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 Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1738
Author(s):  
Selvi Mardalena ◽  
Purhadi Purhadi ◽  
Jerry Dwi Trijoyo Purnomo ◽  
Dedy Dwi Prastyo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Poisson Regression ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Count Response ◽  
The Mean ◽  
Gaussian Regression ◽  
Response Variables

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

scholarly journals Geographically Weighted Multivariate Logistic Regression Model and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
M. Fathurahman ◽  
Purhadi ◽  
Sutikno ◽  
Vita Ratnasari
Keyword(s):  
Logistic Regression ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Multinomial Distribution ◽  
Multivariate Logistic Regression Model ◽  
Ratio Test ◽  
Multivariate Logistic Regression ◽  
Testing Procedures ◽  
Mlr Model

This study investigates the geographically weighted multivariate logistic regression (GWMLR) model, parameter estimation, and hypothesis testing procedures. The GWMLR model is an extension to the multivariate logistic regression (MLR) model, which has dependent variables that follow a multinomial distribution along with parameters associated with the spatial weighting at each location in the study area. The parameter estimation was done using the maximum likelihood estimation and Newton-Raphson methods, and the maximum likelihood ratio test was used for hypothesis testing of the parameters. The performance of the GWMLR model was evaluated using a real dataset and it was found to perform better than the MLR model.

scholarly journals Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Poisson inverse Gaussian regression model

2021 ◽  
Vol 880 (1) ◽  
pp. 012045
Author(s):  
Meylita Sari ◽  
Sutikno ◽  
Purhadi
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Count Data ◽  
Poisson Regression ◽  
Statistical Test ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Test Statistics ◽  
Gaussian Regression

Abstract One of the appropriate methods used to model count data response and its corresponding predictors is Poisson regression. Poisson regression strictly assumes that the mean and variance of response variables should be equal (equidispersion). Nonetheless, some cases of the count data unsatisfied this assumption because variance can be larger than mean (over-dispersion). If overdispersion is violated, causing the underestimate standard error. Furthermore, this will lead to incorrect conclusions in the statistical test. Thus, a suitable method for modelling this kind of data needs to develop. One alternative model to outcome the overdispersion issue in bivariate response variable is the Bivariate Poisson Inverse Gaussian Regression (BPIGR) model. The BPIGR model can produce a global model for all locations. On the other hand, each location and time have different geographic conditions, social, cultural, and economical so that Geographically and Temporally Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR)) is needed. The weighting function spatial-temporal in GTWBPIGR generates a different local model for each period. GTWBPIGR model solves the overdispersion case and generates global models for each period and location. The parameter estimation of the GTWBPIGR model uses the Maximum Likelihood Estimation (MLE) method, followed by Newton Raphson iteration. Meanwhile, the test statistics on the hypothesis testing is simultaneously testing of the GTWBPIGR model is obtained with the Maximum Likelihood Ratio Test (MLRT) approach, using n large samples of the statistical test is chi-square distribution. Moreover, the test statistics for partially testing used the Z-test statistic.

scholarly journals Geographically Weighted Three-Parameters Bivariate Gamma Regression and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 197
Author(s):  
Purhadi ◽  
Anita Rahayu ◽  
Gabriella Hillary Wenur
Keyword(s):  
Maximum Likelihood ◽  
Healthy Lifestyle ◽  
Model Development ◽  
Likelihood Estimation ◽  
Wald Test ◽  
Poor People ◽  
Ratio Test ◽  
Spatial Effects ◽  
Fixed Weight ◽  
Pregnant Mothers

This study discusses model development for response variables following a bivariate gamma distribution using three-parameters, namely shape, scale and location parameters, paying attention to spatial effects so as to produce different parameter estimator values for each location. This model is called geographically weighted bivariate gamma regression (GWBGR). The method used for parameter estimation is maximum-likelihood estimation (MLE) with the Berndt–Hall–Hall-Hausman (BHHH) algorithm approach. Parameter testing consisted of a simultaneous test using the maximum-likelihood ratio test (MLRT) and a partial test using Wald test. The results of GWBGR modeling three-parameters with fixed weight bisquare kernel showed that the variables that significantly affect the rate of infant mortality (RIM) and rate of maternal mortality (RMM) are the percentage of poor people, the percentage of obstetric complications treated, the percentage of pregnant mothers who received Fe3 and the percentage of first-time pregnant mothers under seventeen years of age. While the percentage of households with clean and healthy lifestyle only significant in several regencies and cities.

scholarly journals Comparing of Car-Bym, Generalized Poisson dan Negative Binomial on Tuberculosis Data in Banyumas Districs

2021 ◽  
Vol 5 (1) ◽  
pp. 130-140
Author(s):  
Jajang Jajang ◽  
Budi Pratikno ◽  
Mashuri Mashuri
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Count Data ◽  
Degrees Of Freedom ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Model ◽  
Generalized Poisson ◽  
Central Java ◽  
Area Data

In 2019 the number of people with TB (Tuberculosis) in Banyumas, Central Java, is high (1,910 people have been detected with TB). The number of people infected Tuberculosis (TB) in Banyumas is the count data and it is also the area data. In modeling, the parameter estimation and characteristic of the data need to be considered. Here, we studied comparing Generalized Poisson (GP), negative binomial (NB), and Poisson and CAR.BYM model for TB cases in Banyumas. Here, we use two methods for parameter estimation, maximum likelihood estimation (MLE) and Bayes. The MLE is used for GP and NB models, whereas Bayes is used for Poisson and CAR-BYM. The results showed that Poisson model detected overdispersion where deviance value is 67.38 for 22 degrees of freedom. Therefore, ratio of deviance to degrees of freedom is 3.06 (>1). This indicates that there was overdispersion. The folowing GP, NB, Poisson-Bayes and CAR-BYM are used to modeling TB data in Banyumas and we compare their RMSE. With refer to RMES criteria, we found that CAR-BYM is the best model for modeling TB in Banyumas because its RMSE is smallest.

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.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

Sign in / Sign up

Export Citation Format

Share Document