Dissertation > Excellent graduate degree dissertation topics show

The Statistical Inference for Count Data with Zero-inflation and Over-dispersion

Author: LiKeChun
Tutor: FuYingZi
School: Kunming University of Science and Technology
Course: Applied Mathematics
Keywords: zero-inflation ZIP model ZINB model score test over-dispersion influence diagnostics missing data
CLC: C81
Type: Master's thesis
Year: 2011
Downloads: 7
Quote: 0
Read: Download Dissertation


Count data is a kind of disperse data which are widely exist in daily life and studies. It is proved that Poisson regression modeling which was widely used in past practice and study, is a perfect approach to analysis such data.However, excess zeros relative to common Poisson distribution are often encountered in many application fields. Failure to account for the excess zeros may cause biased parameter estimates and misleading inferences. To account for the preponderance of zero counts, a class of zero-inflated Poisson mixed regression(ZIP) models is applicable for explaining excess zeros, which mixes the Poisson distribution with a degenerate component of point mass at zero. Therefore, the models choose are depend on whether there is zero-inflation exist in the count data. In this paper, a score test is proposed for the testing of zero-inflation. If there is zero-inflation exist, the ZIP model will be more appropriate; otherwise, a common Poisson regression model will be enough and more convenient.Besides, in many practical applications, zero-inflation and lack of independence may arise simultaneously as the hierarchical study design or the data collection procedure. Then a common single-level will no longer account for such data. To solve it, in this paper, a two-level ZIP regression model with random coefficient is proposed and a Bayesian approach is developed.What is more, the ZIP parameter estimates can be severely biased if the non-zero counts are over-dispersed in relation to the Poisson distribution. Then a zero-inflation negative binomial regression model (ZINB), which mixes the negative binomial distribution with a degenerate component of point mass at zero, may be more appropriate than the ZIP model. Therefore, the test for over-dispersion is indispensable for the models choose. In this paper, a score test is proposed for testing over-dispersion. If there is over-dispersion indeed exist in the count data, we can choose the ZINB model; otherwise, we can choose the ZIP model as a alternative model.Unfortunately, in many application fields, the missing data, which bring great trouble to our studies, are often encountered as well as zero-inflation and over-dispersion. To deal with such data and obtain accurate parameter estimate and rational inference, many methods were proposed. However, those methods are all base on the assumption of missing at random (MAR) and come from the same multi-level distribution. But in fact, sometimes the data is missing for the value is exceed its measurement. In this paper, we present a Data Augmentation (DA) method which does not rely on the MAR assumption and can model missing data mechanisms and covariate structure. This method utilizes the Gibbs Sampler as a tool for incorporating there structures and mechanisms. A simulation show that our method is more appropriate under the situation that the data is not missing at random.At last, we have a further discussion and expectation about our models.

Related Dissertations

  1. Research of Irreversible Loss in Flow and Mexed Prosess,TK12
  2. Primary Study on Measurement of Ammonia Emissions from a Farm Using Tunable Diode Laser Absorption Spectroscopic Technology,S158.5
  3. Trajectory Analysis of Wheat Aphids During Long-distance Migration Using HYSPLIT Model,S433
  4. Study on the Matrix Solid-Phase Dispersion Applications of Pesticide Residues in Food,TS207.53
  5. High hydrothermal stability of nickel-based catalyst and hydrogenation of butyne diol,TQ223.162
  6. Empirical Study on Price Level and Price Dispersion in B2C E-commerce Market,F724.6
  7. Image Restoration Method Research and Its Application Based on Probability PCA,TP391.41
  8. Research on the Synthesis of the Pr-zircon Yellow Pigments and the Ceratmic Ink,TQ622.1
  9. Surface Modification of Silica Particals of Different Size and Their Dispersion in Pet,TB383.3
  10. The Suppression Method on Timing Jitter of High Rate Solitons Transmission System,TN929.11
  11. Reduced Complexity MLSE Algorithm Based on BDFE in Optical Fiber Communication System,TN929.11
  12. Research and Design of Electronic Equalization Based on Most Likelihood Sequence Estimation,TN911.5
  13. Electronic Dispersion Compensation in High Speed Optical Communication System with New Modulation Formats,TN929.1
  14. Study on the Two Different Routes of Absorbing APIC in Rats and Enteric-coated APIC Solid Dispersion,R965
  15. Study on the Preparation of New Rapamycin Solid Formulations and Their Pharmacokinetics in Rats,R965
  16. Full- time lens -based optical OFDM systems theory and experiment,TN929.1
  17. YD company fine budget management mode,F275
  18. Water-based casting Cordierite ceramic green sheet and its properties,TQ174.62
  19. Sustained-release drug delivery systems containing avermectin Preparation and Properties,TQ460.1
  20. Based on stimulated Brillouin scattering fiber speed of light dimmable delay characteristics,O437.2

CLC: > Social Sciences > Statistics > Statistical methods
© 2012 www.DissertationTopic.Net  Mobile