average efficiency of small-scale maize producers could be improved by 37% through better use of existing resources and technology. These findings highlight the need for action by government to assist small-scale maize producers improve efficiency.

scholarly journals Effective plots to assess bias and precision in method comparison studies

2016 ◽  
Vol 27 (6) ◽  
pp. 1650-1660 ◽  
Author(s):  
Patrick Taffé
Keyword(s):  
Measurement Errors ◽  
Regression Line ◽  
Latent Trait ◽  
Method Comparison ◽  
Estimation Procedure ◽  
New Method ◽  
Reference Standard ◽  
Limits Of Agreement ◽  
Modeling Framework ◽  
Methods Of Measurement

Bland and Altman’s limits of agreement have traditionally been used in clinical research to assess the agreement between different methods of measurement for quantitative variables. However, when the variances of the measurement errors of the two methods are different, Bland and Altman’s plot may be misleading; there are settings where the regression line shows an upward or a downward trend but there is no bias or a zero slope and there is a bias. Therefore, the goal of this paper is to clearly illustrate why and when does a bias arise, particularly when heteroscedastic measurement errors are expected, and propose two new plots, the “bias plot” and the “precision plot,” to help the investigator visually and clinically appraise the performance of the new method. These plots do not have the above-mentioned defect and still are easy to interpret, in the spirit of Bland and Altman’s limits of agreement. To achieve this goal, we rely on the modeling framework recently developed by Nawarathna and Choudhary, which allows the measurement errors to be heteroscedastic and depend on the underlying latent trait. Their estimation procedure, however, is complex and rather daunting to implement. We have, therefore, developed a new estimation procedure, which is much simpler to implement and, yet, performs very well, as illustrated by our simulations. The methodology requires several measurements with the reference standard and possibly only one with the new method for each individual.

scholarly journals Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 813
Author(s):  
Anita Rahayu ◽  
Purhadi ◽  
Sutikno ◽  
Dedy Dwi Prastyo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Wald Test ◽  
Positive Outcome ◽  
Three Dimensions ◽  
Predictor Variables ◽  
Ratio Test

Gamma distribution is a general type of statistical distribution that can be applied in various fields, mainly when the distribution of data is not symmetrical. When predictor variables also affect positive outcome, then gamma regression plays a role. In many cases, the predictor variables give effect to several responses simultaneously. In this article, we develop a multivariate gamma regression (MGR), which is one type of non-linear regression with response variables that follow a multivariate gamma (MG) distribution. This work also provides the parameter estimation procedure, test statistics, and hypothesis testing for the significance of the parameter, partially and simultaneously. The parameter estimators are obtained using the maximum likelihood estimation (MLE) that is optimized by numerical iteration using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The simultaneous test for the model’s significance is derived using the maximum likelihood ratio test (MLRT), whereas the partial test uses the Wald test. The proposed MGR model is applied to model the three dimensions of the human development index (HDI) with five predictor variables. The unit of observation is regency/municipality in Java, Indonesia, in 2018. The empirical results show that modeling using multiple predictors makes more sense compared to the model when it only employs a single predictor.

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

scholarly journals Architectural marketing capabilities of exporting ventures

2019 ◽  
Vol 36 (6) ◽  
pp. 1026-1041 ◽  
Author(s):  
Vasilis Theoharakis ◽  
Yannis Angelis ◽  
Georgios Batsakis
Keyword(s):  
Financial Performance ◽  
Market Orientation ◽  
Export Performance ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Marketing Capabilities ◽  
Content Type ◽  
Foreign Distributor ◽  
The Impact

