1Class 27Ecological Analysis andContextual AnalysisEcological Fallacy• Ecological fallacy could occur when aresearcher makes an inference aboutindividuals based on aggregate data forgroups. (Why? Individual correlations arenot the same as ecological correlations.)• Voting research example: If richerneighborhoods have higher proportions ofrepublican votes, can we conclude thatindividuals with higher incomes are morelikely to vote republican?Voting Research: EcologicalCorrelation30% 60%30% 60%% voted Republican% high incomeNeighborhood ANeighborhood B1003070total30H inc70L inctotalRepDemA1006040total60H inc40L inctotalRepDemBA positive ecological correlationbetween income and republican.Ecological correlation dependsupon the marginal frequencies ofthe within-areas individualfrequencies. (Robinson 1950)2Voting Research: IndividualCorrelation1003070total30525H inc702545L inctotalRepDemA1006040total603030H inc403010L inctotalRepDemB• Individual correlationdepends upon the internalfrequencies.• Different configurations ofinternal frequencies couldcreate individual correlationsdifferent from ecologicalcorrelations.• Within both neighborhoods Aand B, low income individualsare more likely to voterepublican relative toindividuals with high incomes.Individual Correlation ≠Ecological Correlation30% 60%30%60%% voted Republican% high incomeNeighborhood ANeighborhood BHow Did This Happen?1. High income people tend to voteDemocrats.2. People in neighborhood B tend tovote Republican.3. High income people tend to live inneighborhood B.IncomeNeighborhoodVoting Republicanomitted variable bias3How Does Ecological FallacyHappen in General?• Heterogeneity — Individuals in variousgroups (e.g., neighborhoods) aredifferent in other relevant attributesnot captured by the two variables.• OR the association between theindependent variable and thedependent variable differs byneighborhood.Additional Examples ofEcological Fallacy• Immigrants and illiteracy (Robinson1950)• Religion and suicide (Durkheim)• Country music and suicide (Stack)“Fallacy of Ecological Fallacy”• Schwartz’s article is a critique of theecological fallacy critique.• How does ecological fallacy occur?– Problem of internal validity (omitted variablebias)– Problem of construct validity• E.g. poverty as an individual characteristic andpoverty as a neighborhood characteristic exertdifferent effects on educational attainment.• Ecological causal relationships cannot all be reducedto aggregates of individual relationships.4“Fallacy of Ecological Fallacy”• Hidden assumptions of the ecologicalfallacy critique– Individual models are inherently betterspecified than ecological models– Ecological models are substitutes forindividual models– Only individual characteristics can causeindividual processes“Fallacy of Ecological Fallacy”• Schwartz’s critique of those assumptions– Individual models are inherently better.The essence of the problem is confounding, notecological analysis.– Ecological models are substitutesEcological processes may be the real concern.– Only individual characteristics can causeindividual processes.Cross-level causation is common.Multilevel Models• Many observational data have a hierarchical or clusteredstructure. e.g., students nested in schools.• Multilevel models consider 2+ levels of nested units ofanalysis. The DV is usually measured at the lower (individual)level, while IVs are measured at either the school orindividual level.S1S2 S3N11 N12 N13 N21 N22 N31 N32Nested Data5Multilevel Models• Distinguish the effects of individualcharacteristics from those of the context.• Causal effect may be decomposed into abetween-school effect and within-schooleffect.• Other applications:– 3-level structure - students are nested in classesand classes are nested in schools.– Repeated observations per subject (growthcurve models).What is the Effect of SES on MathAchievement?School 1X: SESY: Math AchievementSchool 2School 30 1-1bcContextual effect, the benefitof attending school 2 vs.school 1.bw: Within-school effect ofSES on math achievement.bbbb: Between-school effect ofSES on math
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