Methods of statistical model estimation:
"Preface Methods of Statistical Model Estimation has been written to develop a particular pragmatic viewpoint of statistical modelling. Our goal has been to try to demonstrate the unity that underpins statistical parameter estimation for a wide range of models. We have sought to represent the t...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2013
|
| Schlagworte: | |
| Online-Zugang: | Cover Inhaltsverzeichnis |
| Zusammenfassung: | "Preface Methods of Statistical Model Estimation has been written to develop a particular pragmatic viewpoint of statistical modelling. Our goal has been to try to demonstrate the unity that underpins statistical parameter estimation for a wide range of models. We have sought to represent the techniques and tenets of statistical modelling using executable computer code. Our choice does not preclude the use of explanatory text, equations, or occasional pseudo-code. However, we have written computer code that is motivated by pedagogic considerations first and foremost. An example is in the development of a single function to compute deviance residuals in Chapter 4. We defer the details to Section 4.7, but mention here that deviance residuals are an important model diagnostic tool for GLMs. Each distribution in the exponential family has its own deviance residual, defined by the likelihood. Many statistical books will present tables of equations for computing each of these residuals. Rather than develop a unique function for each distribution, we prefer to present a single function that calls the likelihood appropriately itself. This single function replaces five or six, and in so doing, demonstrates the unity that underpins GLM. Of course, the code is less efficient and less stable than a direct representation of the equations would be, but our goal is clarity rather than speed or stability. This book also provides guidelines to enable statisticians and researchers from across disciplines to more easily program their own statistical models using R. R, more than any other statistical application, is driven by the contributions of researchers who have developed scripts, functions, and complete packages for the use of others in the general research community"-- |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 243 S. graf. Darst. |
| ISBN: | 9781439858028 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV041149445 | ||
| 003 | DE-604 | ||
| 005 | 20151023 | ||
| 007 | t | ||
| 008 | 130717s2013 |||| |||| 00||| eng d | ||
| 010 | |a 2013013448 | ||
| 020 | |a 9781439858028 |c hardback |9 978-1-4398-5802-8 | ||
| 035 | |a (OCoLC)856829614 | ||
| 035 | |a (DE-599)GBV746403569 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-473 |a DE-634 | ||
| 050 | 0 | |a QA276.8 | |
| 082 | 0 | |a 519.5/44 | |
| 084 | |a SK 830 |0 (DE-625)143259: |2 rvk | ||
| 100 | 1 | |a Hilbe, Joseph M. |d 1944-2017 |e Verfasser |0 (DE-588)128751851 |4 aut | |
| 245 | 1 | 0 | |a Methods of statistical model estimation |c Joseph M. Hilbe ; Andrew P. Robinson |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2013 | |
| 300 | |a XII, 243 S. |b graf. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | 1 | |a "Preface Methods of Statistical Model Estimation has been written to develop a particular pragmatic viewpoint of statistical modelling. Our goal has been to try to demonstrate the unity that underpins statistical parameter estimation for a wide range of models. We have sought to represent the techniques and tenets of statistical modelling using executable computer code. Our choice does not preclude the use of explanatory text, equations, or occasional pseudo-code. However, we have written computer code that is motivated by pedagogic considerations first and foremost. An example is in the development of a single function to compute deviance residuals in Chapter 4. We defer the details to Section 4.7, but mention here that deviance residuals are an important model diagnostic tool for GLMs. Each distribution in the exponential family has its own deviance residual, defined by the likelihood. Many statistical books will present tables of equations for computing each of these residuals. Rather than develop a unique function for each distribution, we prefer to present a single function that calls the likelihood appropriately itself. This single function replaces five or six, and in so doing, demonstrates the unity that underpins GLM. Of course, the code is less efficient and less stable than a direct representation of the equations would be, but our goal is clarity rather than speed or stability. This book also provides guidelines to enable statisticians and researchers from across disciplines to more easily program their own statistical models using R. R, more than any other statistical application, is driven by the contributions of researchers who have developed scripts, functions, and complete packages for the use of others in the general research community"-- | |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Statistik |0 (DE-588)4056995-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Robinson, Andrew |e Verfasser |0 (DE-588)14277507X |4 aut | |
| 856 | 4 | |u http://images.tandf.co.uk/common/jackets/websmall/978143985/9781439858028.jpg |3 Cover | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026124941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026124941 | ||
Datensatz im Suchindex
| _version_ | 1804150550703374336 |
|---|---|
| adam_text | Contents
Preface
їх
Programming and R
1
1.1
Introduction
........................... 1
1.2
R
Specifies
............................ 1
1.2.1
Objects
.......................... 3
1.2.1.1
Veetors
.....................
