1. Sean Canavan David Hann Oregon State University The Presence of Measurement Error in Forestry

2. Why measurement error? Regression assumption Relatively unexplored topic in Forestry

3. Ways in which Measurement Error enters into Forestry: 1 – Mensuration Error 2 – Rounding Error 3 – Sampling Error 4 – Variable Selection Error

4. Mensuration Error: The error that arises when a recorded value is not exactly the same as the true value due to a flaw in the measurement process. Potential Causes: – Misuse of tools – Poor choice of measurement tool – Lack of training – Carelessness – Not possible to measure exactly

5. Rounding Error: The error that arises when a recorded value is not exactly the same as the true value due to rounding. Examples: – Dbh measured to the nearest 0.1” – Dbh recorded to the last whole 0.1” – Dbh tallied by diameter class – Height measured to the nearest foot – Crown ratio recorded to the nearest 10% – Grouping into classes (i.e. crown class)

6. Sampling Error: The error that arises due to estimates being based on only a subset of the entire population of interest. Factors Affecting the Size of Sampling Error: – Sampling design – Sample size – Plot size – Plot shape – Sampling distribution

7. Variable Selection Error: The error that arises when a model is calibrated with one form of a variable and then applied with a different form of the variable. Examples: – A model is calibrated with measured values for a variable and applied with predicted values, or vice versa – Missing values from field measurements are filled in using model predictions or sample means

8. Should we care???

9. Yes! We should!

10. Consequences of Measurement Error: Fuller (1987): In simple linear regression the slope parameter is attenuated in the presence of measurement error Carroll et al. (1995): The real effects of measurement errors may be hidden Observed data display relationships that are not present in the true data The signs of the estimated coefficients may be changed Studies in Forestry:

11. Mensuration Error: Mensuration error in one variable affects the regression coefficients of all the independent variables with which the contaminated variable is correlated - (Kangas 1998) Biased model predictions - (Gertner & Dzialowy 1984, Gertner 1991, Wallach & Genard 1998, & Kozak 1998) Decreased precision of model predictions - (Gertner & Dzialowy 1984, Garcia 1984, McRoberts et al. 1994, Wallach & Genard 1998, and Kozak 1998)

12. Rounding Error: Biased model parameters/estimates - (Swindel & Bower 1972, Smith & Burkhart 1984, Ritchie 1997) Inefficient model parameters - (Kmenta 1986) Heteroskedastic model prediction errors - (Kmenta 1986)

13. Sampling Error: Sampling precision and accuracy are proportional to the size of the sampling unit (Kulow 1966, Smith 1975, Reich & Arvanitis 1992) OLS intercept and slope parameters are biased in the presence of sampling error (Jaakkola 1967) Small plot size can lead to highly skewed distributions (Smith 1975) Choice of sampling design can lead to bias (Kulow 1966, Smith & Burkhart 1984, Hann & Zumrawi 1991) Unintentionally sampling from an unintended population can lead to significant bias in model estimates (Nigh & Love 1999)

14. Variable Selection Error: Fit statistics, specifically R 2, are incorrect and strongly biased upward when predicted data are used in place of actual measurements (Hasenauer & Monserud 1996) Using data with missing values will lead to inefficient parameter estimates with the size of the inefficiency depending on the dispersion of the missing values (Kmenta 1986) Filling in missing values with sample means will lead to biased estimates and no gain in efficiency (Kmenta 1986) Common methods for systems of equations (2SLS, 3SLS, SUR) incorrectly assume independence of errors in forestry situations leading to biased and inconsistent parameter variance estimates (LeMay 1990)

15. Conclusion: Measurement error enters into forestry in many different forms The errors can have very negative effects on model parameters, model estimates, and the variances of model parameters and model estimates.

16. What Comes Next?: Correction techniques do exist for countering the effects of measurement errors in many situations, but typically require knowing something about the form of the errors. People have generally made the assumption that the errors are Normal in distribution. Is this correct? That’s what we’ll talk about tomorrow.