Modeling with Rasters IV

Linear Scale Transformations Advantages

• Direct transformation and transparent

  • mathematically straightforward and easy to interpret

• Consistency across layers (Directly comparable)

  • Applying the same linear scaling to all layers, they are directly comparable

  • no issue of different functions introduction inconsistent behaviour

• Preserves relationships in the data

  • preserves natural spacing and order of values in the original data

• No tuning of parameters needed

  • forget about midpoint, spread or any other parameter

  • won't have to think about things like what is the proper mid point of spread, this issue of relatability is gone

Maximum Score Procedure

• scores between 0 and 1

• always assigned higher values to higher input values

• cannot apply to factors you wish to minimize

• equation for criteria to maximize, benefit

Inverse of Maximum Score Procedure

Needed to invert the max score equation so that lower values = higher suitability

If you don't do this the layer will cancel each other out, but this puts them on the same scale, not more mins or max, just thinking about what is suitable for the raster

• criteria to minimize, cost

When to use Maximum Score

When…

• you are fine with linear scaling, no need for non linear transformation

• you have +ve values or you can shift range of values to +ve

• working with benefits where higher values = more suitable

  • the highest logical vales represents the highest suitability

• directionality is consistent

• data range is not highly skewed, or influenced by extreme outliers

When NOT to use Maximum Score

• data includes both costs and benefits(unless you invert costs)

• data includes negative and positive values(unless you invert costs)

• suitability is not linearly related to the input values(i.e., mid point is most suitable

• you nee to combine multiple facets with very different ranges max score can distorts relative importance

• data distribution is highly skewed - outliers disproportionately affect the scaling

• you ned to reflect more complex relationships- like diminishing returns or thresholds effects

Score Range Procedure

Standardized by dividing in the numerator the pixel vales by minimum by the range of the data

No inversion the base does not change

Gives more weight to lowers values, done in raster calculator

When to use Score Range Procedure

• when linear scaling is needed with a min values of 0, max of 1

• if trying to reflect true suitability or proportional importance across full range of data

• consistent scaling needs: used same score range equation for:

  • both cost and benefit criteria, no need to invert costs

  • rasters that include both positive and negative values, no range shift needed

When NOT to use Score Range Procedure

• non linear relationships

• outliers present

• extreme emphasis on High/Low values needed

Weighted Sum with LST Varibles Assumptions

• linearity

• compensatory nature(high scores in one factor can offset low scores in another)

• Independence(factor are treated independent of each other)

• Normalization of factors(apply max score or score range and you have normalized your data)

Analytical Hierarchy Process

• Structured technique for organizing and analyzing more complex decision problems

• functions as bother a method to derive weights through a pairwise comparison approach, AND a decision rule since it defines hoe to rank alternatives and based on those weights

• provides a comprehensive and rational frameworks for:

  • structuring a problem

  • representing and quantifying its elements at objective and tribute levels

  • relating those element to overall goals

  • evaluation alternative solutions

Pairwise Comparisons

• developed by Saaty(1980) in the context of the AHP

• “best fit” set of weights derived from a “sqaure reciprocal”

• matrix used to compare all possib;le pair of critera(and/or objectives)

• Approach

  • develop pairwise comparison matrix

  • computing criterion weights

  • estimate consistency ration

Pairwise Comparisons: Pros

• only two criteria at a time are considered meaning granularity and systematic comparison and encourages consistency and transparency

• We are only comparing 2 criteria at a time, so it is easier

Pairwise Comparisons: Cons

• scalability(10 evaluation criteria = 45 pairwise comparisons)

• subjectivity and dependency on expertise still exists here