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572 Pages
Revised
22.86 x 15.24 x 3.18
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Industry Reviews
'This is a well-researched practically oriented book on an important class of models relevant to over-dispersed count data. Recommended.' John Nelder, Imperial College London
'Every model currently offered in commercial statistical software is discussed in detail ... well written and can serve as an excellent reference book for applied statisticians who would use negative binomial regression modelling for undergraduate students or graduate students.' Yuehua Wu, Zentralblatt MATH
'I would recommend this book to researchers and students who would like to gain an overview of the negative binomial distribution and its extensions.' Fiona McElduff, University College London
'The text is well-written, easy-to-read but once started, is difficult to put down as each chapter unfolds the intricacies of the distribution.' International Statistical Review
'The second edition of Negative Binomial Regression is a unique statistical textbook. It is a very enjoyable read! It not only provides statistical fundamentals, but also provides historical perspectives and expert insights. This book is an excellent introduction for someone new to modeling count data, as well as an invaluable resource for the experienced practitioner grappling with complex overdispersed data.' Elizabeth Kelly, Statistical Sciences Group, Los Alamos National Laboratory
'As with all of Joe Hilbe's books this text is thorough and scholarly with an extensive list of references. Important theorems and other theoretical results are presented but are presented to be informative rather than to develop and teach the theory.' Michael R. Chernick, Significance
'... a valuable hands-on introduction to negative binomial regression and the analysis of count data in general. I am also pleased to see an advocation of the utility of the negative binomial distribution in applied work.' Psychometrika
| Preface to the second edition | p. xi |
| Introduction | p. 1 |
| What is a negative binomial model? | p. 1 |
| A brief history of the negative binomial | p. 5 |
| Overview of the book | p. 11 |
| The concept of risk | p. 15 |
| Risk and 2x2 tables | p. 15 |
| Risk and 2xk tables | p. 18 |
| Risk ratio confidence intervals | p. 20 |
| Risk difference | p. 24 |
| The relationship of risk to odds ratios | p. 25 |
| Marginal probabilities: joint and conditional | p. 27 |
| Overview of count response models | p. 30 |
| Varieties of count response model | p. 30 |
| Estimation | p. 38 |
| Fit considerations | p. 41 |
| Methods of estimation | p. 43 |
| Derivation of the IRLS algorithm | p. 43 |
| Solving for ∂£ or U - the gradient | p. 48 |
| Solving for2£ | p. 49 |
| The IRLS fitting algorithm | p. 51 |
| Newton-Raphson algorithms | p. 53 |
| Derivation of the Newton-Raphson | p. 54 |
| GLM with OIM | p. 57 |
| Parameterizing from to x' ß | p. 57 |
| Maximum likelihood estimators | p. 59 |
| Assessment of count models | p. 61 |
| Residuals for count response models | p. 61 |
| Model fit tests | p. 64 |
| Traditional fit tests | p. 64 |
| Information criteria fit tests | p. 68 |
| Validation models | p. 75 |
| Poisson regression | p. 77 |
| Derivation of the Poisson model | p. 77 |
| Derivation of the Poisson from the binomial distribution | p. 78 |
| Derivation of the Poisson model | p. 79 |
| Synthetic Poisson models | p. 85 |
| Construction of synthetic models | p. 85 |
| Changing response and predictor values | p. 94 |
| Changing multivariable predictor values | p. 97 |
| Example: Poisson model | p. 100 |
| Coefficient parameterization | p. 100 |
| Incidence rate ratio parameterization | p. 109 |
| Predicted counts | p. 116 |
| Effects plots | p. 122 |
| Marginal effects, elasticities, and discrete change | p. 125 |
| Marginal effects for Poisson and negative binomial effects models | p. 125 |
| Discrete change for Poisson and negative binomial models | p. 131 |
| Parameterization as a rate model | p. 134 |
| Exposure in time and area | p. 134 |
| Synthetic Poisson with offset | p. 136 |
| Example | p. 138 |
| Overdispersion | p. 141 |
| What is overdispersion? | p. 141 |
| Handling apparent overdispersion | p. 142 |
| Creation of a simulated base Poisson model | p. 142 |
| Delete a predictor | p. 145 |
| Outliers in data | p. 145 |
| Creation of interaction | p. 149 |
| Testing the predictor scale | p. 150 |
| Testing the link | p. 152 |
| Methods of handling real overdispersion | p. 157 |
| Scaling of standard errors / quasi-Poisson | p. 158 |
| Quasi-likelihood variance multipliers | p. 163 |
| Robust variance estimators | p. 168 |
| Bootstrapped and jackknifed standard errors | p. 171 |
| Tests of overdispersion | p. 174 |
| Score and Lagrange multiplier tests | p. 175 |
| Boundary likelihood ratio test | p. 177 |
| R2p and R2pdtests for Poisson and negative binomial models | p. 179 |
