scholarly journals A STUDY OF GENERALIZED LINEAR MIXED MODEL FOR COUNT DATA USING HIERARCHICAL BAYES METHOD

2021 ◽  
Vol 14 (2) ◽  
pp. 194-205
Author(s):  
Etis Sunandi ◽  
Khairil Anwar Notodiputro ◽  
Bagus Sartono
Keyword(s):  
Count Data ◽  
Linear Mixed Model ◽  
Hierarchical Bayes ◽  
Estimation Methods ◽  
Model Parameters ◽  
Normal Model ◽  
Parameter Estimator ◽  
Bayes Method ◽  
West Java ◽  
Log Normal

Poisson Log-Normal Model is one of the hierarchical mixed models that can be used for count data. Several estimation methods can be used to estimate the model parameters. The first objective of this study was to examine the performance of the parameter estimator and model built using the Hierarchical Bayes method via Markov Chain Monte Carlo (MCMC) with simulation. The second objective was applied the Poisson Log-Normal model to the West Java illiteracy Cases data which is sourced from the Susenas data on March 2019. In 2019, the incidence of illiteracy is a very rare occurrence in West Java Province. So that, it is suitable as an application case in this study. The simulation results showed that the Hierarchical Bayes parameter estimator through MCMC has the smallest Root Mean Squared Error of Prediction (RMSEP) value and the absolute bias is relatively mostly similar when compared to the Maximum Likelihood (ML) and Penalized Quasi-Likelihood (PQL) methods. Meanwhile, the empirical results showed that the fixed variable is the number of respondents who have a maximum education of elementary school have the greatest risk of illiteracy. Also, the diversity of census blocks significantly affects illiteracy cases in West Java 2019.

scholarly journals Characterization of the Log-Normal Model for Received Signal Strength Measurements in Real Wireless Sensor Networks

2020 ◽  
Vol 9 (1) ◽  
pp. 12 ◽  
Author(s):  
José Vallet García
Keyword(s):  
Empirical Studies ◽  
Path Loss ◽  
Signal Strength ◽  
Received Signal Strength ◽  
Wireless Sensor ◽  
Model Parameters ◽  
Normal Model ◽  
Path Loss Exponent ◽  
Localization Algorithms ◽  
Log Normal

Using the classical received signal strength (RSS)-distance log-normal model in wireless sensor network (WSN) applications poses a series of characteristic challenges derived from (a) the model’s structural limitations when it comes to explaining real observations, (b) the inherent hardware (HW) variability typically encountered in the low-cost nodes of WSNs, and (c) the inhomogeneity of the deployment environment. The main goal of this article is to better characterize how these factors impact the model parameters, an issue that has received little attention in the literature. For that matter, I qualitatively elaborate on their effects and interplay, and present the results of two quantitative empirical studies showing how much the parameters can vary depending on (a) the nodes used in the model identification and their position in the environment, and (b) the antenna directionality. I further show that the path loss exponent and the reference power can be highly correlated. In view of all this, I argue that real WSN deployments are better represented by random model parameters jointly accounting for HW and local environmental characteristics, rather than by deterministic independent ones. I further argue that taking this variability into account results in more realistic models and plausible results derived from their usage. The article contains example values of the mean and standard deviation of the model parameters, and of the correlation between the path loss exponent and the reference power. These can be used as a guideline in other studies. Given the sensitivity of localization algorithms to the proper model selection and identification demonstrated in the literature, the structural limitations of the log-normal model, the variability of its parameters and their interrelation are all relevant aspects that practitioners need to be aware of when devising optimal localization algorithms for real WSNs that rely on this popular model.

scholarly journals Logit-normal mixed model for Indian monsoon precipitation

2014 ◽  
Vol 21 (5) ◽  
pp. 939-953
Author(s):  
L. R. Dietz ◽  
S. Chatterjee
Keyword(s):  
Mixed Model ◽  
Linear Mixed Model ◽  
Indian Monsoon ◽  
Extreme Rainfall ◽  
Estimation Methods ◽  
Underlying Structure ◽  
Normal Model ◽  
Monsoon Precipitation ◽  
Tuning Parameters ◽  
Climatic Event

Abstract. Describing the nature and variability of Indian monsoon precipitation is a topic of much debate in the current literature. We suggest the use of a generalized linear mixed model (GLMM), specifically, the logit-normal mixed model, to describe the underlying structure of this complex climatic event. Four GLMM algorithms are described and simulations are performed to vet these algorithms before applying them to the Indian precipitation data. The logit-normal model was applied to light, moderate, and extreme rainfall. Findings indicated that physical constructs were preserved by the models, and random effects were significant in many cases. We also found GLMM estimation methods were sensitive to tuning parameters and assumptions and therefore, recommend use of multiple methods in applications. This work provides a novel use of GLMM and promotes its addition to the gamut of tools for analysis in studying climate phenomena.

