ICSA - International Conference on Statistics and Analytics 2019

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Secretariat of ICSA 2019 — Fri, 26 Feb 2021 00:00:00 +0000

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Preface

Secretariat of ICSA 2019 — Fri, 26 Feb 2021 00:00:00 +0000

Preface

Comparison of Poisson and Quasi-Poisson Regression: A Simulation study

A Gabriella, S Abdullah, S M Soemartojo — Fri, 26 Feb 2021 00:00:00 +0000

Poisson regression is often used to model count data. However, it requires the assumption of equidispersion which not always met in the real application data. Quasi-Poisson can be considered as an alternative to handle this problem. The objective of this essay is to explain about the Quasi-Poisson regression, the likelihood construction, parameter estimation, and its implementation in real life data. The numerical method used in this study is Newton-Raphson which is equivalent to Iterative Weighted Least Square (IWLS) at the end of calculation. The simulation results for the data with the above problem showed that, in case of overdispersion, Quasi-Poisson regression with Maximum Quasi-Likelihood method provided a good fit to the data compared to Poisson regression.

Identification of Factors Affecting Tuberculosis in West Java using Spatial Modeling

Yusma Yanti, Septian Rahardiantoro — Fri, 26 Feb 2021 00:00:00 +0000

Tuberculosis (TB) is an infectious disease caused by the bacillus Mycobacterium tuberculosis. In 2017 WHO records there are 1.7 billion TB sufferers in the world. Whereas in the same year TB sufferers in Indonesia reached 421 thousand cases and 10 thousand of them were in the province of West Java. In this study, the factors that suspected to influence TB include poverty, population density and malnutrition were analyzed by looking at the spatial aspects. In addition to these factors, smoking and consuming alcoholic beverages can also trigger TB. The method used was Spatial Autoregressive Model (SARM), Spatial Error Model (SEM), and Generalized Spatial Model (GSM), then the best model is chosen based on the best criteria of lagrange multiplayer test. The result indicated that SEM performed better than others, with the following significant variables were malnutrition and unemployment factor.

Group Lasso for Identifying Tuberculosis Influenced Factors in West Java

Septian Rahardiantoro, Anang Kurnia — Fri, 26 Feb 2021 00:00:00 +0000

Tuberculosis (TB) is a disease caused by bacteria that can affect serious infection in the lungs. It can spread from one person to another through tiny droplets released into the air via coughs and sneezes. West Java is one of the locations with the largest TB sufferer in Indonesia. This research used the number of TB cases data in West Java 2017 to identify group of factors that can influence TB infections. The group factors applied include health factor, environment factor, health facility factor, and demography factor. The method that used in this research was group lasso. After the group factors have been identified, the ordinary least square applied to determine significant factors to affect TB infections based on these group factors. The selected group factors of this research was health factor, environment factor, and health facility factor significant to influence TB cases. Furthermore, number of diarrhea sufferers, unemployment, and number of malnutrition sufferers were significant to be the variables that important to affect the TB cases in West Java based on ordinary least square.

Identification of New Positive Tuberculosis Cases in Aceh Besar District Using Ordinary Criging

Zurnila Marli Kesuma, Latifah Rahayu, Aja Fatimah Zohra — Fri, 26 Feb 2021 00:00:00 +0000

Tuberculosis is a contagious infectious disease caused by Mycobacterium tuberculosis. The risk level of transmission of pulmonary tuberculosis with positive smear of acid-resistant bacteria (BTA). BTA is greater hight risk than pulmonary tuberculosis with negative smear. This study aims to predict areas of the number of new BTA positive tuberculosis cases in Aceh Besar district spatially using the kriging method. The data used are secondary data coordinate the point of the number of new cases of positive smear tuberculosis in each puskesmas in the province of Aceh in 2015-2017. The experimental semivariogram calculation is the first step in estimating using ordinary kriging, which is a reference for getting the parameters to be used in theoretical semivariogram calculations. In this case, the semivariogram suitable for new cases of smear positive tuberculosis is the one of the Spherical model. The sill value used is 126.530, the nugget=62, while the range used is based on the distance of each class = 0.158. The results of the analysis showed that the regions with the lowest positive BTA Tuberculosis prediction cases were around Pulo Aceh Sub-District, Montasik Sub-District, and Indrapuri Sub-District, with less than 15 cases. Whereas the region with the most positive predictions of new cases of BTA Tuberculosis was around Baitussalam Sub-District and Jantho City, with more than 30 cases.

