gidm: A command for generalized inflated discrete models

2019 ◽  
Vol 19 (3) ◽  
pp. 698-718
Author(s):  
Yiwei Xia ◽  
Yisu Zhou ◽  
Tianji Cai
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Discrete Distributions ◽  
Discrete Models

In this article, we describe the gidm command for fitting generalized inflated discrete models that deal with multiple inflated values in a distribution. Based on the work of Cai, Xia, and Zhou (Forthcoming, Sociological Methods & Research: Generalized inflated discrete models: A strategy to work with multimodal discrete distributions), generalized inflated discrete models are fit via maximum likelihood estimation. Specifically, the gidm command fits Poisson, negative binomial, multinomial, and ordered outcomes with more than one inflated value. We illustrate this command through examples for count and categorical outcomes.

scholarly journals Identifying Stabilising Effects on Survey Based Life Satisfaction Using Quasi-maximum Likelihood Estimation

2021 ◽  
Author(s):  
Johannes Klement
Keyword(s):  
Life Satisfaction ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Measurement Instrument ◽  
Likelihood Estimation ◽  
Satisfaction Scale ◽  
Quasi Maximum Likelihood ◽  
The Stability

AbstractTo which extent do happiness correlates contribute to the stability of life satisfaction? Which method is appropriate to provide a conclusive answer to this question? Based on life satisfaction data of the German SOEP, we show that by Negative Binomial quasi-maximum likelihood estimation statements can be made as to how far correlates of happiness contribute to the stabilisation of life satisfaction. The results show that happiness correlates which are generally associated with a positive change in life satisfaction, also stabilise life satisfaction and destabilise dissatisfaction with life. In such as they lower the probability of leaving positive states of life satisfaction and increase the probability of leaving dissatisfied states. This in particular applies to regular exercise, volunteering and living in a marriage. We further conclude that both patterns in response behaviour and the quality of the measurement instrument, the life satisfaction scale, have a significant effect on the variation and stability of reported life satisfaction.

scholarly journals Maximum Likelihood Estimation of Functionals of Discrete Distributions

2017 ◽  
Vol 63 (10) ◽  
pp. 6774-6798 ◽  
Author(s):  
Jiantao Jiao ◽  
Kartik Venkat ◽  
Yanjun Han ◽  
Tsachy Weissman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Discrete Distributions

scholarly journals On Poisson-Weighted Lindley Distribution and Its Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 1-13
Author(s):  
R. Shanker ◽  
K. K. Shukla
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial Distribution ◽  
Goodness Of Fit ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Poisson Mixture ◽  
Lindley Distribution ◽  
Generalized Poisson ◽  
And Behavior

In this paper the nature and behavior of its coefficient of variation, skewness, kurtosis and index of dispersion of Poisson- weighted Lindley distribution (P-WLD), a Poisson mixture of weighted Lindley distribution, have been proposed and the nature and behavior have been explained graphically. Maximum likelihood estimation has been discussed to estimate its parameters. Applications of the proposed distribution have been discussed and its goodness of fit has been compared with Poisson distribution (PD), Poisson-Lindley distribution (PLD), negative binomial distribution (NBD) and generalized Poisson-Lindley distribution (GPLD).

Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (4) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

Recurrence formula and the maximum likelihood estimation of the age in a simple branching process

1982 ◽  
Vol 19 (04) ◽  
pp. 776-784 ◽  
Author(s):  
M. Adès ◽  
J.-P. Dion ◽  
G. Labelle ◽  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimate ◽  
Branching Process ◽  
Negative Binomial ◽  
Recurrence Formula ◽  
Likelihood Estimation ◽  
Likelihood Estimate ◽  
Offspring Distribution ◽  
Watson Process

In this paper, we consider a Bienaymé– Galton–Watson process {Xn ; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p 0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p 0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.

scholarly journals Estimasi Model Regresi Binomial Negatif Bivariat (BNBR) Pada Penderita Kusta di Jawa Timur

2019 ◽  
Vol 5 (2) ◽  
pp. 29-38
Author(s):  
WIGID HARIADI ◽  
Sulantari Sulantari
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Regression Model ◽  
Negative Binomial ◽  
Likelihood Estimation ◽  
Negative Binomial Regression ◽  
Predictor Variables ◽  
Negative Binomial Regression Model ◽  
Variable Ratio ◽  
Newton Raphson

Abstract. One of the methods used to overcome overdispersion in poisson regression model is a bivariate negative binomial regression model also known as BNBR Model. Leprosy is a dangerous infectious disease, because it can cause paralysis. Leprosy is divided into 2 types, namely is a leprosy Pausibasilier(PB) type and leprosy Multibasilier (MB) type. Where PB type leprosy is a dry leprosy and MB type leprosy is a wet leprosy. Analysis of the data used to model the number of PB leprosy and MB leprosy cases and find out what factor influence it in East Java, the writer uses the BNBR models. Parameter estimation of the BNBR model uses to Maximum likelihood estimation (MLE) methods with Newton-Raphson iteration as well as testing the hypothesis using MLRT methods. After regression analysis, the results are obtained that of the 10 predictor variables tested, both in PB leprosy and MB leprosy, there are 3 predictor variables that are not significant in the model, namely are: variable percentage of poor population, variable ratio of population who did not graduated SMA, and variable ratio of health facilities. Abstrak. Salah satu metode yang digunakan untuk mengatasi overdispersi dalam regresi Poisson yakni dengan regresi binomial negatif bivariat atau dikenal juga dengan model regresi BNBR. Penyakit Kusta adalah salah satu penyakit menular yang berbahaya, karena dapat menyebabkan kelumpuhan. Jenis penyakit kusta terbagi menjadi 2, yakni Kusta tipe Pausibasiler (PB) dan tipe Multibasiler.(MB). Dimana kusta tipe PB merupakan Kusta kering, dan kusta tipe MB adalah kusta basah. Analisis data yang digunakan untuk memodelkan besarnya jumlah kasus kusta tipePB dan tipe MB, kemudian untuk mengetahui faktor apa saja yang mempengaruhinya di Jawa Timur, penulis menggunakan model BNBR. Penaksiran parameter model BNBR menggunakan Maximum Likelihood Estimation (MLE) dengan iterasi Newton-Raphson serta melakukan pengujian hipotesis menggunakan metode MLRT. Setelah dilakukan analisis regresi, diperoleh hasil bahwa dari 10 variabel prediktor yang diujikan, baik pada kusta tipe PB maupun tipe MB, terdapat 3 variabel prediktor yang tidak signifikan dalam model, yakni: variabel presentase penduduk miskin, variabel rasio penduduk yang tidak tamat SMA, dan variabel rasio sarana kesehatan.

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