Analyzing discontinuities in longitudinal count data: A multilevel generalized linear mixed model.

2020 ◽  
Author(s):  
James L. Peugh ◽  
Sarah J. Beal ◽  
Meghan E. McGrady ◽  
Michael D. Toland ◽  
Constance Mara
Keyword(s):  
Count Data ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Generalized Linear Mixed Model ◽  
Longitudinal Count Data

scholarly journals Comparing Bayesian Spatial Conditional Overdispersion and the Besag–York–Mollié Models: Application to Infant Mortality Rates

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 282
Author(s):  
Mabel Morales-Otero ◽  
Vicente Núñez-Antón
Keyword(s):  
Infant Mortality ◽  
Count Data ◽  
Spatial Dependence ◽  
Poisson Model ◽  
Mortality Rates ◽  
Estimation Methods ◽  
Neighborhood Structure ◽  
Specific Context ◽  
Count Data Models ◽  
Conditional Mean

In this paper, we review overdispersed Bayesian generalized spatial conditional count data models. Their usefulness is illustrated with their application to infant mortality rates from Colombian regions and by comparing them with the widely used Besag–York–Mollié (BYM) models. These overdispersed models assume that excess of dispersion in the data may be partially caused from the possible spatial dependence existing among the different spatial units. Thus, specific regression structures are then proposed both for the conditional mean and for the dispersion parameter in the models, including covariates, as well as an assumed spatial neighborhood structure. We focus on the case of response variables following a Poisson distribution, specifically concentrating on the spatial generalized conditional normal overdispersion Poisson model. Models were fitted by making use of the Markov Chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximation (INLA) algorithms in the specific context of Bayesian estimation methods.

scholarly journals Flexible models for overdispersed and underdispersed count data

2021 ◽  
Author(s):  
Dexter Cahoy ◽  
Elvira Di Nardo ◽  
Federico Polito
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Hypergeometric Functions ◽  
Natural Generalization ◽  
Model Parameters ◽  
Probability Models ◽  
Limiting Behavior ◽  
Poisson Models ◽  
Special Cases ◽  
Flexible Models

AbstractWithin the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard Poisson distribution. We derive some properties of gfPd and more specifically we study moments, limiting behavior and other features of fPd. The skewness suggests that fPd can be left-skewed, right-skewed or symmetric; this makes the model flexible and appealing in practice. We apply the model to real big count data and estimate the model parameters using maximum likelihood. Then, we turn to the very general class of weighted Poisson distributions (WPD’s) to allow both overdispersion and underdispersion. Similarly to Kemp’s generalized hypergeometric probability distribution, which is based on hypergeometric functions, we analyze a class of WPD’s related to a generalization of Mittag–Leffler functions. The proposed class of distributions includes the well-known COM-Poisson and the hyper-Poisson models. We characterize conditions on the parameters allowing for overdispersion and underdispersion, and analyze two special cases of interest which have not yet appeared in the literature.

scholarly journals Experimental Verification of Real-Time Flow-Rate Estimations in a Tilting-Ladle-Type Automatic Pouring Machine

2021 ◽  
Vol 11 (15) ◽  
pp. 6701
Author(s):  
Yuta Sueki ◽  
Yoshiyuki Noda
Keyword(s):  
Real Time ◽  
Molten Metal ◽  
Flow Rate ◽  
Kalman Filters ◽  
Estimation Method ◽  
Estimation Methods ◽  
Liquid Volume ◽  
Model Parameters ◽  
Rate Estimation ◽  
Time Flow

This paper discusses a real-time flow-rate estimation method for a tilting-ladle-type automatic pouring machine used in the casting industry. In most pouring machines, molten metal is poured into a mold by tilting the ladle. Precise pouring is required to improve productivity and ensure a safe pouring process. To achieve precise pouring, it is important to control the flow rate of the liquid outflow from the ladle. However, due to the high temperature of molten metal, directly measuring the flow rate to devise flow-rate feedback control is difficult. To solve this problem, specific flow-rate estimation methods have been developed. In the previous study by present authors, a simplified flow-rate estimation method was proposed, in which Kalman filters were decentralized to motor systems and the pouring process for implementing into the industrial controller of an automatic pouring machine used a complicatedly shaped ladle. The effectiveness of this flow rate estimation was verified in the experiment with the ideal condition. In the present study, the appropriateness of the real-time flow-rate estimation by decentralization of Kalman filters is verified by comparing it with two other types of existing real-time flow-rate estimations, i.e., time derivatives of the weight of the outflow liquid measured by the load cell and the liquid volume in the ladle measured by a visible camera. We especially confirmed the estimation errors of the candidate real-time flow-rate estimations in the experiments with the uncertainty of the model parameters. These flow-rate estimation methods were applied to a laboratory-type automatic pouring machine to verify their performance.

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