| Negative binomial overdispersion | p. 180 |
| Negative binomial regression | p. 185 |
| Varieties of negative binomial | p. 185 |
| Derivation of the negative binomial | p. 187 |
| Poisson-gamma mixture model | p. 188 |
| Derivation of the GLM negative binomial | p. 193 |
| Negative binomial distributions | p. 199 |
| Negative binomial algorithms | p. 207 |
| NB-C: canonical negative binomial | p. 208 |
| NB2: expected information matrix | p. 210 |
| NB2: observed information matrix | p. 215 |
| NB2: R maximum likelihood function | p. 218 |
| Negative binomial regression: modeling | p. 221 |
| Poisson versus negative binomial | p. 221 |
| Synthetic negative binomial | p. 225 |
| Marginal effects and discrete change | p. 236 |
| Binomial versus count models | p. 239 |
| Examples: negative binomial regression | p. 248 |
| Modeling number of marital affairs | p. 248 |
| Heart procedures | p. 259 |
| Titanic survival data | p. 263 |
| Health reform data | p. 269 |
| Alternative variance parameterizations | p. 284 |
| Geometric regression: NB = 1 | p. 285 |
| Derivation of the geometric | p. 285 |
| Synthetic geometric models | p. 286 |
| Using the geometric model | p. 290 |
| The canonical geometric model | p. 294 |
| NB 1: The linear negative binomial model | p. 298 |
| NB 1 as QL-Poisson | p. 298 |
| Derivation of NB 1 | p. 301 |
| Modeling with NB 1 | p. 304 |
| NB 1: R maximum likelihood function | p. 306 |
| NB-C: Canonical negative binomial regression | p. 308 |
| NB-C overview and formulae | p. 308 |
| Synthetic NB-C models | p. 311 |
| NB-C models | p. 315 |
| NB-H: Heterogeneous negative binomial regression | p. 319 |
| The NB-P model: generalized negative binomial | p. 323 |
| Generalized Waring regression | p. 328 |
| Bivariate negative binomial | p. 333 |
| Generalized Poisson regression | p. 337 |
| Poisson inverse Gaussian regression (PIG) | p. 341 |
| Other count models | p. 343 |
| Problems with zero counts | p. 346 |
| Zero-truncated count models | p. 346 |
| Hurdle models | p. 354 |
| Theory and formulae for hurdle models | p. 356 |
| Synthetic hurdle models | p. 357 |
| Applications | p. 359 |
| Marginal effects | p. 369 |
| Zero-inflated negative binomial models | p. 370 |
| Overview of ZIP/ZINB models | p. 370 |
| ZINB algorithms | p. 371 |
| Applications | p. 374 |
| Zero-altered negative binomial | p. 376 |
| Tests of comparative fit | p. 377 |
| ZINB marginal effects | p. 379 |
| Comparison of models | p. 382 |
| Censored and truncated count models | p. 387 |
| Censored and truncated models - econometric parameterization | p. 387 |
| Truncation | p. 388 |
| Censored models | p. 395 |
| Censored Poisson and NB2 models - survival parameterization | p. 399 |
| Handling endogeneity and latent class models | p. 407 |
| Finite mixture models | p. 408 |
| Basics of finite mixture modeling | p. 408 |
| Synthetic finite mixture models | p. 412 |
| Dealing with endogeneity and latent class models | p. 416 |
| Problems related to endogeneity | p. 416 |
| Two-stage instrumental variables approach | p. 417 |
| Generalized method of moments (GMM) | p. 421 |
| NB2 with an endogenous multinomial treatment variable | p. 422 |
| Endogeneity resulting from measurement error | p. 425 |
| Sample selection and stratification | p. 428 |
| Negative binomial with endogenous stratification | p. 429 |
| Sample selection models | p. 433 |
| Endogenous switching models | p. 438 |
| Quantile count models | p. 441 |
| Count panel models | p. 447 |
| Overview of count panel models | p. 447 |
| Generalized estimating equations: negative binomial | p. 450 |
| The GEE algorithm | p. 450 |
| GEE correlation structures | p. 452 |
| Negative binomial GEE models | p. 455 |
| GEE goodness-of-fit | p. 464 |
| GEE marginal effects | p. 466 |
| Unconditional fixed-effects negative binomial model | p. 468 |
| Conditional fixed-effects negative binomial model | p. 474 |
| Random-effects negative binomial | p. 478 |
| Mixed-effects negative binomial models | p. 488 |
| Random-intercept negative binomial models | p. 488 |
| Non-parametric random-intercept negative binomial | p. 494 |
| Random-coefficient negative binomial models | p. 496 |
| Multilevel models | p. 500 |
| Bayesian negative binomial models | p. 502 |
| Bayesian versus frequentist methodology | p. 502 |
| The logic of Bayesian regression estimation | p. 506 |
| Applications | p. 510 |
| Constructing and interpreting interaction terms | p. 520 |
| Data sets, commands, fiinctions | p. 530 |
| References and further reading | p. 532 |
| Index | p. 541 |
| Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780521198158
ISBN-10: 0521198151
Published: 17th March 2011
Format: Hardcover
Language: English
Number of Pages: 572
Audience: General Adult
Publisher: Cambridge University Press
Country of Publication: GB
Edition Number: 2
Edition Type: Revised
Dimensions (cm): 22.86 x 15.24 x 3.18
Weight (kg): 1.13
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