The Analysis of Stochastic Processes Using Glim

ISBN-13: 9780387977614 / Angielski / Miękka / 1992 / 294 str.

James K. Lindsey

Opis

The aim of this book is to present a survey of the many ways in which the statistical package GLIM may be used to model and analyze stochastic processes. Its emphasis is on using GLIM interactively to apply statistical techniques, and examples are drawn from a wide range of applications including medicine, biology, and the social sciences. It is based on the author's many years of teaching courses along these lines to both undergraduate and graduate students. The author assumes that readers have a reasonably strong background in statistics such as might be gained from undergraduate courses and that they are also familiar with the basic workings of GLIM. Topics covered include: the analysis of survival data, regression and fitting distributions, time series analysis (including both the time and frequency domains), repeated measurements, and generalized linear models.

Spis treści

1. Normal Theory Models and Some Extensions.- 1. Linear Regression.- 2. Analysis of Variance.- 3. Analysis of Covariance.- 4. The Extension to Non-Normal Models.- 5. Fitting Distributions.- 6. Further GLIM Instructions.- 2. Markov Chains.- 1. Binary Point Processes.- 2. Multi-state Markov Chains.- 3. Stationarity.- 4. Reversibility and Equilibrium.- 5. Random Walks.- 6. The Mover-Stayer Model.- 3. Point and Renewal Processes.- 1. Point Processes.- 2. The Poisson Process.- 3. Kaplan-Meier Estimation.- 4. Probability Plots.- 5. Fitting a Distribution.- 6. A Nonhomogeneous Point Process.- 7. An Example with Periodicity.- 4. Survival Curves.- 1. Censored Data.- 2. The Hazard Function.- 3. Exponential Distribution.- 4. Pareto Distribution.- 5. Weibull Distribution.- 6. Extreme Value Distribution.- 7. Log Normal Distribution.- 8. Log Logistic Distribution.- 9. Gamma Distribution.- 10. Inverse Gaussian Distribution.- 11. Cox Proportional Hazards Model.- 12. Piecewise Exponential Distribution.- 5. Growth Curves.- 1. Exponential Growth: Continuous Data.- 2. Exponential Growth: Count Data.- 3. The Logistic Growth Curve.- 4. The Gomperz Growth Curve.- 6. Time Series: The Time Domain.- 1. Trends and Correlograms.- 2. Autoregression and Random Walks.- 3. Examination of the Distribution Assumptions.- 4. Mis-specification of the Linear Model.- 5. Serial Correlation in Regression Analysis.- 7. Time Series: The Frequency Domain.- 1. Data Preparation: Filtering and Tapering.- 2. Periodograms.- 3. Fitting an Autoregression by Spectral Analysis.- 4. Bloomfield’s Exponential Model.- 5. Comparison of Spectra.- 8. Repeated Measurements.- 1. Descriptive Methods.- 2. Autoregression.- 3. Random Effects.- 4. A Generalized Linear Autoregression “Model”.- 5. A Generalized Linear Random Effects Model.- 6. A Multivariate Logistic Model.- 9. Stochastic Processes and Generalized Linear Models.- 1. A Logistic Growth Curve with Autoregression.- 2. Conditional Generalized Linear Autoregression.- 3. Exponential Dispersion Models.- 4. Two Sources of Dependence in Panel Data.- 5. Binary Crossover Trials.- 6. A Binary Model for Learning.- Appendix I - GLIM Commands.- Appendix II - GLIM Macros.- Appendix III - Data Tables.- References.