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ویرایش: 2 نویسندگان: P. McCullagh, John A. Nelder سری: Chapman & Hall/CRC Monographs on Statistics & Applied Probability ISBN (شابک) : 0412317605, 9780412317606 ناشر: Chapman and Hall/CRC سال نشر: 1989 تعداد صفحات: 526 زبان: English فرمت فایل : DJVU (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) حجم فایل: 7 مگابایت
کلمات کلیدی مربوط به کتاب مدل های خطی تعمیم یافته: برنامه نویسی خطی، کاربردی، ریاضیات، علوم و ریاضی، احتمال و آمار، کاربردی، ریاضیات، علوم و ریاضی، آمار، ریاضیات، علوم و ریاضیات، کتاب های درسی جدید، مستعمل و اجاره ای، بوتیک تخصصی
در صورت تبدیل فایل کتاب Generalized Linear Models به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب مدل های خطی تعمیم یافته نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
موفقیت نسخه اول مدل های خطی تعمیم یافته منجر
به به روز رسانی ویرایش دوم شد، که همچنان به ارائه یک درمان قطعی
و یکپارچه از روش ها برای تجزیه و تحلیل انواع مختلف داده ها
ادامه می دهد. امروزه، به دلیل وضوح، غنای محتوا و ارتباط مستقیم
با کاربردهای کشاورزی، بیولوژیکی، بهداشتی، مهندسی و سایر
کاربردها محبوب باقی مانده است.
نویسندگان بر بررسی روشی که یک متغیر پاسخ به ترکیبی از توضیحی
بستگی دارد تمرکز می کنند. متغیرها، درمان و متغیرهای طبقه بندی.
آنها تاکید خاصی بر مورد مهمی دارند که در آن وابستگی از طریق
ترکیب خطی و ناشناخته متغیرهای توضیحی رخ می دهد.
نسخه دوم شامل موضوعاتی است که به هسته نسخه اول
اضافه شده است. از جمله روشهای احتمال شرطی و حاشیهای، معادلات
تخمینی و مدلهایی برای اثرات پراکندگی و اجزای پراکندگی. بحث در
مورد سایر موضوعات - مدلهای لاگ خطی و مرتبط، مدلهای رگرسیون
نسبت شانس، مدلهای پاسخ چندجملهای، مدلهای خطی معکوس و مرتبط،
توابع شبه احتمال، و بررسی مدلها گسترش یافت و بازنگریهای
قابلتوجهی را به همراه داشت.
BR> درک مطالب صرفاً به دانش نظریه ماتریس و ایده های اساسی
نظریه احتمال نیاز دارد، اما در بیشتر موارد، کتاب مستقل است.
بنابراین، مدلهای خطی تعمیمیافته با نمونههای
کار شده، تمرینهای فراوان و موضوعاتی که مستقیماً برای محققان
بسیاری از رشتهها استفاده میشود، به عنوان متن ایدهآل، راهنمای
خودآموزی و مرجع عمل میکند.
The success of the first edition of Generalized Linear
Models led to the updated Second Edition, which
continues to provide a definitive unified, treatment of methods
for the analysis of diverse types of data. Today, it remains
popular for its clarity, richness of content and direct
relevance to agricultural, biological, health, engineering, and
other applications.
The authors focus on examining the way a response variable
depends on a combination of explanatory variables, treatment,
and classification variables. They give particular emphasis to
the important case where the dependence occurs through some
unknown, linear combination of the explanatory variables.
The Second Edition includes topics added to
the core of the first edition, including conditional and
marginal likelihood methods, estimating equations, and models
for dispersion effects and components of dispersion. The
discussion of other topics-log-linear and related models, log
odds-ratio regression models, multinomial response models,
inverse linear and related models, quasi-likelihood functions,
and model checking-was expanded and incorporates significant
revisions.
Comprehension of the material requires simply a knowledge of
matrix theory and the basic ideas of probability theory, but
for the most part, the book is self-contained. Therefore, with
its worked examples, plentiful exercises, and topics of direct
use to researchers in many disciplines, Generalized
Linear Models serves as ideal text, self-study guide,
and reference.
