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

2. 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

3. Multiple Linear Regression

4. Linear Regression: 2 Predictors
Mathworks.com

5. Non-Linear Regression

6. 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.

7. Brown Shrimp Size
Add graph from work

8. Terminology Plant uses: I prefer: 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
The covariate and the predictor will be different in cases like predicting effects of climate change in the future.

9. Douglas Fir Habitat Model1
Habitat Quality
1000
Precipitation (mm)

10. Predictor
Model
Prediction

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

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

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

14. Data Response Variable Covariates Predictors
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

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

16. 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”?

17. 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
Plant uses Accuracy a little differently

18. Types of Errors Gross errors Random Systematic errors Transcription
Sinks in DEMs
Random
Estimated using probability theory
Systematic errors
“Drift” in instruments
Dropped lines in Landsat
All of these types of uncertainty can be compensated for in some cases.

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

20. Occurrences of Polar Bears
From The Global Biodiversity Information Facility ( 2011)

21. Systematic Errors
Landsat Scan line Error

22. 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

23. What’s the Impact on Models?

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

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

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

27. CONUS Annual Percip.

28. Covariate Uncertinaty

29. Min Temp of Coldest Month
After applying a filter to the raster

30. Histograms
hist(Temp,breaks=400)

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

33. Correlation plots

34. California Correlations

35. California Predictors

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

37. Covariate Occurrence Histograms
Precipitation with Douglas-Fir Occurrences

38. Douglas Fir Model In HEMI 2
Green shows a histogram of precipitation for all of California
Histograms are scaled to go from 0 to 1 (all values)
Green: Histogram of all of California
Red: Histogram of Douglas-Fir Occurrences

39. Doug-Fir Height vs. Precip.

40. Douglas Fir Height
After gridding to coarse grid cells

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

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

43. More Complicated
Associated species
Trophic levels
Temporal
Cyclical

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

45. 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?

46. 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

47. Additional Slides

48. Dimensions of uncertainty
Space
Time
Attribute
Scale
Relationships

49. 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?

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

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