9 Steps of Ordinal Ranking or QOL Index Building Linked to Excel file

Modeling Methodologies Ordinal Ranking -- most popular, creates a technique for normalizing and summing together a variety of variables Factor Analysis -- also popular, a sophisticated statistical technique to cluster and order multiple variables Other clustering or additive techniques also used

ORDINAL RANKING PROCEDURE Describe Modeling Technique Show Example Perform a “hands-on” exercise

Steps After Defining the Goal of the Study: 1. Select Geographic Places/Scale to be Ranked 2. Select Variables/Measures used to study the Places 3. Assign measures of value to each Variable 4. Determine utility functions for each Variable and replace Variable measure with corresponding utility measure

Steps continued 5. Rank Variables, highest to lowest 6. Give relative weights to adjacent Variables 7. Calculate absolute weights for entire system 8. Create weighted utility table 9. Rank the Places

Purpose: Example Study GOAL Upon Graduation, Select the best cities to start your career Measures Best city should have: Good Market Good business climate Good work force Strong Community Spirit

1.Select Geographic Places to be Ranked

Translating Ideas/Measures into Variables: 2.Select Variables used to study the Places Translating Ideas/Measures into Variables: Good Market People Have Jobs = Low Unemployment People Have Money = High Income Good Business Climate Costs are Low = Low Housing Cost Good Work Force People are Talented = Highly Educated Strong Community Spirit People work together well = Many Volunteers

2.Select Variables used to study the Places, continued

3.Assign measures of value to each Variable and Indicate if it is a GOOD or BAD

3.Assign measures of value to each Variable, continued

Need to Create Measurement System Common to All Variables 4. Determine utility functions for each Variable and replace Variable measure with corresponding utility measure Need to Create Measurement System Common to All Variables Problem Not all variables measured in same units Example Unemployment is in % and Income is in $ Solution Translate all variables into “utils” or units of utility

Utility Conversion Equations For a GOOD Uvi = (Xvi - MINv)/ (MAXv - MINv) Notation: Xvi = Variable v measured in units for place i MAXv = Maximum value of variable v MINv = Minimum value of variable v Uvi = Variable v measured in "utils" for place i v = subscript representing all variables i = subscript representing all places

Utility Conversion Equations, continued For a BAD Uvi = (MAXv - Xvi)/ (MAXv - MINv)

Utility Conversions

5. Rank Variables most important to least Most important Variable Ranked first, next most important ranked second, next third, until all included

6. Give relative weights to adjacent Variables Indicate how much more important two adjacently ranked variables are, always >1 Lowest variable assigned weight of one

7. Calculate absolute weights for entire system Absolute Weights indicate the over-all impact of a variable to the model Note that the highest ranking variable has the greatest weight

7. cont. Actual Calculations

8. Create weighted utility table and sum results Multiply Utility Measures by Absolute Weights, result is Weighted Utility Sum Weighted Utility to Determine QOL for a place

9. Rank the Places

10. Critique results What about weather in St. Paul

CONCLUDING REMARKS

CONCLUDING REMARKS Means for greater understanding Need to also Map your results Consider where to go from here