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Examples of MCA

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Title: Examples of MCA


1
Examples of MCA
  • Dating
  • Best place to live or retire

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Recent MESM projects with MCA
  • Prioritize invasive species and treatment
    locations in Santa Monica Mtns.
  • Prioritize sites
  • Ventura Foothills, Blue oak woodland, Santa Clara
    River, Goleta Brownfields, Valley oak restoration
  • Map stress index of watersheds
  • Chiapas, Los Padres
  • Campus Climate Neutral 1 policy ranking

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What is Multicriteria Analysis?
  • Decision analysis
  • A set of systematic procedures for analyzing
    complex decision problems (multiple, conflicting
    and incommensurate objectives)
  • The purpose of any GIS-based decision analysis
    is to provide insights and understanding, rather
    than to prescribe a correct solution. Often
    the process of attempting to structure the
    decision problem is more useful in achieving
    these aims than the numeric output of the
    GIS-based modeling. (Malczewski 2000)

6
Types of decisions
  • Sites
  • Pick best alternative (site)
  • IHOP, landfill
  • Identify set of good alternatives
  • Top 10 beaches or destinations
  • Set of graduate schools to apply to
  • Rank all alternatives (i.e., a map)
  • Regional vulnerability, sustainability index
  • Set of Sites
  • Pick best region or area
  • Areas for agriculture, corridors

7
Elements of multicriteria analysis
  • Goal(s)
  • Decision maker(s)
  • Preferences (weights)
  • Attitude toward risk
  • Evaluation criteria
  • Objectives (desired state)
  • Attributes (measure performance in relation to
    objectives)
  • Alternatives
  • Outcomes of alternative by criteria
  • Decision rules
  • Sensitivity analysis

8
Decision matrix
Source Malczewski 1999
Rank 1
Rank 2
Rank m
9
Hierarchy of criteria
  • Many to many relationship possible

Source Malczewski 1999
10
Criterion map scales
Source Malczewski 1999
11
Point allocation
Source McCoy et al. 2003
12
Why weight?
  • To express the importance (to the decision maker)
    of each criterion in relation to each other
  • But also dependent on the range of criteria
    values
  • Why not just ask decision maker for their
    weights?
  • What if decision maker cannot weight criteria?

13
AHP pairwise comparison
  • Calculate weights and consistency ratio from
    comparison matrix

14
Simplified version of AHP
Source Strager and Rosenberger 2005
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Goal Identify high priority lands for protecting
terrestrial biodiversity in California
Source Regan et al. in press
16
Basketball analogy of risk
  • Goal assemble a championship caliber team for a
    given budget
  • Alternatives
  • Kobe Bryant with four mediocre players
  • Five good (but not great) players
  • What if Kobe got hurt?
  • What if the other four players (or even one of
    them) was terrible?
  • In an environmental context
  • map analysis was based on erroneous data or
    things change
  • weakest link

17
Choice of decision rule How to aggregate
criteria?
Source Moffett and Sarkar 2006
18
Integration matrix
Source WWF
19
Boolean logic
  • AND logic
  • OR logic

Source Jiang and Eastman 2000
20
Weighted Linear Combination
  • Compensatory tends to average
  • Assumptions
  • Linearity desirability of additional attribute
    unit is constant for any level of attribute
  • Additivity no interaction (correlation) between
    attributes
  • Tends to be ad hoc with little theoretical support

21
Ideal point or compromise programming
  • Orders a set of alternatives on the basis of
    their distance from an ideal point in
    multicriteria space
  • Can also consider the maximum distance from
    negative ideal (risk-averse)
  • Compromise method prefers closest to ideal and
    farthest from negative ideal

22
Concordance/Discordance Analysis (Outranking)
  • Based on pairwise comparison of alternatives
  • Concordance is all criteria for which A is not
    worse than B (but not how much better)
  • Discordance is all criteria for which A is worse
    than B (but not how much better)

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VisualizationQuantiles
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VisualizationRadar plots
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VisualizationConsumers Reports
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Highlights
  • When to use MCA instead of statistics or process
    models?
  • Rich literature in multicriteria analysis
  • Dont reinvent the wheel or make a wobbly wheel
  • Start from objectives, not data
  • Select method that is consistent with
  • Assumptions (ranking outcomes, criteria, and
    alternatives, risk)
  • Type of decision (best alternative, good
    alternatives, or rank all alternatives)
  • Criteria are usually facts, weights are social
    values
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