Contents ... 3 Preface to the first edition ... 12 Preface ... 14 CHAPTER 1 Introduction ... 16 1.1 Background ... 16 1.1.1 The problem of looking at data ... 18 1.1.2 Theory as pattern ... 19 1.1.3 Model fitting ... 20 1.1.4 What is a good model? ... 22 1.2 The origins of generalized linear models ... 23 1.2.1 Terminology ... 23 1.2.2 Classical linear models ... 24 1.2.3 R.A. Fisher and the design of experiments ... 25 1.2.4 Dilution assay ... 26 1.2.5 Probit analysis ... 28 1.2.6 Log it models for proportions ... 29 1.2.7 Log-linear models for counts ... 29 1.2.8 Inverse polynomials ... 31 1.2.9 Survival data ... 31 1.3 Scope of the rest of the book ... 32 1.4 Bibliographic notes ... 34 1.5 Further results and exercises 1 ... 34 CHAPTER 2 An outline of generalized linear models ... 36 2.1 Processes in model fitting ... 36 2.1.1 Model selection ... 36 2.1.2 Estimation ... 38 2.1.3 Prediction ... 40 2.2 The components of a generalized linear model ... 41 2.2.1 The generalization ... 42 2.2.3 Link functions ... 46 2.2.4 Sufficient statistics and canonical links ... 47 2.3 Measuring the goodness of fit ... 48 2.3.1 The discrepancy of a fit ... 48 2.3.2 The analysis of deviance ... 50 2.4 Residua ls ... 52 2.4.1 Pearson residual ... 52 2.4.2 Anscombe residual ... 53 2.4.3 Deviance residual ... 54 2.5 An algorithm for fitting generalized linear models ... 55 2.5.1 Justification of the fitting procedure ... 56 2.6 Bibliographic notes ... 58 2.7 Further results and exercises 2 ... 59 CHAPTER 3 Models for continuous data with constant variance ... 63 3.1 Introduction ... 63 3.2 Error structure ... 64 3.3 Systematic component (linear predictor) ... 66 3.3.1 Continuous covariates ... 66 3.3.2 Qualitative covariates ... 67 3.3.3 Dummy variates ... 69 3.3.4 Mixed terms ... 70 3.4 Model formulae for linear predictors ... 71 3.4.1 Individual terms ... 71 3.4.2 The dot operator ... 71 3.4.3 The + operator ... 72 3.4.4 The crossing (*) and nesting (/) operators ... 73 3.4.5 Operators for the removal of terms ... 74 3.4.6 Exponential operator ... 75 3.5 Aliasing ... 76 3.5.1 Intrinsic aliasing with factors ... 78 3.5.2 Aliasing in a two-way cross-classification ... 80 3.5.3 Extrinsic aliasing ... 83 3.5.4 Functional relations among covariates ... 84 3.6 Estimation ... 85 3.6.1 The maximum-likelihood equations ... 85 3.6.2 Geometrical interpretation ... 86 3.6.3 Information ... 87 3.6.4 A model with two covariates ... 89 3. 6.5 The information surface ... 92 3.6.6 Stability ... 93 3.7 Tables as data ... 94 3.7.1 Empty cells ... 94 3.7.2 Fused cells ... 96 3.8 Algorithms for least squares ... 96 3.8.1 Methods based on the information matrix ... 97 3.8.2 Direct decomposition methods ... 100 3.8.3 Extension to generalized linear models ... 103 3.9 Selection of covariates ... 104 3.10 Bibliographic notes ... 108 3.11 Further results and exercises 3 ... 108 CHAPTER 4 Binary data ... 113 4.1 Introduction ... 113 4.1.1 Binary responses ... 113 4.1.2 Covariate classes ... 114 4.1.3 Contingency tables ... 115 4.2 Binomial distribution ... 116 4.2.1 Genesis ... 116 4.2.2 Moments and cumulants ... 117 4.2.3 Normal limit ... 118 4.2.4 Poisson limit ... 120 4.2.5 Transformations ... 120 4.3 Models for binary responses ... 122 4.3.1 Link Junctions ... 122 4.3.2 Parameter interpretation ... 125 4.3.3 Retrospective sampling ... 126 4.4 Likelihood functions for binary data ... 129 4.4.l Log likelihood for binomial data ... 129 4.4.2 Parameter estimation ... 130 4.4.3 Deviance function ... 133 4.4.4 Bias and precision of estimates ... 134 4.4.5 Sparseness ... 135 4.4.6 Extrapolation ... 137 4.5 Over-dispersion ... 139 4.5.1 Genesis ... 139 4.5.2 Parameter estimation ... 141 4.6 Example ... 143 4.6.1 Habitat preferences of lizards ... 143 4.7 Bibliographic notes ... 150 4.8 Further results and exercises 4 ... 150 CHAPTER 5 Models for polytomous data ... 164 5.1 Introduction ... 164 5.2 Measurement scales ... 165 5.2.1 General points ... 165 5.2.2 Models for ordinal scales ... 166 5.2.3 Models for interval scales ... 170 5.2.4 Models for nominal scales ... 174 5.2.5 Nested or hierarchical response scales ... 175 5.3 The multinomial distribution ... 179 5.3.1 Genesis ... 