Statistical tools for nonlinear regression: a practical guide with S-PLUS and R examples
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Springer
2004
|
| Edition: | 2. ed. |
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 227 - 229 |
| Physical Description: | XIV, 232 S. graph. Darst. : 25 cm, 425 gr. |
| ISBN: | 0387400818 |
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MARC
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| 245 | 1 | 0 | |a Statistical tools for nonlinear regression |b a practical guide with S-PLUS and R examples |c S. Huet ... |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2004 | |
| 300 | |a XIV, 232 S. |b graph. Darst. : 25 cm, 425 gr. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
to the Second Edition
.................................
XI
Preface to the First Edition
..................................XIII
1
Nonlinear Regression Model and Parameter Estimation
... 1
1.1
Examples
............................................... 1
1.1.1
Pasture Regrowth: Estimating a Growth Curve
....... 1
1.1.2
Radioimmunological Assay of
Cortisol:
Estimating a
Calibration Curve
................................. 2
1.1.3
Antibodies Anticoronavirus Assayed by an
ELISA
Test: Comparing Several Response Curves
............ 6
1.1.4
Comparison of Immature and Mature Goat Ovocytes:
Comparing Parameters
............................. 8
1.1.5
Isomerization: More than One Independent Variable
... 9
1.2
The Parametric Nonlinear Regression Model
................ 10
1.3
Estimation
............................................. 11
1.4
Applications
............................................ 13
1.4.1
Pasture Regrowth: Parameter Estimation and Graph
of Observed and Adjusted Response Values
........... 13
1.4.2 Cortisol
Assay: Parameter Estimation and Graph of
Observed and Adjusted Response Values
............. 13
1.4.3
ELISA Test:
Parameter Estimation and Graph of
Observed and Adjusted Curves for May and June
..... 14
1.4.4
Ovocytes: Parameter Estimation and Graph of
Observed and Adjusted Volume of Mature and
Immature Ovocytes in Propane-Diol
................. 15
1.4.5
Isomerization: Parameter Estimation and Graph of
Adjusted versus Observed Values
.................... 16
1.5
Conclusion and References
................................ 17
1.6
Using nls2
............................................. 18
VI
Contents
2
Accuracy of Estimators, Confidence Intervals and Tests
.... 29
2.1
Examples
............................................... 29
2.2
Problem Formulation
.................................... 30
2.3
Solutions
............................................... 30
2.3.1
Classical Asymptotic Results
....................... 30
2.3.2
Asymptotic Confidence Intervals for
λ
............... 32
2.3.3
Asymptotic Tests of
λ
=
Ao
against
λ φ
Ao
........... 33
2.3.4
Asymptotic Tests of
ΛΘ
=
Lo
against
Λθ φ
Lo
........ 34
2.3.5
Bootstrap Estimations
............................. 35
2.4
Applications
............................................ 38
2.4.1
Pasture Regrowth: Calculation of a Confidence
Interval for the Maximum Yield
..................... 38
2.4.2 Cortisol
Assay: Estimation of the Accuracy of the
Estimated Dose
Ď
................................. 39
2.4.3
ELISA Test:
Comparison of Curves
.................. 40
2.4.4
Ovocytes: Calculation of Confidence Regions
.......... 42
2.4.5
Isomerization: An Awkward Example
................ 43
2.4.6
Pasture Regrowth: Calculation of a Confidence
Interval for A
=
exp
Θ3
............................. 47
2.5
Conclusion
............................................. 49
2.6
Using nls2
............................................. 49
3
Variance Estimation
....................................... 61
3.1
Examples
............................................... 61
3.1.1
Growth of Winter Wheat Tillers: Few Replications
___ 61
3.1.2
Solubility of Peptides in Txichloacetic Acid Solutions:
No Replications
................................... 63
3.2
Parametric Modeling of the Variance
....................... 65
3.3
Estimation
............................................. 66
3.3.1
Maximum Likelihood Estimation
.................... 66
3.3.2
Quasi-Likelihood Estimation
........................ 67
3.3.3
Three-Step Estimation
............................. 69
3.4
Tests and Confidence Regions
............................. 69
3.4.1
The
Wald Test.................................... 69
3.4.2
The Likelihood Ratio Test
.......................... 70
3.4.3
Bootstrap Estimations
............................. 71
3.4.4
Links Between Testing Procedures and Confidence
Region Computations
.............................. 72
3.4.5
Confidence Regions
................................ 73
3.5
Applications
............................................ 74
3.5.1
Growth of Winter Wheat Tillers
.................... 74
3.5.2
Solubility of Peptides in Trichloacetic Acid Solutions
... 78
3.6
Using nls2
............................................. 83
Contents
VII
4
Diagnostics
of Model Misspecification
..................... 93
4.1
Problem Formulation
.................................... 93
4.2
Diagnostics of Model Misspecifications with Graphics
........ 94
4.2.1
Pasture Regrowth Example: Estimation Using a
Concave-Shaped Curve and Plot for Diagnostics
....... 95
4.2.2
Isomerization Example: Graphics for Diagnostic
....... 95
4.2.3
Peptides Example: Graphics for Diagnostic
........... 97
4.2.4 Cortisol
Assay Example: How to Choose the Variance
Function Using Replications
........................ 99
4.2.5
Trajectory of Roots of Maize: How to Detect
Correlations in Errors
..............................103
4.2.6
What Can We Say About the Experimental Design?