Purpose The importance of architectural marketing capabilities (i.e. marketing planning and implementation) in exporting ventures has been recognised. However, extant literature has not taken into account the explicit roles and required synergy between the exporter and their foreign distributor in delivering these capabilities. Drawing from the resource-based theory, the purpose of this paper is to examine the complementarity of distributor implementation capability and market orientation with exporter planning capability. Design/methodology/approach The study was carried out using a survey. Data were collected from 147 Greek exporters who replied to our questionnaire and the hypotheses were tested using the full information maximum likelihood estimation procedure. Findings The results support the hypotheses about the importance of exporter planning capability on financial performance and the complementary role of distributor market orientation. Further, the authors find that the distributor’s implementation capability partially mediates the impact of the exporter’s planning capability on financial performance. Originality/value This study contributes to a better understanding about the complementarity of exporter and distributor capabilities. It demonstrates the crucial role of the distributor in the deployment of architectural capabilities for the export venture: the distributor’s market orientation and implementation capability have the final say in achieving higher levels of export performance.

scholarly journals DECONVOLUTING PREFERENCES AND ERRORS: A MODEL FOR BINOMIAL PANEL DATA

2010 ◽  
Vol 26 (6) ◽  
pp. 1846-1854 ◽  
Author(s):  
Mogens Fosgerau ◽  
Søren Feodor Nielsen
Keyword(s):  
Maximum Likelihood ◽  
Panel Data ◽  
Maximum Likelihood Estimation ◽  
Unknown Parameter ◽  
Random Variables ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Choice Experiments ◽  
Stated Choice ◽  
Stated Choice Experiments

In many stated choice experiments researchers observe the random variablesVt,Xt, andYt= 1{U+δ⊤Xt+ εt<Vt},t≤T, whereδis an unknown parameter andUand εtare unobservable random variables. We show that under weak assumptions the distributions ofUand εtand also the unknown parameterδcan be consistently estimated using a sieved maximum likelihood estimation procedure.

scholarly journals Augmented pseudo-likelihood estimation for two-phase studies

2019 ◽  
Vol 29 (2) ◽  
pp. 344-358
Author(s):  
Claudia Rivera-Rodriguez ◽  
Sebastien Haneuse ◽  
Molin Wang ◽  
Donna Spiegelman
Keyword(s):  
Phase I ◽  
Phase Ii ◽  
Likelihood Estimation ◽  
Weighted Likelihood ◽  
Finite Sample ◽  
Cross Sectional Survey ◽  
Two Phase ◽  
Cross Sectional ◽  
Pseudo Likelihood ◽  
Pseudo Likelihood Estimation

In many public health and medical research settings, information on key covariates may not be readily available or too expensive to gather for all individuals in the study. In such settings, the two-phase design provides a way forward by first stratifying an initial (large) phase I sample on the basis of covariates readily available (including, possibly, the outcome), and sub-sampling participants at phase II to collect the expensive measure(s). When the outcome of interest is binary, several methods have been proposed for estimation and inference for the parameters of a logistic regression model, including weighted likelihood, pseudo-likelihood and maximum likelihood. Although these methods yield consistent estimation and valid inference, they do so solely on the basis of the phase I stratification and the detailed covariate information obtained at phase II. Moreover, they ignore any additional information that is readily available at phase I but was not used as part of the stratified sampling design. Motivated by the potential for efficiency gains, especially concerning parameters corresponding to the additional phase I covariates, we propose a novel augmented pseudo-likelihood estimator for two-phase studies that makes use of all available information. In contrast to recently-proposed weighted likelihood-based methods that calibrate to the influence function of the model of interest, the methods we propose do not require the development of additional models and, therefore, enjoy a degree of robustness. In addition, we expand the broader framework for pseudo-likelihood based estimation and inference to permit link functions for binary regression other than the logit link. Comprehensive simulations, based on a one-time cross sectional survey of 82,887 patients undergoing anti-retroviral therapy in Malawi between 2005 and 2007, illustrate finite sample properties of the proposed methods and compare their performance competing approaches. The proposed method yields the lowest standard errors when the model is correctly specified. Finally, the methods are applied to a large implementation science project examining the effect of an enhanced community health worker program to improve adherence to WHO guidelines for at least four antenatal visits, in Dar es Salaam, Tanzania.

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