З
1.2.1.2
Subset
t ing
................... 7
1.2.2
Container
Objects....................
7
1.2.2.1
Lists
....................... 8
1.2.2.2
Dataframes
................... 9
1.2.3
Functions
......................... 10
1.2.3.1
Arguments
................... 11
1.2.3.2
Body
...................... 13
1.2.3.3
Environments and Scope
........... 14
1.2.4
Matrices
.......................... 16
1.2.5
Probability Families
................... 19
1.2.6
Flow Control
....................... 22
1.2.6.1
Conditional Execution
............. 23
1.2.6.2
Loops
...................... 23
1.2.7
Numerical Optimization
................. 25
1.3
Programming
........................... 27
1.3.1
Programming Style
.................... 27
1.3.2
Debugging
......................... 28
1.3.2.1
Debugging in Batch
.............. 29
1.3.3
Object-Oriented Programming
............. 30
1.3.4 S3
Classes
......................... 30
1.4
Making
R
Packages
....................... 34
1.4.1
Building a Package
.................... 35
1.4.2
Testing
.......................... 36
1.4.3
Installation
........................ 36
1.5
Further Reading
......................... 37
1.6
Exercises
............................. 37
v
VI
Statistics and Likelihood-Based Estimation
39
2.1
Introduction
........................... 39
2.2
Statistical Models
........................ 39
2.3
Maximum Likelihood Estimation
................ 41
2.3.1
Process
.......................... 41
2.3.2
Estimation
........................ 45
2.3.2.1
Exponential Family
.............. 46
2.3.3
Properties
......................... 47
2.4
Interval Estimates
........................ 49
2.4.1 Wald
Intervals
...................... 49
2.4.2
Inverting the LRT: Profile Likelihood
......... 50
2.4.3
Nuisance Parameters
................... 52
2.5
Simulation for Fun and Profit
................. 56
2.5.1
Pseudo-Random Number Generators
.......... 56
2.6
Exercises
............................. 59
Ordinary Regression
61
3.1
Introduction
........................... 61
3.2
Least-Squares Regression
.................... 62
3.2.1
Properties
......................... 64
3.2.2
Matrix Representation
.................. 66
3.2.3
QR Decomposition
.................... 69
3.2.4
Example
.......................... 71
3.3
Maximum-Likelihood Regression
................ 74
3.4
Infrastructure
.......................... 76
3.4.1
Easing Model Specification
............... 76
3.4.2
Missing Data
........................ 77
3.4.3
Link Function
....................... 78
3.4.4
Initializing the Search
.................. 78
3.4.5
Making Failure Informative
............... 79
3.4.6
Reporting Asymptotic
SE
and
CI
............ 79
3.4.7
The Regression Function
................. 80
3.4.8 S3
Classes
......................... 82
3.4.8.1
Print
...................... 82
3.4.8.2
Fitted Values
.................. 83
3.4.8.3
Residuals
.................... 84
3.4.8.4
Diagnostics
................... 85
3.4.8.5
Metrics of Fit
................. 87
3.4.8.6
Presenting a Summary
............ 89
3.4.9
Example Redux
...................... 91
3.4.10
Follow-up
......................... 94
3.5
Conclusion
............................ 94
3.6
Exercises
............................. 94
Vil
Generalized
Linear
Models
97
4.1
Introduction
........................... 97
4.2
GLM: Families and Terms
................... 99
4.3
The Exponential Family
..................... 102
4.4
The IRLS Fitting Algorithm
.................. 104
4.5
Bernoulli or Binary Logistic Regression
............ 105
4.5.1
IRLS
............................