... 107
4.3
Diagnostics of Model Misspecifications with Tests
............110
4.3.1
RIA
of
Cortisol:
Comparison of Nested Models
........110
4.3.2
Tests Using Replications
...........................110
4.3.3 Cortisol
Assay Example: Misspecification Tests Using
Replications
......................................112
4.3.4
Ovocytes Example: Graphics of Residuals and
Misspecification Tests Using Replications
.............112
4.4
Numerical Troubles During the Estimation Process: Peptides
Example
...............................................114
4.5
Peptides Example: Concluded
.............................118
4.6
Using nls2
.............................................119
5
Calibration and Prediction
................................135
5.1
Examples
...............................................135
5.2
Problem Formulation
....................................137
5.3
Confidence Intervals
.....................................137
5.3.1
Prediction of a Response
...........................137
5.3.2
Calibration with Constant Variances
.................139
5.3.3
Calibration with
Nonconstant
Variances
..............141
5.4
Applications
............................................142
5.4.1
Pasture Regrowth Example: Prediction of the Yield at
Time x0
= 50.....................................142
5.4.2 Cortisol
Assay Example
............................143
5.4.3
Nasturtium Assay Example
.........................144
5.5
References
..............................................145
5.6
Using nls2
.............................................145
6
Binomial Nonlinear Models
................................153
6.1
Examples
...............................................153
6.1.1
Assay of an Insecticide with
a
Synergist:
A Binomial
Nonlinear Model
..................................153
6.1.2
Vaso-Constriction in the Skin of the Digits: The Case
of Binary Response Data
...........................155
VIII Contents
6.1.3
Mortality of Confused Flour Beetles: The Choice of a
Link Function in a Binomial Linear Model
............156
6.1.4
Mortality of Confused Flour Beetles
2:
Survival
Analysis Using a Binomial Nonlinear Model
..........158
6.1.5
Germination of
Orobranche: Overdispersion
...........159
6.2
The Parametric Binomial Nonlinear Model
.................160
6.3
Overdispersion, Underdispersion
...........................161
6.4
Estimation
.............................................162
6.4.1
Case of Binomial Nonlinear Models
..................162
6.4.2
Case of Overdispersion or Underdispersion
............164
6.5
Tests and Confidence Regions
.............................165
6.6
Applications
............................................167
6.6.1
Assay of an Insecticide with
a
Synergist:
Estimating
the Parameters
....................................167
6.6.2
Vaso-Constriction in the Skin of the Digits: Estimation
and Test of Nested Models
.........................171
6.6.3
Mortality of Confused Flour Beetles: Estimating the
Link Function and Calculating Confidence Intervals
for the LD90
......................................172
6.6.4
Mortality of Confused Flour Beetles
2:
Comparison of
Curves and Confidence Intervals for the ED50
.........174
6.6.5
Germination of
Orobranche:
Estimating
Overdispersion Using the Quasi-Likelihood
Estimation Method
................................177
6.7
Using nls2
.............................................180
7
Multinomial and
Poisson
Nonlinear Models
................199
7.1
Multinomial Model
......................................199
7.1.1
Pneumoconiosis among Coal Miners: An Example of
Multicategory Response Data
......................200
7.1.2
A Cheese Tasting Experiment
.......................200
7.1.3
The Parametric Multinomial Model
..................201
7.1.4
Estimation in the Multinomial Model
................204
7.1.5
Tests and Confidence Intervals
......................206
7.1.6
Pneumoconiosis among Coal Miners: The Multinomial
Logit Model
......................................208
7.1.7
Cheese Tasting Example: Model Based on Cumulative
Probabilities
......................................210
7.1.8
Using nls2
.......................................213
7.2
Poisson
Model
..........................................221
7.2.1
The Parametric
Poisson
Model
......................222
7.2.2
Estimation in the
Poisson
Model
....................222
7.2.3 Cortisol
Assay Example: The
Poisson
Nonlinear Model
. 223
7.2.4
Using nls2
.......................................225
Contents
IX
References
.....................................................227
Index..........................................................231
Statistical Took for Nonlinear Regression, Second Edition, presents methods for analyzing
data using parametric nonlinear regression models. The new edition has been expanded
to include binomial, multinomial, and
Poisson
nonlinear models. Using examples from
experiments in agronomy and biochemistry, it shows how to apply these methods. It con¬
centrates on presenting the methods in an intuitive way rather than developing the theo¬
retical backgrounds.
