Sean Canavan David Hann Oregon State University

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

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 R2, 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.