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 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 geographically and temporally weighted bivariate Gamma regression model

2021 ◽  
Vol 880 (1) ◽  
pp. 012044
Author(s):  
Desy Wasani ◽  
Purhadi ◽  
Sutikno
Keyword(s):  
Maximum Likelihood ◽  
Panel Data ◽  
Gamma Distribution ◽  
Likelihood Estimation ◽  
Complete Information ◽  
Model Parameters ◽  
Large Sample Size ◽  
Ratio Test ◽  
Spatial Effects ◽  
Test Statistic

Abstract Geographically Weighted Regression (GWR) study potential relationships in regression models that distinguish geographic spaces using non-stationary parameters to overcome spatial effects. The use of gamma regression, namely regression with the dependent variable with a gamma distribution, can be an alternative if the data do not follow a normal distribution. Gamma distribution is a continuous set of non-negative values, generally skewed to the right or positive skewness. Gamma regression is developed to be Bivariate Gamma Regression (BGR) when there are two dependent variables with gamma distribution. If the observation units are location points, spatial effects may occur. The Geographically Weighted Bivariate Gamma Regression (GWBGR) model can be a solution for spatial heterogeneity. However, during its development, many cases require information from panel data. Using panel data can provide complete information because it covers several periods, but it allows for temporal effects. This study developed a Geographically and Temporally Weighted Bivariate Gamma Regression (GTWBGR) model to handle spatial and temporal heterogeneity simultaneously. The estimation of the GTWBGR model parameters uses the Maximum Likelihood Estimation (MLE) method that followed by the numerical iteration of Berndt Hall Hall Hausman (BHHH). The simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT) method to get a test statistic. With a large sample size, the distribution of the test statistic approaches chi-square. Meanwhile, partial testing uses the Z test statistic.

Catch-–effort maximum likelihood estimation of important population parameters

1997 ◽  
Vol 54 (4) ◽  
pp. 890-897 ◽  
Author(s):  
W R Gould ◽  
K H Pollock
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Regression Models ◽  
Model Development ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Linear Regression Models ◽  
Estimation Of Parameters ◽  
Regression Methods ◽  
Regression Techniques

The relative ease with which linear regression models are understood explains the popularity of such techniques in estimating population size with catch-effort data. However, the development and use of the regression models require assumptions and approximations that may not accurately reflect reality. We present the model development necessary for maximum likelihood estimation of parameters from catch-effort data using the program SURVIV, the primary intent being to present biologists with a vehicle for producing maximum likelihood estimates in lieu of using the traditional regression techniques. The differences between the regression approaches and maximum likelihood estimation will be illustrated with an example of commercial fishery catch-effort data and through simulation. Our results indicate that maximum likelihood estimation consistently provides less biased and more precise estimates than the regression methods and allows for greater model flexibility necessary in many circumstances. We recommend the use of maximum likelihood estimation in future catch-effort studies.

Parametric estimation and inference

2019 ◽  
pp. 165-185
Author(s):  
M. D. Edge
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Function ◽  
Maximum Likelihood Estimators ◽  
Wald Test ◽  
Parametric Model ◽  
Parametric Estimation ◽  
Ratio Test ◽  
Sampling Variance ◽  
Squared Error Loss Function ◽  
Squared Error

If it is reasonable to assume that the data are generated by a fully parametric model, then maximum-likelihood approaches to estimation and inference have many appealing properties. Maximum-likelihood estimators are obtained by identifying parameters that maximize the likelihood function, which can be done using calculus or using numerical approaches. Such estimators are consistent, and if the costs of errors in estimation are described by a squared-error loss function, then they are also efficient compared with their consistent competitors. The sampling variance of a maximum-likelihood estimate can be estimated in various ways. As always, one possibility is the bootstrap. In many models, the variance of the maximum-likelihood estimator can be derived directly once its form is known. A third approach is to rely on general properties of maximum-likelihood estimators and use the Fisher information. Similarly, there are many ways to test hypotheses about parameters estimated by maximum likelihood. This chapter discusses the Wald test, which relies on the fact that the sampling distribution of maximum-likelihood estimators is normal in large samples, and the likelihood-ratio test, which is a general approach for testing hypotheses relating nested pairs of models.

scholarly journals Detecting Differential Item Functioning Using the Logistic Regression Procedure in Small Samples

2016 ◽  
Vol 41 (1) ◽  
pp. 30-43 ◽  
Author(s):  
Sunbok Lee
Keyword(s):  
Logistic Regression ◽  
Maximum Likelihood ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Wald Test ◽  
Small Samples ◽  
Ratio Test ◽  
Chi Square ◽  
Ml Estimation ◽  
Item Functioning

The logistic regression (LR) procedure for testing differential item functioning (DIF) typically depends on the asymptotic sampling distributions. The likelihood ratio test (LRT) usually relies on the asymptotic chi-square distribution. Also, the Wald test is typically based on the asymptotic normality of the maximum likelihood (ML) estimation, and the Wald statistic is tested using the asymptotic chi-square distribution. However, in small samples, the asymptotic assumptions may not work well. The penalized maximum likelihood (PML) estimation removes the first-order finite sample bias from the ML estimation, and the bootstrap method constructs the empirical sampling distribution. This study compares the performances of the LR procedures based on the LRT, Wald test, penalized likelihood ratio test (PLRT), and bootstrap likelihood ratio test (BLRT) in terms of the statistical power and type I error for testing uniform and non-uniform DIF. The result of the simulation study shows that the LRT with the asymptotic chi-square distribution works well even in small samples.

scholarly journals Regresi Logistik untuk Pemodelan Indeks Pembangunan Kesehatan Masyarakat Kabupaten/Kota di Pulau Kalimantan

2018 ◽  
Author(s):  
Muhammad Fathurahman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Likelihood Estimation ◽  
Ratio Test ◽  
Chi Square ◽  
Fisher Scoring

Regresi logistik merupakan model regresi yang paling sering digunakan untuk pemodelan data kategorik. Pada penelitian ini dilakukan pemodelan regresi logistik dan penerapannya pada Indeks Pembangunan Kesehatan Masyarakat (IPKM) kabupaten/kota di Pulau Kalimantan tahun 2013. Metode Maximum Likelihood Estimation (MLE) digunakan untuk penaksiran parameter. Metode Likelihood Ratio Test (LRT) dan uji Wald digunakan untuk pengujian parameter. Hasil penelitian menunjukkan bahwa penaksir parameter dengan metode MLE berbentuk fungsi yang tidak eksplisit. Sehingga digunakan pendekatan numerik dengan metode Fisher Scoring. Berdasarkan metode LRT dan uji Wald, statistik uji untuk pengujian parameter mendekati distribusi chi-square dan distribusi normal standar. Berdasarkan model regresi logistik terbaik, faktor-faktor yang berpengaruh terhadap IPKM kabupaten/kota di Pulau Kalimantan tahun 2013 adalah Indeks Pembangunan Manusia (IPM), tingkat kepadatan penduduk dan persentase penduduk miskin.

A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽  
2005 ◽  
Vol 1 (2) ◽  
pp. 81-85 ◽  
Author(s):  
Stefan C. Schmukle ◽  
Jochen Hardt
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Null Model ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Fit Indices ◽  
Cautionary Note ◽  
Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

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