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Extended Poisson Models for Count Data With Inflated Frequencies

Count data often exhibits inflated counts for zero. There are numerous papers in the literature that show how to fit Poisson regression models that account for the zero inflation. However, in many situations the frequencies of zero and of some other value k tends to be higher than the Poisson model can fit appropriately. Recently, Sheth-Chandra (2011), Lin and Tsai (2012) introduced a mixture model to account for the inflated frequencies of zero and k. In this dissertation, we study basic properties of this mixture model and parameter estimation for grouped and ungrouped data. Using stochastic representation we show how the EM algorithm can be adapted to obtain maximum likelihood estimates of the parameters. We derive the observed information matrix which yields standard errors of the EM estimates using ideas from Louis (1982). We also derive asymptotic distributions to test significance of the inflation points. We use real life examples to illustrate the procedure of fitting our model via EM algorithm. The second part of this dissertation deals with a generalization of this mixture model where the one parameter Poisson distribution is replaced by a two parameter Conway-Maxwell-Poisson (CMP) distribution, which unlike the Poisson distribution accounts for both over and under dispersion in the count data. The CMP distribution has recently gained popularity, and a CMP model for zero inflated count data was introduced by Sellers and Raim (2016). We discuss properties of the CMP distribution and propose a new mixture distribution, namely zero and k inflated Conway-Maxwell-Poisson (ZkICMP) to address inflated counts with over and under dispersions. We develop regression models based on ZkICMP and discuss parameter estimation using analytical and numerical methods. Finally, we compare goodness of fit of inflated and standard models on simulated and real life data examples

Application of Mixture Models for Doubly Inflated Count Data

In health and social science and other fields where count data analysis is important, zero-inflated models have been employed when the frequency of zero count is high (inflated). Due to multiple reasons, there are scenarios in which an additional count value of k \u3e 0 occurs with high frequency. The zero- and k-inflated Poisson distribution model (ZkIP) is more appropriate for such situations. The ZkIP model is a mixture distribution with three components: degenerate distributions at 0 and k count and a Poisson distribution. In this article, we propose an alternative and computationally fast expectation–maximization (EM) algorithm to obtain the parameter estimates for grouped zero and k-inflated count data. The asymptotic standard errors are derived using the complete data approach. We compare the zero- and k-inflated Poisson model with its zero-inflated and non-inflated counterparts. The best model is selected based on commonly used criteria. The theoretical results are supplemented with the analysis of two real-life datasets from health sciences

EM Estimation for Zero- and \u3ci\u3ek\u3c/i\u3e-Inflated Poisson Regression Model

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we provide details for obtaining parameter estimates of the ZkIP regression model using the Expectation-Maximization (EM) algorithm for a given data. We derive the standard errors of the EM estimates by computing the complete, missing, and observed data information matrices. We present the analysis of two real-life data using the methods outlined in the paper

Audit of buying patterns of drugs from various pharmacies in Northern India

A study was conducted to gather data regarding drug buying practices in Delhi to compare the same in rural pharmacies in surrounding area. A cross sectional study was conducted as exit interviews using pretested Performa with customers visiting randomly selected pharmacies of Delhi and rural Haryana. Out of 280 consumers interviewed 140 belonged to urban areas and 140 to rural areas. In both areas male and younger consumers are significantly high. Most consumers in both set ups took medication after physician’s prescription in comparison to self medication. Source of information for self medication was media in urban and friends in rural areas. Alteration in brand name was more in rural areas. Antimicrobials and NSAIDs in rural areas and drugs for cardiovascular diseases and oral hypoglycemic drugs in urban areas are major purchased drug groups

Relative benefits/losses of India aligning with RCEP and BRICS countries under the conjecture of free trade area in goods

The present study works out the relative benefits/losses of India aligning with RCEP and BRICS member countries under the conjecture of free trade area in good trade only. The study uses partial (SMART model) and general equilibrium (GTAP model) tools for this assessment. The main focus in the study is to compare the benefits/losses to Indian economy associated with both policy scenarios. The results reveal that it would be beneficial for India to align with other RCEP member countries under the policy of free trade area in goods trade. If India wants to join BRICS FTA in the near future then it must negotiate for the entry of its own specialized products into their markets and in reciprocity, it should allow the entry of their specialized products in to the domestic market. The results are in favor to make free trade area between RCEP countries which is more beneficial for India in comparison to make BRICS FTA

Understanding Eating Behaviors of New Dehli\u27s Youth

This qualitative study documents perceived benefits of and barriers to engaging in healthy eating behaviors among adolescents in New Delhi, India. Researchers explored factors that influenced the consumption of breakfast, fruits and vegetables, and soft drinks in this population and adolescents’ ideas about how to intervene to encourage or discourage, respectively, these behaviors. Students (n=151 6th and 8th graders) from five private schools participated in focus group discussions. Findings showed that the majority of youth eat breakfast that may consist of traditional and Western choices. Despite sound knowledge of the benefits of fruits and vegetables consumption, adolescents do not eat the recommended daily servings due to flavor preferences. Soft drink consumption was, reportedly, universal. Several factors influenced these decisions and details are herein provided. The paucity of studies on this subject provides researchers with the opportunity to explore how eating patterns of Indian youth might be shaping the health and disease landscape of India in the upcoming decades. The study adds to the slim body of literature on the subject and could be used to inform future nutrition interventions in India