Zero-truncated Poisson-Lindley distribution

Afida Nurul Hilma, Dian Lestari, Sindy Devila — Fri, 26 Feb 2021 00:00:00 +0000

In order to find a counting distribution that can handle the condition when the data has no zero-count. Distribution named Zero-truncated Poisson-Lindley distribution is developed. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero-truncated Poisson-Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method. Then, the application of the model to real data is given.

Completeness of P-Summable as Hilbert Space with Its Dual Space

Muhammad Ryan Sanusi, Endang Rusyaman, Diah Chaerani — Fri, 26 Feb 2021 00:00:00 +0000

Hilbert space is a complete inner product space, meaning that each Cauchy sequence converges to a point in that space. One of the vector spaces that will be examined as the inner product space is p-summable space. The inner product space is a subset of vector spaces that have special properties that must be fulfilled. One way to prove vector space is the inner product space is to use parallelogram equality theorems. After it is known that the vector space is the inner product space, the completeness of the space will be proven using the dual space. The space used is the p-summable space, data that can be changed in a sequence form will be usable in this study. The results of this study will be useful as another application in determining a Hilbert space by using a method that is different from the definition. The analysis used will show comparison of the speed of completion accuracy will be a benchmark in this study, so that will be a new reference in determining a space is Hilbert space.

Hurdle Negative Binomial Regression Model

Ayu Andika, Sarini Abdullah, Siti Nurrohmah — Fri, 26 Feb 2021 00:00:00 +0000

Poisson regression is a common regression model used for count data with equidispersion. However, in real data application, overdispersion often encountered, suggesting the seek for alternative model to the Poisson regression. In overdispersion data due to excess zeros and additional overdispersion in positive values, one of alternative model that can be used is hurdle negative binomial model. Hurdle negative binomial model is a two-part model consists of binary model and zero-truncated negative binomial model. In this study we discuss hurdle negative binomial model and Bayesian approach for the model’s parameter estimation, then apply the method for modelling frequency of motoric complication in people with early Parkinson’s disease. Markov Chain Monte Carlo with Gibbs Sampling (MCMC-GS) was implemented to sample the regression parameters from their posterior distribution. The result showed that hurdle negative binomial model fit the data satisfactorily, as implied by the convergence and unimodality of posterior density of the parameters of interest. We also identified risk factors for motoric complications.

Truncated Spline Estimation of Percentage Poverty Modeling in Papua Province

Ni Putu Ayu Mirah Mariati, Nyoman Budiantara, Vita Ratnasari — Fri, 26 Feb 2021 00:00:00 +0000

In estimating the regression curve there are three approaches, namely parametric regression, nonparametric regression and semiparametric regression. Nonparametric regression approach has high flexibility. Nonparametric regression approach that is quite popular is Truncated Spline. Truncated Spline is a polynomial pieces which have segmented and continuous. One of the advantages of Spline is that it can handle data that changes at certain sub intervals, so this model tends to search for data estimates wherever the data pattern moves and there are points of knots. In reality, data patterns often change at certain sub intervals, one of which is data on poverty in the Papua Province. Papua Province is ranked first in the percentage of poor people in Indonesia. The best of model Truncated Spline in nonparametric regression for the poverty model in Papua Province is using a combination of knot.

Cox Piecewise Constant Hazard Model with Bayesian Method

Amanda Putri Tiyas Pratiwi, Sarini Abdullah, Ida Fithriani — Fri, 26 Feb 2021 00:00:00 +0000

Cox PH model is one of the survival models that is widely used for analyzing time-to-event data. Cox PH model consists of two main components, the baseline hazard consisting of time-dependent component; and the exponential function accomodating explanatory variables. The baseline hazard is not estimated in the Cox PH model, thus not accommodating the need for hazard rate estimation. Therefore, in this paper we discuss the estimation of baseline hazard through piecewise constant hazard using Bayesian method. Gamma distribution is assumed for the piecewise constant baseline hazard, and normal distribution is assumed for the regression coefficient. Sampling from the posterior is conducted using Markov chain Monte Carlo through Gibbs sampling. Echocardiogram data containing 106 observations and 6 explanatory variables were used in analysis. The result showed that the baseline hazard functions were estimated and each of parameters in the model is converged as shown by the trace plot and posterior density plot.

Estimation Curve Semiparametric Regression with the Spline Linear Approach to Poverty Data in Bali Province

I Wayan Sudiarsa — Fri, 26 Feb 2021 00:00:00 +0000

In semiparametric regression, nonparametric components can be approached by spline. Splines are pieces of polynomial that are segmented and continuous. The one advantages of spline is the presence of knot points that indicate changes in the pattern of data behavior. This research purposetoobtain semiparametric regression curve estimation with linear spline approach. The method of optimization approach used by ordinary least square (OLS). Based on this research, there are two variables that have a significant effect on the percentage of poor people in Bali Province, namely the Open Unemployment the rate of economic growth. The total variance of response that can be explained by predictor in this model is 67.97% with MSE of 9.7854.

