3_GLMs - Motivating texts Advanced Topics in Forest...

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Advanced Topics in Forest Biometrics – FOR6934 Review of General Linear Models Motivating texts Schabenberger, O. and F.J. Pierce (2002) Contemporary Statistical Models for the Plant and Soil Sciences . CRC Press, NY, NY. Littell, R.C., G.A. Milliken, W.W. Stroup, and R.D. Wolfinger (1996) SAS System for Mixed Models . SAS Institute, Cary,NC. What is a model? ± A scientific model is an abstraction of reality ± Models can be further classified: ² Mathematical models ² Stochastic models ² Statistical models Mathematical models ± Mathematical models are mechanistic (deterministic) devices ± A given set of inputs gives an output that is predicted with certainty ± Example: the weight of a brazil nut fruit, Y, under silvicultural treatment i is: Y = µ + τ i where: i is the i th treatment effect Deterministic models have no random components Stochastic models ± Mathematical models ignore uncertainty, whereas stochastic models include random effects ± Example: the weight of a brazil nut fruit, Y, under silvicultural treatment i is: Y = + i + e where: e is a random variable with mean zero and variance σ 2 ± The expected value of Y under treatment i is: E[ Y i ] = + i Why do we need stochastic elements? (Adapted from Schabenberger and Pierce 2002) ± The model is not correct for a particular observation, but correct on average ± Assumptions are necessary to abstract phenomenon ± It is often impossible to measure/observe all variables ± Stochastic models are often more parsimonious ± When you have real data, you have sampling error What is sampling error?
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Statistical models ± Statistical models are stochastic models that contain
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This note was uploaded on 07/23/2011 for the course FOR 6934 taught by Professor Staff during the Spring '08 term at University of Florida.

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3_GLMs - Motivating texts Advanced Topics in Forest...

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