The examples are analyzed with the free software nls2 updated to deal with the new mod¬
els included in the second edition. The nls2 package is implemented in S-PLUS and R. Its
main advantages are to make the model-building, estimation, and validation tasks easy to
do. More precisely,
•
complex models can be easily described using a symbolic syntax. The regression func¬
tion as well as the variance function can be defined explicitly as functions of indepen¬
dent variables and of unknown parameters, or they can be defined as the solution to a
system of differentia] equations. Moreover, constraints on the parameters can easily be
added to the model. It is thus possible to test nested hypotheses and to compare several
datasets.
•
several additional tools are included in the package for calculating confidence regions
for functions of parameters or calibration intervals, using classical methodology or
bootstrap. Moreover, some graphical tools are proposed for visualizing the fitted curves,
the residuals, the confidence regions, and the numerical estimation procedure.
This book is aimed at scientists who are not familiar with statistical theory, but have a
basic knowledge of statistical concepts. It includes methods based on classical nonlinear
regression theory and more modern methods, such as bootstrap, which have proved effec¬
tive in practice. The additional chapters of the second edition assume some practical expe¬
rience in data analysis using generalized linear models. The book will be of interest both
to practitioners as a guide and reference book, and to students as a tutorial book.
Sylvie
Huet and Emmanuel jolivet are senior researchers and Annie
Bouvier
is a comput¬
ing engineer at
INRA,
National Institute of Agronomical Research, France; Marie-Anne
Poursat is an associate professor of statistics at the University Paris XI.
|
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV019315963 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:57:29Z |
| institution | BVB |
| isbn | 0387400818 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012783513 |
| oclc_num | 52092090 |
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| owner_facet | DE-739 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-706 DE-634 DE-11 DE-578 |
| physical | XIV, 232 S. graph. Darst. : 25 cm, 425 gr. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples S. Huet ... 2. ed. New York [u.a.] Springer 2004 XIV, 232 S. graph. Darst. : 25 cm, 425 gr. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 227 - 229 Analyse de régression Estimation d'un paramètre Niet-lineaire modellen gtt Regressieanalyse gtt Théories non linéaires Nonlinear theories Parameter estimation Regression analysis S-PLUS (DE-588)4321162-8 gnd rswk-swf Programm (DE-588)4047394-6 gnd rswk-swf Nichtlineare Regression (DE-588)4251077-6 gnd rswk-swf Nichtlineare Regression (DE-588)4251077-6 s S-PLUS (DE-588)4321162-8 s Programm (DE-588)4047394-6 s DE-604 Huet, Sylvie Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012783513&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012783513&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples Analyse de régression Estimation d'un paramètre Niet-lineaire modellen gtt Regressieanalyse gtt Théories non linéaires Nonlinear theories Parameter estimation Regression analysis S-PLUS (DE-588)4321162-8 gnd Programm (DE-588)4047394-6 gnd Nichtlineare Regression (DE-588)4251077-6 gnd |
| subject_GND | (DE-588)4321162-8 (DE-588)4047394-6 (DE-588)4251077-6 |
| title | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples |
| title_auth | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples |
| title_exact_search | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples |
| title_full | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples S. Huet ... |
| title_fullStr | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples S. Huet ... |
| title_full_unstemmed | Statistical tools for nonlinear regression a practical guide with S-PLUS and R examples S. Huet ... |
| title_short | Statistical tools for nonlinear regression |
| title_sort | statistical tools for nonlinear regression a practical guide with s plus and r examples |
| title_sub | a practical guide with S-PLUS and R examples |
| topic | Analyse de régression Estimation d'un paramètre Niet-lineaire modellen gtt Regressieanalyse gtt Théories non linéaires Nonlinear theories Parameter estimation Regression analysis S-PLUS (DE-588)4321162-8 gnd Programm (DE-588)4047394-6 gnd Nichtlineare Regression (DE-588)4251077-6 gnd |
| topic_facet | Analyse de régression Estimation d'un paramètre Niet-lineaire modellen Regressieanalyse Théories non linéaires Nonlinear theories Parameter estimation Regression analysis S-PLUS Programm Nichtlineare Regression |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012783513&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012783513&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT huetsylvie statisticaltoolsfornonlinearregressionapracticalguidewithsplusandrexamples |