1. Best Model Dylan Loudon

2. Linear Regression Results Erin Alvey

3. Who will you trust? Field technicians? Software programmers? Statisticians? Instructors? GIS technicians? Other researchers? Yourself?

4. Regression (Correlation) Modeling Creates a model in N-Dimensional “Hyper-Space” Defined by: –Covariates –Response variables –Mathematics used to create the model –Statistics used to optimize parameters –Options for model evaluation –Predictor variables

5. Multiple Linear Regression

6. Linear Regression: 2 Predictors Mathworks.com

7. Non-Linear Regression

8. Regression Methods Continuous Regression: –Linear Regression –Generalized Linear Models (GLM) –Generalized Additive Models (GAMs) Categorical Regression (trees): –Regression Trees –Classification and regression trees (CART) Machine Learning: –Maximum Entropy (Maxent) –NPMR, HEMI, BRTs, etc.

9. Brown Shrimp Size Add graph from work

10. Terminology Plant uses: –Measured value and response variable –Explanatory variable I prefer: –Response variable –I’ll use “measured value” to identify measured values in field data –Covariate: Explanatory variable used to build the model –Predictor: Explanatory variable used to predict

11. Douglas Fir Habitat Model Habitat Quality Precipitation (mm) 0 1000 0 1

12. Predictor Model Prediction

13. Predictor Model Prediction Field Data Covariate Model Selection and Parameter Estimation

14. Predictor Model Prediction Field or Sample Data Covariate Model Selection and Parameter Estimation Model Validation

15. Douglas-Fir sample data Create the Model Model “Parameters” Precip To Points Extract Text File To Raster Prediction Attributes

16. Data Response Variable –From the field data (sample data) Covariates –From the field or remotely sensed Predictors –Typically remotely sensed –Sample as covariates for training –Can be different for predicting to new scenarios

17. Response Variable What is the: –Spatial uncertainty? –Temporal uncertainty? –Measurement uncertainty? Will it answer your question?

18. Covariate Variables What is the: –Spatial uncertainty? –Temporal uncertainty? –Measurement uncertainty? How well does the collection time of the covariates match the field data? Do they co-vary with the phenomena? Do the covariates “correlate”?

19. Types of uncertainty Accuracy (bias) Precision (repeatability) Reliability (consistency of a set of measurements) Resolution (fineness of detail) Logical consistency –Adherence to structural rules, attributes, and relationships Completeness

20. Types of Errors Gross errors –Transcription –Sinks in DEMs Random –Estimated using probability theory Systematic errors –“Drift” in instruments –Dropped lines in Landsat

21. Gross Errors Lat/Lon: – Reversed –0, names, dates, etc. Dates: –Extended in databases Measurements: –Inconsistent units –Inconsistent protocols –What can you expect from a field team?

22. Occurrences of Polar Bears From The Global Biodiversity Information Facility (www.gbif.org, 2011)www.gbif.org

23. Systematic Errors Landsat Scan line Error

24. Response Variable Qualification Tools Maps (various resolutions) Examine the data values: –How many digits? –Repeating patterns, gross errors? “Documentation” Measurements: –Occurrences? –Binary: Histogram –Categorical: Histogram –Continuous: Histogram

25. What’s the Impact on Models?

26. Significant Digits How many digits to represent 1 meter? –Geographic: Lat/Lon? –UTM: Eastings/Northings?

27. Significant Digits Geographic: –1 digit = 1 degree –1 degree ~ 110 km –0.00001 ~ 1.1 meters UTM: –1 digit = 1 meter

28. Covariate Qualification Maps Documentation Examine the data: –How many digits? Integer or floating point? –Repeating patterns? Histograms

29. CONUS Annual Percip.

30. Covariate Uncertinaty

31. Min Temp of Coldest Month

32. Histograms hist(Temp,breaks=400 )

34. Covariate Correlation Correlation Plots Pearson product-moment correlation coefficient Spearman’s rho – non parametric correlation coefficient

35. Correlation plots

36. California Correlations

37. California Predictors

38. Response vs. Covariates For Occurrences: –Histogram covariates at occurrences vs. overall covariates For Binary Data: –Histogram covariates for each value For Categorical Data : –Histogram covariates for each value –Or scatter plots For Continuous Data –Scatter plots

39. Covariate Occurrence Histograms Precipitation with Douglas-Fir Occurrences

40. Douglas Fir Model In HEMI 2 Green: Histogram of all of California Red: Histogram of Douglas-Fir Occurrences

41. Doug-Fir Height vs. Precip.

42. Douglas Fir Height

43. Terrestrial Predictors Elevation: –Slope –Aspect –Absolute Aspect Distance to: –Roads –Streams (streamline) Climate –Precip –Temp Soil Type RS: –Landsat –MODIS –NDVI, etc.

44. Marine Predictors Temp DO2 Salinity Depth Rugosity (roughness) Current (at depths) Wind

45. More Complicated Associated species Trophic levels Temporal Cyclical

46. Predictor Layers Means, mins, maxes Range of values Heterogeneity Spatial layers: –Distance to… –Topography: elevation, slope, aspect

47. Field Data and Predictors As close to field measurements as possible Clean and aggregate data as needed –Documenting as you go Estimate overall uncertainty Answer the question: –What spatial, temporal, and measurement scales are appropriate to model at given the data?

48. Temporal Issues Divide data into months, seasons, years, decades. –Consistent between predictors and response Extract predictors as close to sample location and dates as possible Use the “best” predictor layers

49. Additional Slides

50. Dimensions of uncertainty Space Time Attribute Scale Relationships

51. Basic Tools Histograms: What is the distribution of occurrences of values (range and shape) Scattergrams: What is the relationship between response and predictor variables and between predictor variables QQPlots: Are the residuals normally distributed?

52. Types of Data “God does not play dice” –Einstein “the end of certainty” –Prigogine, 1977 Nobel Prize What remains is: –Quantifiable probability with uncertainty

53. Uncertainty Factors Inherent uncertainty in the world Limitation of human congnition Limitation of measurement Uncertainty in processing and analysis