Predictive Models I

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Predictive Models I

• RNR/Geog 420/520
• Spring 2000

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Predictive Models

• Important to understand what we are attempting to
  predict
• These models predict location
• This prediction is based on reasoned or measured
  relationships
• No predictive model is perfect
• Some are more efficient than others

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Broad Model Types

• Deductive models are based on reasoning in which
  the conclusion follows necessarily the presented
  premises
• Inductive models base validity on observations
  about part of a class as evidence for a
  proposition about the whole class

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The Goal of Predictive Models

• Models in a GIS should maintain a high percentage
  of correct predictions while decreasing the area
  needed to obtain these predictions

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Why Make Predictive Models

• Resource management
• Reduce costs but maintain service
• Planning decisions
• Discover favored habitats

• Understand behavior
• Discover preferences
• Prove theories
• Disprove theories

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Components of a Model

• Variables
• Study Group
• Control Group
• Suitable Statistical model/test

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Variable Selection

• Variables are usually selected because they are
  thought to exert influence on the phenomena being
  studied
• The data type (i.e. nominal vs. continuous) of a
  variable can restrict the types of models it is
  possible to make
• GIS allow researcher to control continuous data

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Study Group

• Locations where phenomena being investigated are
  located
• A good study group requires good collection
  strategy
• SAMPLE(ltmask_gridgt, grid, ..., grid)
• zone x y cellvalue1 cellvaluen

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Control Group

• Often necessary to discover the significance of
  spatial patterns
• For example, is it significant if 75 of coyote
  dens are located within 50 meters of houses?

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Trend Surface Models

• Based strictly on location
• Trend surface models use a polynomial regression
  to fit a least-squares surface to input points
• As the order of the polynomial is increased, the
  surface being fitted becomes progressively more
  complex
• Two variations Linear and Logistic
• TREND(ltpoint_cover point_filegt, spot_item,
  order,LINEAR LOGISTIC, cellsize, xmin,
  ymin, xmax, ymax)

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Linear/Logistic Trend Surfaces

• Linear Trend Surfaces
• Useful for continuous data
• Uses x, y, and z values to model data trends
• Z values are continuous
• Creates smooth surfaces
• Surface complexity increases as order of
  polynomial increases

• Logistic Trend Surfaces
• Useful for binary types of data (e.g. yes/no)
• Uses x, y, and z to model trends.
• Z values are 0 or 1
• Creates smooth surfaces
• Surface complexity increases as order of
  polynomial increases

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First Order Trend Surfaces
Based on Site Locations (Logistic)
Based on Pottery Counts (Linear)
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Third Order Trend Surfaces
Based on Site Locations (Logistic)
Based on Pottery Counts (Linear)
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Locational Characteristic Models

• Based on values of variables at the study group
  locations
• Univariate Analysis (Kolmogorov-Smirnov)
• Multivariate Analysis (multiple regression,
  cluster, classification, principle component)

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Kolmogorov Smirnov Test

• Statistic is the maximum difference between
  cumulative proportions of two samples, usually
  study group and control group
• Use GRIDs SAMPLE command to extract values for
  both groups
• Preference can be seen graphically

Significance at 5 level reached if
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Multiple Regression Models

• Regression models measure relationship between
  dependent and independent variables
• The dependent variable in linear regression is
  generally a real number
• The dependent variable in logistic regression is
  either a 1 or a 0

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Data Used in Regressions

• Linear
• Dep var1 var2
• 43 840 149
• 22 852 155
• 69.4 854 151
• 15 805 134
• 46 853 062

• Logistic
• Dep var1 var2
• 1 840 149
• 0 852 155
• 1 854 151
• 0 805 134
• 1 853 062

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Creating Multiple Regression Models in GRID

• Subject SAMPLE results to regression
• Statistics Software
• GRIDs REGRESSION command
• Results of the regression include coefficients
  and a constant, or y-intercept
• Model made by multiplying variables by
  coefficients
• surface 1.250 (-0.029 x img1) (0.263 x img2)

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Results of GRIDs Regression

• Grid gt regression hsam.txt logistic brief lt
• coef coef
• ------ ----------------
• 0 -3.797
• 1 -0.001
• 2 0.014
• 3 0.006
• 4 0.000
• 5 0.055
• ------ ----------------
• RMS Error 0.393
• Chi-Square 51.608

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Results of STATAs Regression
--------------------------------------------------
---------------------------- Logit Estimates
Number of obs
383
chi2(13) 53.88
Prob
( chi2 0.0000 Log Likelihood -220.37417
Pseudo R2
0.1089   -----------------------------------------
------------------------------------- site
Coef. Std. Err. t P(t
95 Conf. Interval ----------------------------
-------------------------------------------------
aspew .0004698 .002341 0.201
0.841 -.0041336 .0050731 aspns
.0021229 .0023099 0.919 0.359
-.0024193 .006665 elev -.0038272
.0042056 -0.910 0.363 -.0120971
.0044428 relfa -.1647048 .0695988
-2.366 0.018 -.3015648 -.0278448
relfm .2218111 .0720802 3.077 0.002
.0800717 .3635505 texture -.5435591
.2748572 -1.978 0.049 -1.084042
-.0030762 ridge .0014501 .0032384
0.448 0.655 -.0049179 .0078182 sd1
.0001864 .0004607 0.405 0.686
-.0007195 .0010924 sd2 -.0001118
.0012555 -0.089 0.929 -.0025806
.0023571 sd3 -.0052209 .0021802
-2.395 0.017 -.009508 -.0009337
shelter -.0012764 .0015435 -0.827
0.409 -.0043115 .0017587 slope
.0752924 .0386194 1.950 0.052
-.0006493 .1512342 wadist .0007286
.0007215 1.010 0.313 -.0006902
.0021474 _cons 3.439327 4.429328
0.776 0.438 -5.270564
12.14922 -----------------------------------------
------------------------------------- The
corrected Y-intercept constant 4.0704389
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Regression Model
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Probability Models
Group 1
Group 2
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Model Strength