Fuzzy Set Profiling and Community Analysis Techniques Mark

Fuzzy Set Profiling and Community Analysis Techniques Mark Schafer Associate Professor Dept. of Agricultural Economics & Agribusiness LSU Ag. Center Ashley Barras Ph. D Candidate Department of Sociology LSU

Acknowledgement • Funded Research – Minerals Management Service – Cooperative Agreement • MO 7 AC 13301 • Keithly, Fannin, and Schafer 2007 -2010 – Assessing the Impact of OCS Activities on Public Infrastructure, Services, and Population in Coastal Communities Following Hurricanes Katrina and Rita – Role: Develop parish profiles

Talk Outline 1. Fuzzy-set basics 2. Samples of Fuzzy-Set Community Profile Elements 3. Fuzzy-set Analysis Walk Through 4. Concluding Thoughts 5. Applications to Impact Analysis

Fuzzy-set Basics • A fuzzy-set is a continuous set that has been calibrated to indicate degrees of membership • Based in Set-Theory. (Ragin 2000) – Cases may be full or partial members of sets – Calibration involves finding meaningful differences between cases • Fuzzy sets are binary and metric at same time – Combine categorical and metric assessment in a single instrument

Fuzzy-Set Plot for 64 : Louisiana Parishes

Community Profiling Using Fuzzy-set Concepts • Parish Profiles development – Use Secondary data – Develop profile elements – Group “like” parishes into one of four classifications: • Full member of set • Partial member, mostly in • Partial member, mostly out • Not member

Examples • • Education Profile Elements: 1. Adequate School District Performance 2. Instructional Focus Labor Market Profile Elements: 1. Low Unemployment 2. Competitive Per Capita Personal Income 3. Large Business Presence

Adequate Performance Map

Instructional Focus Map

Competitive Per Capita Income

Low Unemployment

Large Business Presence

Community Analysis Techniques using Fuzzy-sets • Fuzzy-set Qualitative Comparative Analysis (Fs. QCA) – Fuzzy-set theory – Combinatorial logic – Boolean minimization • Analyzes combinations of case characteristics – Whether any single condition or – Combination of condtions – Is necessary or sufficient • To produce an outcome

Steps in Fuzzy-set Analysis 1. Define Outcome 2. Define Conditions 3. Generate Truth Table • Linking conditions to outcomes 4. Generate Solution Table • Minimization of pathways or configurations • Necessary and sufficient conditions • Identify whether outcome can be reached by one or multiple combinations pathways

Table 4: Truth Table for Fuzzy-Set Analysis of Poor School District Performance in Louisiana Conditions Outcome Instruct Low Un. Emp Comp. Income Large Firm N Poor Perf. Consist 1 0 0 0 3 1 . 899 0 0 12 1 . 850 0 1 3 0 . 754 0 1 0 0 3 0 . 724 0 1 1 0 7 0 . 719 0 1 0 0 15 0 . 680 1 1 1 0 3 0 . 638 1 1 5 0 . 618 1 1 0 1 3 0 . 605 0 1 1 1 7 0 . 423 ** 61

Solution Table 5: Solution Table for Fuzzy-Set Analysis of Poor School District Performance in Louisiana Causal Combination Coverage Consistency 1. Not low Unemployment* Not Competitive Per Capita Income* No Large Business Presence . 344 . 847 N Rows Frequency threshold Consistency threshold 61 9 (of 16 possible) 3 0. 85

Necessary and Sufficient Conditions • Three Necessary Conditions: – High Unemployment – Inadequate Per Capita Income – No large business presence • Sufficient Conditions: – No single condition is sufficient – One set of conditions (pathway) to poor district performance • Note: Instructional focus was neither necessary nor sufficient – Can be seen in truth table

Table 4: Truth Table for Fuzzy-Set Analysis of Poor School District Performance in Louisiana Conditions Outcome Instruct Low Un. Emp Comp. Income Large Firm N Poor Perf. Consist 1 0 0 0 3 1 . 899 0 0 12 1 . 850 0 1 3 0 . 754 0 1 0 0 3 0 . 724 0 1 1 0 7 0 . 719 0 1 0 0 15 0 . 680 1 1 1 0 3 0 . 638 1 1 5 0 . 618 1 1 0 1 3 0 . 605 0 1 1 1 7 0 . 423 ** 61

Concluding Thoughts Fuzzy-set analysis is • • • Is concept focused Promotes analysis of complex relationships Can incorporate both quantitative and qualitative data Promotes focus on relevant diversity across communities or cases Can be used to explore complexity Can be used to sharpen focus of standard econometric techniques

Impact Analysis • Sharpen focus by grouping parishes or communities • Assess necessity and sufficiency of conditions for outcomes • Fuzzy-set analysis can incorporate time dimension – Quick recovery period after 2005 hurricanes – Increasing (or decreasing) reliance on OCS related activity for employment • May help make use of “limited” data -Depends on capacity to link available data to conceptual focus