An Alternative Distribution for Modelling Overdispersion Count Data: Poisson Shanker Distribution

A Meytrianti, S Nurrohmah, M Novita — Fri, 26 Feb 2021 00:00:00 +0000

Poisson distribution is a common distribution for modelling count data with assumption mean and variance has the same value (equidispersion). In fact, most of the count data have mean that is smaller than variance (overdispersion) and Poisson distribution cannot be used for modelling this kind of data. Thus, several alternative distributions have been introduced to solve this problem. One of them is Shanker distribution that only has one parameter. Since Shanker distribution is continuous distribution, it cannot be used for modelling count data. Therefore, a new distribution is offered that is Poisson-Shanker distribution. Poisson-Shanker distribution is obtained by mixing Poisson and Shanker distribution, with Shanker distribution as the mixing distribution. The result is a mixture distribution that has one parameter and can be used for modelling overdispersion count data. In this paper, we obtain that Poisson-Shanker distribution has several properties are unimodal, overdispersion, increasing hazard rate, and right skew. The first four raw moments and central moments have been obtained. Maximum likelihood is a method that is used to estimate the parameter, and the solution can be done using numerical iterations. A real data set is used to illustrate the proposed distribution. The characteristics of the Poisson-Shanker distribution parameter is also obtained by numerical simulation with several variations in parameter values and sample size. The result is MSE and bias of the estimated parameter theta will increase when the parameter value rises for a value of n and will decrease when the value of n rises for a parameter value.

Beta-Burr Type X Distribution with Application to Luteinizing Hormone Data

A A D Ikram, S Nurrohmah, I Fithriani — Fri, 26 Feb 2021 00:00:00 +0000

Beta-Burr Type X distribution is a three parameter distribution and can model right skewed, left skewed, and symmetric data. Beta-Burr Type X distribution is the result of composition distribution functions of beta distribution and Burr Type X distribution. In this study, the characteristics such as probability density function (PDF), cumulative distribution function (CDF), the r-th moment, mean, and variance are presented. The maximum likelihood method is used to estimate the parameters of Beta-Burr Type X distribution, and the solution is obtained using a numerical method. As an illustration, Beta-Burr Type X distribution is used to model the data of luteinizing hormone in female blood samples.

Alpha Power Transformed Lindley Distribution

L A Rosa, S Nurrohmah, I Fithriani — Fri, 26 Feb 2021 00:00:00 +0000

The one parameter Lindley distribustion (theta) has been widely used in various field such as biology, technique, medical, and industries. Lindley distribution is capable for modelling data with monotone increasing hazard rate. However, in real life, there are situations where the hazard rate is not monotone. Therefore, to enhance the Lindley distribution capabilities
for modelling data, a modification can be used by using Alpha Power Transformed method. The result of the modification of Lindley distribution is commonly called Alpha Power Transformed Lindley distribution (APTL) distribution that has two parameters (alpha, theta). This new APTL distribution is appropriate in modelling data with decreasing or unimodal shaped of probability density function, and has hazard rates with increasing, decreasing, and upside-down bathtub shaped. The properties of the proposed distribution are discussed include probability density function, cumulative distribution function, survival function, hazard rate function, moment generating function, and rth moment. The
model parameters are obtained using maximum likelihood method. The waiting time data is used as an illustration to describe the utility of APTL distribution.

Bayesian Method for Hurdle Regression

S S Hasanah, S Abdullah, Dian Lestari — Fri, 26 Feb 2021 00:00:00 +0000

Hurdle model is an alternative model to overcome overdispersion caused by excess zero. The model consists of two stages: a binary process that determines whether the response variable has zero values or positive values, and the second stage to model only the positive counts. The first stage is modelled using binary logistic regression, and the next stage is modeled with the zero-truncated model using Poisson regression. Bayesian method was employed to estimate the models’ parameters. Non-informative priors were specified for the parameters, and combined with the likelihood from the data, the non-closed form of posterior distributions were obtained, thus leading to the use of Markov Chain Monte Carlo (MCMC) with Gibbs Sampling to obtain samples from the posterior distributions. This method was applied to model the frequency of motoric complication in people with Parkinson’s disease. The result showed that subtotal scores from the three parts of Movement Disorder Society-Unified Parkinson’s Disease Rating Scale (MDS-UPDRS) could explain the frequency of motoric complication well, implied by the significance of the regression coefficients.