Growth Curve Models and Statistical Diagnostics

Growth-curve models are generalized multivariate analysis-of-variance models. These models are especially useful for investigating growth problems on short times in economics, biology, medical research, and epidemiology. This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. The authors provide complete proofs of theorems as well as practical data sets and MATLAB code.

Sommario

1 Introduction.- 1.1 General Remarks.- 1.2 Statistical Diagnostics in Multivariate Analysis.- 1.3 Growth Curve Model (GCM).- 1.4 Summary.- 1.5 Preliminary Results.- 1.6 Further Readings.- 2 Generalized Least Square Estimation.- 2.1 General Remarks.- 2.2 Generalized Least Square Estimation.- 2.3 Admissible Estimate of Regression Coefficient.- 2.4 Bibliographical Notes.- 3 Maximum Likelihood Estimation.- 3.1 Maximum Likelihood Estimation.- 3.2 Rao's Simple Covariance Structure (SCS).- 3.3 Restricted Maximum Likelihood Estimation.- 3.4 Bibliographical Notes.- 4 Discordant Outlier and Influential Observation.- 4.1 General Remarks.- 4.2 Discordant Outlier Detection in the GCM with SCS.- 4.3 Influential Observation in the GCM with SCS.- 4.4 Discordant Outlier Detection in the GCM with UC.- 4.5 Influential Observation in the GCM with UC.- 4.6 Bibliographical Notes.- 5 Likelihood-Based Local Influence.- 5.1 General Remarks.- 5.2 Local Influence Assessment in the GCM with SCS.- 5.3 Local Influence Assessment in the GCM with UC.- 5.4 Bibliographical Notes.- 6 Bayesian Influence Assessment.- 6.1 General Remarks.- 6.2 Bayesian Influence Analysis in the GCM with SCS.- 6.3 Bayesian Influence Analysis in the GCM with UC.- 6.4 Bibliographical Notes.- 7 Bayesian Local Influence.- 7.1 General Remarks.- 7.2 Bayesian Local Influence in the GCM with SCS.- 7.3 Bayesian Local Influence in the GCM with UC.- 7.4 Bibliographical Notes.- Appendix Data sets used in this book.- References.- Author Index.

Riassunto

Growth-curve models are generalized multivariate analysis-of-variance models. These models are especially useful for investigating growth problems on short times in economics, biology, medical research, and epidemiology. This book systematically introduces the theory of the GCM with particular emphasis on their multivariate statistical diagnostics, which are based mainly on recent developments made by the authors and their collaborators. The authors provide complete proofs of theorems as well as practical data sets and MATLAB code.

Testo aggiuntivo

From the reviews:

"The book is well written and contains a goodly number of real-data applications." ISI

Short Book Reviews, Vol.23/1, April 2003

"This book offers an extensive view of Growth Curve Models and a wide range of issues related with statistical diagnosis. … Each chapter ends with some bibliographical notes that inform the reader about historical sources as well as about recent developments. The bibliographic list is impressive! … the information given about Growth Curve Models and Statistical Diagnosis is excellent. The book is written very rigorously and precisely and I strongly recommend it for statisticians or for applied scientists with some mathematical and statistical background." (Prof. C. García-Olaverri, Kwantitatieve Methoden, Vol. 72B5, 2003)

"The authors have written a basic book on a well developed and important field in multivariate statistical analysis. It will undoubtedly serve as a reference in this field." (Arjun K. Gupta, Zentralblatt MATH, Vol. 1024, 2003)

"This book presents methods for analyzing repeated measures and longitudinal data using the growth curve models (GCMs), with specific focus on the generalized multivariate analysis of variance (GMANOVA) model. … For researchers, the book’s main strength is its level of detail. … Theoreticians in multivariate analysis will find this book to be a good reference for this particular GCM and multivariate regression diagnosis." (Andrew M. Kuhn, Technometrics, Vol. 45 (3), 2003)

"Models are discussed for data variously described as growth curves, longitudinal data, or multilevel data. The text supplements the growing number of references on techniques for longitudinal data by focusing on diagnostics for outliers and influential observations. … the book is well written and does contain a goodly number of real-data applications." (J. O. Ramsey, Short Book Reviews, Vol. 23 (1), 2003)

Relazione

From the reviews:
"The book is well written and contains a goodly number of real-data applications." ISI
Short Book Reviews, Vol.23/1, April 2003
"This book offers an extensive view of Growth Curve Models and a wide range of issues related with statistical diagnosis. ... Each chapter ends with some bibliographical notes that inform the reader about historical sources as well as about recent developments. The bibliographic list is impressive! ... the information given about Growth Curve Models and Statistical Diagnosis is excellent. The book is written very rigorously and precisely and I strongly recommend it for statisticians or for applied scientists with some mathematical and statistical background." (Prof. C. García-Olaverri, Kwantitatieve Methoden, Vol. 72B5, 2003)
"The authors have written a basic book on a well developed and important field in multivariate statistical analysis. It will undoubtedly serve as a reference in this field." (Arjun K. Gupta, Zentralblatt MATH, Vol. 1024, 2003)
"This book presents methods for analyzing repeated measures and longitudinal data using the growth curve models (GCMs), with specific focus on the generalized multivariate analysis of variance (GMANOVA) model. ... For researchers, the book's main strength is its level of detail. ... Theoreticians in multivariate analysis will find this book to be a good reference for this particular GCM and multivariate regression diagnosis." (Andrew M. Kuhn, Technometrics, Vol. 45 (3), 2003)
"Models are discussed for data variously described as growth curves, longitudinal data, or multilevel data. The text supplements the growing number of references on techniques for longitudinal data by focusing on diagnostics for outliers and influential observations. ... the book is well written and does contain a goodly number of real-data applications." (J. O. Ramsey, Short Book Reviews, Vol. 23 (1), 2003)

Dettagli sul prodotto

• Autori: Kai-Tai Fang, Jian-Xi Pan, Jian-Xin Pan
• Editore: Springer, Berlin
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 26.10.2010
• EAN: 9781441928641
• ISBN: 978-1-4419-2864-1
• Pagine: 388
• Dimensioni: 155 mm x 23 mm x 229 mm
• Peso: 616 g
• Illustrazioni: XVII, 388 p.
• Serie: Springer Series in Statistics; Springer Series in Statistics
• Categorie: Scienze naturali, medicina, informatica, tecnica > Matematica > Teoria delle probabilità, stocastica, statistica matematica; C, Epidemiology & medical statistics, Statistics, Mathematics and Statistics, Statistics for Life Sciences, Medicine, Health Sciences, Statistical Theory and Methods, Probability Theory and Stochastic Processes, Probability & statistics, Probabilities, Stochastics, Probability Theory, Biostatistics