179 5.3.2 Moments and cumulants ... 180 5.3.3 Generalized inverse matrices ... 183 5.3.4 Quadratic forms ... 184 5.3.5 Marginal and conditional distributions ... 185 5.4 Likelihood functions ... 186 5.4.1 Log likelihood for multinomial responses ... 186 5.4.2 Para meter estimation ... 187 5.4.3 Deviance function ... 189 5.5 Over-dispersion ... 189 5.6 Examples ... 190 5.6.1 A cheese-tasting experiment ... 190 5.6.2 Pneumoconiosis among coalminers ... 193 5.7 Bibliographic notes ... 197 5.8 Further results and exercises 5 ... 199 CHAPTER 6 Log-linear models ... 208 6.1 Introduction ... 208 6.2 Likelihood functions ... 209 6.2.1 Poisson distribution ... 209 6.2.2 The Poisson log-likelihood function ... 212 6.2.3 Over-dispersion ... 213 6.2.4 Asymptotic theory ... 215 6.3 Examples ... 215 6.3.1 A biological assay of tuberculins ... 215 6.3.2 A study of wave damage to cargo ships ... 219 6.4 Log-linear models and multinomial response models ... 224 6.4.1 Comparison of two or more Poisson means ... 224 6.4.2 Multinomial response models ... 226 6.4.3 Summary ... 228 6.5 Multiple responses ... 229 6.5.1 Introduction ... 229 6.5.2 Independence and conditional independence ... 230 6.5.3 Canonical correlation models ... 232 6.5.4 Multivariate regression models ... 234 6.5.5 Multivariate model formulae ... 237 6.5.6 Log-linear regression models ... 238 6.5.7 Likelihood equations ... 240 6.6 Example ... 244 6.6.1 Respiratory ailments of coalminers ... 244 6.6.2 Parameter interpretation ... 248 6.7 Bibliographic notes ... 250 6.8 Further results and exercises 6 ... 251 CHAPTER 7 Conditional likelihoods ... 260 7.1 Introduction ... 260 7.2 Marginal and conditional likelihoods ... 261 7.2.1 Marginal likelihood ... 261 7.2.2 Conditional likelihood ... 263 7.2.3 Exponential-family models ... 267 7.2.4 Profile likelihood ... 269 7.3 Hypergeometric distributions ... 270 7.3.1 Central hypergeometric distribution ... 270 7.3.2 Non-central hypergeometric distribution ... 272 7.3.3 Multivariate hypergeometric distribution ... 275 7.3.4 Multivariate non-central hypergeometric distribution ... 276 7.4 Some applications involving binary data ... 277 7.4.1 Comparison of two binomial probabilities ... 277 7.4.2 Combination of information fr om several 2x2 tables ... 280 7.4.3 Example: flle-et- Vilaine study of oesophageal cancer ... 282 7.5 Some applications involving polytomous data ... 285 7.5.1 Matched pairs: nominal response ... 285 7.5.2 Ordinal responses ... 288 7.5.3 Example ... 291 7.6 Bibliographic notes ... 292 7.7 Further results and exercises 7 ... 294 CHAPTER 8 Models for data with constant coefficient of variation ... 300 8.1 Introduction ... 300 8.2 The gamma distribution ... 302 8.3 Models with gamma-distributed observations ... 304 8.3.1 The variance function ... 304 8.3.2 The deviance ... 305 8.3.3 The canonical link ... 306 8.3.4 Multiplicative models: log link ... 307 8.3.5 Linear models: identity link ... 309 8.3.6 Estimation of the dispersion parameter ... 310 8.4 Examples ... 311 8.4.1 Car insurance claims ... 311 8.4.2 Clotting times of blood ... 315 8.4.3 Modelling rainfall data using two generalized linear models ... 317 8.4.4 Developmental rate of Drosophila melanogaster ... 321 8.5 Bibliographic notes ... 328 8.6 Further results and exercises 8 ... 329 CHAPTER 9 Quasi-likelihood functions ... 338 9.1 Introduction ... 338 9.2 Independent observations ... 339 9.2.1 Covariance functions ... 339 9.2.2 Construction of the quasi-likelihood function ... 340 9.2.3 Parameter estimation ... 342 9.2.4 Example: incidence of leaf-blotch on barley ... 343 9.3 Dependent observations ... 347 9.3.1 Quasi-likelihood estimating equations ... 347 9.3.2 Quasi-likelihood function ... 348 9.3.3 Example: estimation of probabilities from marginal frequencies ... 351 9.4 Optimal estimating functions ... 354 9.4.1 Introduction ... 354 9.4.2 Combination of estimating functions ... 355 9.4.3 Example: estimation for megalithic stone rings ... 358 9.5 Optimality criteria ... 362 9.6 Extended quasi-likelihood ... 364 9.7 Bibliographic notes ... 367 9.8 Further results and exercises 9 ... 367 CHAPTER 10 Joint modelling of mean and dispersion ... 372 10.1 Introduction ... 372 10.2 Model specification ... 