Ill
4.6
Grouped Binomial Models
................... 114
4.7
Constructing a GLM Function
................. 120
4.7.1
A Summary Function
.................. 125
4.7.2
Other Link Functions
.................. 128
4.8
GLM Negative Binomial Model
................ 129
4.9
Offsets
.............................. 133
4.10
Dispersion. Over- and Under-
.................. 136
4.11
Goodness-of-Fit and Residual Analysis
............ 139
4.11.1
Goodness-of-Fit
...................... 139
4.11.2
Residual Analysis
..................... 141
4.12
Weights
.............................. 143
4.13
Conclusion
............................ 143
4.14
Exercises
............................. 144
Maximum Likelihood Estimation
145
5.1
Introduction
........................... 145
5.2
MLE for GLM
.......................... 146
5.2.1
The Log-Likelihood
................... 146
5.2.2
Parameter Estimation
.................. 148
5.2.3
Residuals
......................... 149
5.2.4
Deviance
......................... 150
5.2.5
Initial Values
....................... 151
5.2.6
Printing the Object
................... 151
5.2.7
GLM Function
...................... 153
5.2.8
Fitting for a New Family
................ 157
5.3
Two-Parameter MLE
...................... 160
5.3.1
The Log-Likelihood
................... 160
5.3.2
Parameter Estimation
.................. 162
5.3.3
Deviance and Deviance Residuals
............ 163
5.3.4
Initial Values
....................... 165
5.3.5
Printing and Summarizing the Object
......... 165
5.3.6
GLM Function
...................... 165
5.3.7
Building on the Model
.................. 171
5.3.8
Fitting for a New Family
................ 173
5.4
Exercises
............................. 176
Vlil
6
Panel Data
177
6.1
What Is
a Panel Model?
.................... 177
6.1.1
Fixed- or Random-Effects Models
............ 181
6.2
Fixed-Effects
Model
....................... 181
6.2.1
Unconditional Fixed-Effects Models
.......... 181
6.2.2
Conditional Fixed-Effects Models
............ 183
6.2.3
Coding a Conditional Fixed-Effects Negative Binomial
185
6.3
Random-Intercept Model
.................... 188
6.3.1
Random-Effects Models
................. 188
6.3.2
Coding a Random-Intercept Gaussian Model
..... 191
6.4
Handling More Advanced Models
............... 194
6.Г)
The EM Algorithm
....................... 194
6.5.1
A Simple Example
.................... 196
6.5.2
The Random-Intercept Model
.............. 197
6Љ
Further Reading
......................... 201
6.7
Exercises
............................. 202
7
Model Estimation Using Simulation
203
7.1
Simulation: Why and When?
.................. 203
7.2
Synthetic Statistical Models
.................. 205
7.2.1
Developing Synthetic Models
.............. 205
7.2.2
Monte Carlo Estimation
................. 209
7.2.3
Reference Distributions
................. 216
7.3
Bayesian Parameter Estimation
................ 219
7.3.1
Gibbs Sampling
...................... 229
7.4
Discussion
............................ 230
7.5
Exercises
............................. 231
Bibliography
233
Index
239
|
| any_adam_object | 1 |
| author | Hilbe, Joseph M. 1944-2017 Robinson, Andrew |
| author_GND | (DE-588)128751851 (DE-588)14277507X |
| author_facet | Hilbe, Joseph M. 1944-2017 Robinson, Andrew |
| author_role | aut aut |
| author_sort | Hilbe, Joseph M. 1944-2017 |
| author_variant | j m h jm jmh a r ar |
| building | Verbundindex |
| bvnumber | BV041149445 |
| callnumber-first | Q - Science |
| callnumber-label | QA276 |
| callnumber-raw | QA276.8 |
| callnumber-search | QA276.8 |
| callnumber-sort | QA 3276.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 830 |
| ctrlnum | (OCoLC)856829614 (DE-599)GBV746403569 |
| dewey-full | 519.5/44 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/44 |
| dewey-search | 519.5/44 |
| dewey-sort | 3519.5 244 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03356nam a2200397 c 4500</leader><controlfield tag="001">BV041149445</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20151023 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">130717s2013 |||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2013013448</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781439858028</subfield><subfield code="c">hardback</subfield><subfield code="9">978-1-4398-5802-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)856829614</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBV746403569</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-473</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA276.8</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5/44</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 830</subfield><subfield code="0">(DE-625)143259:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hilbe, Joseph M.</subfield><subfield code="d">1944-2017</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)128751851</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Methods of statistical model estimation</subfield><subfield code="c">Joseph M. Hilbe ; Andrew P. Robinson</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton [u.a.]</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XII, 243 S.</subfield><subfield code="b">graf. