Description:

Examination of regression techniques and assumptions used to develop static and dynamic equations of tree and stand attributes

Prerequisites: ST 552 with C or above or instructor approval.

Learning Objectives:

• Examine assumptions and their impact on linear regression. A models is defined not only by its fit to data, basically shape, but also by the fulfilment of the assumptions on which computations are executed. The students will learn:
  • To identify whether or not the assumptions arte met
  • To examine the consequences of violating assumptions
  • To minimize the consequences of assumption violations
• Nonlinear modeling. Linear models are very rare encountered in real applications. To this end we will focus on non-linear models as the natural generalization of linear models. The students will lean the foundation of
  • mixed models
  • nonlinear models
  • systems of simultaneous equations
  • generalized linear models
  • parsimonious nonlinear models
• Select an appropriate model.  The students will identify a solution for a real problem. The problem will be either an aspect of their research or a given problem of interest in forestry.

The statistical theory will be discussed in the context of forest modeling and implemented in exercises and homework assignments. Therefore, at the completion of the class the students will have a personalized library of forest models, as well as an extensive references to be used in subsequent analyses.

Learning Outcomes

• Develop linear and nonlinear models
• Choose among possible nonlinear models
• Enhance skills on using modeling software, such as R or SAS

 Learning resources

• Kutner, M.H., C.J. Nachtsheim, J. Neter, and William Li. 2005. Applied Linear Statistical Models. 5th Edition. McGraw-Hill/Irwin, Boston. ISBN 0-07-238688-6.
• Draper, N.R. and H. Smith. 1998. Applied Regression Analysis, 3rd Edition. John Wiley & Sons, Inc. New York. 706p.
• Kmenta, J. 1997. Elements of Econometrics, 2nd Edition. University of Michigan Press, Ann Arbor. 786p.
• Weiskittel, A.R., D.W. Hann, J.A. Kershaw, Jr., J.K. Vanclay. 2011. Forest growth and yield modeling. Wiley-Blackwell, Oxford, 415p. Available for online reading from OSU library website: http://osulibrary.orst.edu/.
• Venables, W.N., Smith, D.M., and the R Core Team, 2015. An Introduction to R. Available online: http://cran.r-project.org/doc/manuals/R-intro.pdf
• Chambers and Hastie (1993) Statistical models in S

Software:

• R
• SAS

Topics

• Simple linear regression: estimation, assumptions
• Multiple linear regression: estimation, assumptions
• Nonlinear models:
• Mixed effects models
• Nonlinear regression
• Generalized linear models
• Parsimonious nonlinear models