373 10.3 Interaction between mean and dispersion effects ... 374 10.4 Extended quasi-likelihood as a criterion ... 375 10.5 Adjustments of the estimating equations ... 376 10.5.1 Adjustment for kurtosis ... 376 10.5.2 Adjustment for degrees of freedom ... 377 10.6 Joint optimum estimating equations ... 379 10.7 Example: the production of leaf-springs for trucks ... 380 10.8 Bibliographic notes ... 385 1O.9 Further results and exercises 10 ... 386 CHAPTER 11 Models with additional non-linear parameters ... 387 11.1 Introduction ... 387 11.2 Parameters in the variance function ... 388 11.3 Parameters in the link function ... 390 11.3.1 One link parameter ... 390 11.3.2 More than one link parameter ... 392 11.3.3 Transformation of data vs transformation of fitted values ... 393 11.4 Non-linear parameters in the covariates ... 394 11.5 Examples ... 396 11.5.1 The effects of fertilizers on coastal Bermuda grass ... 396 11.5.2 Assay of an insecticide with a synergist ... 399 11.5.3 Mixtures of drugs ... 401 11.6 Bibliographic notes ... 404 11.7 Further results and exercises 11 ... 404 CHAPTER 12 Model checking ... 406 12.1 Introduction ... 406 12.2 Techniques in model checking ... 407 12.3 Score tests for extra pai- ameters ... 408 12.4 Smoothing as an aid to informal checks ... 409 12.5 The raw materials of model checking ... 411 12.6 Checks for systematic departure from model ... 413 12.6.1 Informal checks using residuals ... 413 12.6.2 Checking the variance function ... 415 12.6.3 Checking the link function ... 416 12.6.4 Checking the scales of covariates ... 416 12.6.5 Checks for compound systematic discrepancies ... 418 12.7 Checks for isolated departures from the model ... 418 12.7.1 Measure of leverage ... 420 12.7.2 Measure of consistency ... 421 12.7.3 Measure of influence ... 421 12.7.4 Informal assessment of extreme values ... 422 12.7.5 Extreme points and checks for systematic discrepancies ... 423 12.8 Examples ... 424 12.8.1 Damaged carrots in an insecticide experiment ... 424 12.8.2 Minitab tree data ... 425 12.8.3 Insurance claims (continued) ... 428 12.9 A strategy for model checking? ... 429 12.10 Bibliographic notes ... 430 12.11 Further results and exercises 12 ... 431 CHAPTER 13 Models for survival data ... 434 13.1 Introduction ... 434 13.1.1 Survival functions and hazard functions ... 434 13.2 Proportional -hazards models ... 436 13.3 Estimation with a specified survival distribution ... 437 13.3.1 The exponential distribution ... 438 13.3.2 The Weibull distribution ... 438 13.3.3 The extreme-value distribution ... 439 13.4 Example: remission times for leukemia ... 440 13.5 Cox\'s proportional-hazards model ... 441 13.5.1 Partial likelihood ... 441 13.5.2 The treatment of ties ... 442 13.5.3 Numerical methods ... 444 13.6 Bibliographic notes ... 445 13.7 Further results and exercises 13 ... 445 CHAPTER 14 Components of dispersion ... 447 14.1 Introduction ... 447 14.2 Linear models ... 448 14.3 Non-linear models ... 449 14.4 Parameter estimation ... 452 14.5 Example: A salamander mating experiment ... 454 14.5.1 Introduction ... 454 14.5.2 Experimental procedure ... 456 14.5.3 A linear logistic model with random effects ... 459 14.5.4 Estimation of the dispersion parameters ... 463 14.6 Bibliographic notes ... 465 14.7 Further results and exercises 14 ... 467 CHAPTER 15 Further topics ... 470 15.1 Introduction ... 470 15.2 Bias adjustment ... 470 15.2.1 Models with canonical link ... 470 15.2.2 Non-canonical models ... 472 15.2.3 Example: Lizard data (continued) ... 473 15.3 Computation of Bartlett adjustments ... 474 15.3.1 General theory ... 474 15.3.2 Computation of the adjustment ... 475 15.3.3 Example: exponential regression model ... 478 15.4 Generalized additive models ... 480 15.4.1 Algorithms for fitting ... 480 15.4.2 Smoothing methods ... 481 15.4.3 Conclusions ... 482 15.5 Bibliographic notes ... 482 15.6 Further results and exercises 15 ... 482 APPENDIX A Elementary likelihood theory ... 484 Scalar parameter ... 484 Vector parameter ... 487 APPENDIX B Edgeworth series ... 489 APPENDIX C Likelihood-ratio statistics ... 491 References ... 494 Index of data sets ... 515 Author index ... 516 Subject index ... 521