Academic literature on the topic 'Pseudo-Poisson Maximum Likelihood'

Abstract. Poisson regression is a statistical method used to analyze the relationship between the response variable and the predictor variable where the data from the response variable is in the form of count data and follows the Poisson distribution. Poisson regression is used to model rare or rare events, so that the response variable is very likely to have a value of zero. Poisson regression is a regression model whose response variable is non-negative. Usually, this model fits the linear regression applied to the log-transformed response variable. However, when the response variable data has a value of zero and is modeled using a log-linear model it will create a biased estimator as well as log-linear regression where heteroscedasticity occurs in the response variable will produce a biased parameter estimator. However, the pseudo poisson maximum likelihood (PPML) provides a natural way to deal with the problem. The purpose of this study is to determine the factors that influence leprosy cases in West Java in 2018 using PPML estimates. The results show that health facilities, healthy homes, and health insurance are factors that influence the number of leprosy cases in West Java in 2018. Using the AIC value, it shows that the use of PPML estimates produces better results than the log-linear model.
 Abstrak. Regresi poisson merupakan suatu metode statistika yang digunakan untuk menganalisa hubungan antara variabel respon dengan variabel prediktor dimana data dari variabel respon berbentuk data cacahan atau count data dan mengikuti distribusi poisson. Regresi poisson digunakan untuk memodelkan kejadian langka atau jarang terjadi, sehingga variabel respon sangat memungkinkan memiliki nilai nol. Regresi poisson merupakan model regresi yang variabel responnya bernilai non-negatif. Biasanya, model ini cocok dengan regresi linier yang diterapkan pada variabel respon yang ditransformasikan log. Namun, ketika data variabel respon memiliki nilai nol dan dimodelkan menggunakan model log-linear akan menciptakan suatu penaksir yang bias begitu juga regresi log-linear yang terjadi heteroskedastisitas pada variabel responnya akan menghasilkan suatu penaksir parameter yang bias. Namun, pseudo poisson maximum likelihood (PPML) menyediakan cara alami untuk menangani masalah tersebut. Tujuan penelitian ini yaitu untuk mengetahui faktor yang berpengaruh terhadap kasus kusta di Jawa Barat tahun 2018 menggunakan estimasi PPML. Hasil penelitian menunjukkan bahwa fasilitas kesehatan, rumah sehat, dan jaminan kesehatan menjadi faktor yang berpengaruh terhadap jumlah kasus kusta di Jawa Barat tahun 2018. Dengan menggunakan nilai AIC, menunjukkan bahwa penggunaan estimasi PPML menghasilkan hasil yang lebih baik dari pada model log-linear.

Purpose The purpose of this study is to account for a recent non-mainstream econometric approach using microdata and how it can inform research in business administration. More specifically, the paper draws from the applied microeconometric literature stances in favor of fitting Poisson regression with robust standard errors rather than the OLS linear regression of a log-transformed dependent variable. In addition, the authors point to the appropriate Stata coding and take into account the possibility of failing to check for the existence of the estimates – convergency issues – as well as being sensitive to numerical problems. Design/methodology/approach The author details the main issues with the log-linear model, drawing from the applied econometric literature in favor of estimating multiplicative models for non-count data. Then, he provides the Stata commands and illustrates the differences in the coefficient and standard errors between both OLS and Poisson models using the health expenditure dataset from the RAND Health Insurance Experiment (RHIE). Findings The results indicate that the use of Poisson pseudo maximum likelihood estimators yield better results that the log-linear model, as well as other alternative models, such as Tobit and two-part models. Originality/value The originality of this study lies in demonstrating an alternative microeconometric technique to deal with positive skewness of dependent variables.

COVID-19 country spikes have been reported at varying temporal scales as a result of differences in the disease-driving factors. Factors affecting case load and mortality rates have varied between countries and regions. We investigated the association between socio-economic, weather, demographic and health variables with the reported cases of COVID-19 in Eswatini using the maximum likelihood estimation method for count data. A generalized Poisson regression (GPR) model was fitted with the data comprising 15 covariates to predict COVID-19 risk in the whole of Eswatini. The results show that the variables that were key determinants in the spread of the disease were those that included the proportion of elderly above 55 years at 98% (95% CI: 97–99%) and the proportion of youth below the age of 35 years at 8% (95% CI: 1.7–38%) with a pseudo R-square of 0.72. However, in the early phase of the virus when cases were fewer, results from the Poisson regression showed that household size, household density and poverty index were associated with reported COVID-19 cases in the country. We then produced a disease-risk map of predicted COVID-19 in Eswatini using variables that were selected by the regression model at a 5% significance level. The map could be used by the country to plan and prioritize health interventions against COVID-19. The identified areas of high risk may be further investigated to find out the risk amplifiers and assess what could be done to prevent them.

In this article, we present ppmlhdfe, a new command for estimation of (pseudo-)Poisson regression models with multiple high-dimensional fixed effects (HDFE). Estimation is implemented using a modified version of the iteratively reweighted least-squares algorithm that allows for fast estimation in the presence of HDFE. Because the code is built around the reghdfe package ( Correia, 2014 , Statistical Software Components S457874, Department of Economics, Boston College), it has similar syntax, supports many of the same functionalities, and benefits from reghdfe‘s fast convergence properties for computing high-dimensional leastsquares problems. Performance is further enhanced by some new techniques we introduce for accelerating HDFE iteratively reweighted least-squares estimation specifically. ppmlhdfe also implements a novel and more robust approach to check for the existence of (pseudo)maximum likelihood estimates.