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="520" ind1="1" ind2=" "><subfield code="a">"Preface Methods of Statistical Model Estimation has been written to develop a particular pragmatic viewpoint of statistical modelling. Our goal has been to try to demonstrate the unity that underpins statistical parameter estimation for a wide range of models. We have sought to represent the techniques and tenets of statistical modelling using executable computer code. Our choice does not preclude the use of explanatory text, equations, or occasional pseudo-code. However, we have written computer code that is motivated by pedagogic considerations first and foremost. An example is in the development of a single function to compute deviance residuals in Chapter 4. We defer the details to Section 4.7, but mention here that deviance residuals are an important model diagnostic tool for GLMs. Each distribution in the exponential family has its own deviance residual, defined by the likelihood. Many statistical books will present tables of equations for computing each of these residuals. Rather than develop a unique function for each distribution, we prefer to present a single function that calls the likelihood appropriately itself. This single function replaces five or six, and in so doing, demonstrates the unity that underpins GLM. Of course, the code is less efficient and less stable than a direct representation of the equations would be, but our goal is clarity rather than speed or stability. This book also provides guidelines to enable statisticians and researchers from across disciplines to more easily program their own statistical models using R. R, more than any other statistical application, is driven by the contributions of researchers who have developed scripts, functions, and complete packages for the use of others in the general research community"--</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Statistik</subfield><subfield code="0">(DE-588)4056995-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Statistik</subfield><subfield code="0">(DE-588)4056995-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Robinson, Andrew</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)14277507X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://images.tandf.co.uk/common/jackets/websmall/978143985/9781439858028.jpg</subfield><subfield code="3">Cover</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bamberg - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026124941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-026124941</subfield></datafield></record></collection> |
| id | DE-604.BV041149445 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:40:43Z |
| institution | BVB |
| isbn | 9781439858028 |
| language | English |
| lccn | 2013013448 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026124941 |
| oclc_num | 856829614 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-634 |
| owner_facet | DE-473 DE-BY-UBG DE-634 |
| physical | XII, 243 S. graf. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Hilbe, Joseph M. 1944-2017 Verfasser (DE-588)128751851 aut Methods of statistical model estimation Joseph M. Hilbe ; Andrew P. Robinson Boca Raton [u.a.] CRC Press 2013 XII, 243 S. graf. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "Preface Methods of Statistical Model Estimation has been written to develop a particular pragmatic viewpoint of statistical modelling. Our goal has been to try to demonstrate the unity that underpins statistical parameter estimation for a wide range of models. We have sought to represent the techniques and tenets of statistical modelling using executable computer code. Our choice does not preclude the use of explanatory text, equations, or occasional pseudo-code. However, we have written computer code that is motivated by pedagogic considerations first and foremost. An example is in the development of a single function to compute deviance residuals in Chapter 4. We defer the details to Section 4.7, but mention here that deviance residuals are an important model diagnostic tool for GLMs. Each distribution in the exponential family has its own deviance residual, defined by the likelihood. Many statistical books will present tables of equations for computing each of these residuals. Rather than develop a unique function for each distribution, we prefer to present a single function that calls the likelihood appropriately itself. This single function replaces five or six, and in so doing, demonstrates the unity that underpins GLM. Of course, the code is less efficient and less stable than a direct representation of the equations would be, but our goal is clarity rather than speed or stability. This book also provides guidelines to enable statisticians and researchers from across disciplines to more easily program their own statistical models using R. R, more than any other statistical application, is driven by the contributions of researchers who have developed scripts, functions, and complete packages for the use of others in the general research community"-- Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Robinson, Andrew Verfasser (DE-588)14277507X aut http://images.tandf.co.uk/common/jackets/websmall/978143985/9781439858028.jpg Cover Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026124941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hilbe, Joseph M. 1944-2017 Robinson, Andrew Methods of statistical model estimation Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Methods of statistical model estimation |
| title_auth | Methods of statistical model estimation |
| title_exact_search | Methods of statistical model estimation |
| title_full | Methods of statistical model estimation Joseph M. Hilbe ; Andrew P. Robinson |
| title_fullStr | Methods of statistical model estimation Joseph M. Hilbe ; Andrew P. Robinson |
| title_full_unstemmed | Methods of statistical model estimation Joseph M. Hilbe ; Andrew P. Robinson |
| title_short | Methods of statistical model estimation |
| title_sort | methods of statistical model estimation |
| topic | Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik |
| url | http://images.tandf.co.uk/common/jackets/websmall/978143985/9781439858028.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026124941&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hilbejosephm methodsofstatisticalmodelestimation AT robinsonandrew methodsofstatisticalmodelestimation |