Trend in BMI z-score among Private Schools’ Students in Delhi using Multiple Imputation for Growth Curve Model

Objective: The aim of the study is to assess the trend in mean BMI z-score among private schools’ students from their anthropometric records when there were missing values in the outcome. Methodology: The anthropometric measurements of student from class 1 to 12 were taken from the records of two private schools in Delhi, India from 2005 to 2010. These records comprise of an unbalanced longitudinal data that is not all the students had measurements recorded at each year. The trend in mean BMI z-score was estimated through growth curve model. Prior to that, missing values of BMI z-score were imputed through multiple imputation using the same model. A complete case analysis was also performed after excluding missing values to compare the results with those obtained from analysis of multiply imputed data. Results: The mean BMI z-score among school student significantly decreased over time in imputed data (β= -0.2030, se=0.0889, p=0.0232) after adjusting age, gender, class and school. Complete case analysis also shows a decrease in mean BMI z-score though it was not statistically significant (β= -0.2861, se=0.0987, p=0.065). Conclusions: The estimates obtained from multiple imputation analysis were better than those of complete data after excluding missing values in terms of lower standard errors. We showed that anthropometric measurements from schools records can be used to monitor the weight status of children and adolescents and multiple imputation using growth curve model can be useful while analyzing such dat

Association of Breakfast Intake with Obesity, Dietary and Physical Activity Behavior Among Urban School-Aged Adolescents in Delhi, India: Results of a Cross-Sectional Study

In developed countries, regular breakfast consumption is inversely associated with excess weight and directly associated with better dietary and improved physical activity behaviors. Our objective was to describe the frequency of breakfast consumption among school-going adolescents in Delhi and evaluate its association with overweight and obesity as well as other dietary, physical activity, and sedentary behaviors. Methods: Design: Cross-sectional study. Setting: Eight schools (Private and Government) of Delhi in the year 2006. Participants: 1814 students from 8th and 10th grades; response rate was 87.2%; 55% were 8th graders, 60% were boys and 52% attended Private schools. Main outcome measures: Body mass index, self-reported breakfast consumption, diet and physical activity related behaviors, and psychosocial factors. Data analysis: Mixed effects regression models were employed, adjusting for age, gender, grade level and school type (SES). Results: Significantly more Government school (lower SES) students consumed breakfast daily as compared to Private school (higher SES) students (73.8% vs. 66.3%; p<0.01). More 8th graders consumed breakfast daily vs. 10th graders (72.3% vs. 67.0%; p<0.05). A dose-response relationship was observed such that overall prevalence of overweight and obesity among adolescents who consumed breakfast daily (14.6%) was significantly lower vs. those who only sometimes (15.2%) or never (22.9%) consumed breakfast (p<0.05 for trend). This relationship was statistically significant for boys (15.4 % vs. 16.5% vs. 26.0; p<0.05 for trend) but not for girls. Intake of dairy products, fruits and vegetables was 5.5 (95% CI 2.4-12.5), 1.7 (95% CI 1.1-2.5) and 2.2 (95% CI 1.3-3.5) times higher among those who consumed breakfast daily vs. those who never consumed breakfast. Breakfast consumption was associated with greater physical activity vs. those who never consumed breakfast. Positive values and beliefs about healthy eating; body image satisfaction; and positive peer and parental influence were positively associated with daily breakfast consumption, while depression was negatively associated. Conclusion: Daily breakfast consumption is associated with less overweight and obesity and with healthier dietary-and physical activity-related behaviors among urban Indian students. Although prospective studies should confirm the present results, intervention programs to prevent or treat childhood obesity in India should consider emphasizing regular breakfast consumption.Obesity Prevention Center, University of MinnesotaPRIME program of the University of Texas, School of Public Health (Stigler, PI)Center for Health Promotion and Disease Prevention Research in Underserved Population

The Basins of Convergence in the Planar Restricted Four-body Problem with Variable Mass

We have studied the existence, location and stability of the libration points in the model of restricted four-body problem (R4BP) with variable mass. It is assumed that three primaries, one dominant primary and the other two with equal masses, are always forming an equilateral triangle. We have determined the equations of motion of the above mentioned problem for the fourth body which is an infinitesimal mass. The libration points have been determined numerically for different values of the parameters considered. It is found that there are eight or ten libration points out of which six are non-collinear and two or four are collinear depending upon the values of mass parameter and the constant of proportionality occurring in Jeans’ law. The regions of motion of the infinitesimal mass have been drawn and investigated. We have also examined the stability of each libration point and found that all the libration points are unstable. Further, the Newton-Raphson basins of attraction are drawn for different set of parameters used