Class 8Class OutlineIndex and ScaleSlide 4Slide 5Guttman ScaleBogardus Social Distance MeasureConstructing an IndexAn Example: Clinical Measure of Depression--the CES-D ScaleExamine ItemsSlide 11Checking Correlations Among ItemsHistogram of Total CES-D ScoreIndex as a Weighted MeanAssign Scores for ResponsesWays to Handle Missing Data in Index ConstructionSegregation IndexSlide 19Slide 20Class 8Indexes and ScalesClass Outline•Indexes versus Scales•Guttman Scale•Index Construction–CES-D (measure of depression)–Segregation indexIndex and ScaleSimilarities:•Both are composite measurements, i.e., measurements based on multiple items.•Both are ordinal measures, which rank order units of analysis in terms of specific variables.•Both are often used as interval measures in practice. That is, we treat them as continuous variables.Index and ScaleDifference:•Index: accumulate scores assigned to individual attributes.–Unweighted: Index = score1 + score2 + score3 + …–Weighted: Index= w1*score1 + w2*score2 + w3*score3 + …•Scale: assign scores to patterns of responses.Why do we need them? 1. Inadequacy of single indicators Single indicators are often insufficient for abstract or latent (unobservable) variables such as alienation, religiosity, prejudice, well-being, quality of life, ability, etc. 2. Data reduction Index and scale construction is an efficient way to summarize data when we have many variables to work with but want a clear, sharp result. (e.g., GPA)Index and ScaleGuttman Scale3+2 3-2 3*2 3/2 321 Y Y Y Y Y2 Y Y Y Y N3 Y Y Y N N4 Y Y N N N5 Y N N N N6 N N N N NResponse PatternsThe difficulty levels of the five math problems follow a clear pattern.Bogardus Social Distance MeasureAre you willing to…?Permit sex offenders to live in your countryLive in your communityLive in your neighborhoodLive next door to youLet your child marry a sex offender1 Y Y Y Y Y2 Y Y Y Y N3 Y Y Y N N4 Y Y N N N5 Y N N N N6 N N N N NResponse PatternsConstructing an Index•Select items for a composite index. •Examine empirical relationships.•Assign scores for responses.•Handle missing data.An Example: Clinical Measure of Depression--the CES-D Scale1. On how many days during the past week did you feel you could not shake off the blues even with help from your family and friends? [0, 1, 2, 3, 4, 5, 6, 7]2. On how many days during the past week did you feel bothered by things that don't usually bother you? [0, 1, 2, 3, 4, 5, 6, 7]3. On how many days during the past week did you think your life had been a failure? [0, 1, 2, 3, 4, 5, 6, 7]4. On how many days during the past week did you feel happy? [0, 1, 2, 3, 4, 5, 6, 7]5. On how many days during the past week did you feel that people were unfriendly? [0, 1, 2, 3, 4, 5, 6, 7]6. …. summarize Variable | Obs Mean Std. Dev. Min Max-------------+-------------------------------------------------------- id | 6196 446073.6 183696.2 101003 771015 ces_d | 5318 16.06168 15.16228 0 126 numans | 5367 19.74511 1.88859 0 20 mu003rer | 5281 .3686802 .9919353 0 7 mu004rer | 5268 .5442293 1.007349 0 7 mu005rer | 5280 .2681818 .9086162 0 7 mu006rer | 5265 5.451472 1.688951 0 7 mu007rer | 5268 .6753986 1.153571 0 7 mu008rer | 5273 .7344965 1.432888 0 7 mu009rer | 5287 5.812559 1.743115 0 7 mu010rer | 5275 .1672038 .6882907 0 7 mu011rer | 5280 .3909091 .9510827 0 7 mu012rer | 5281 .8763492 1.340246 0 7 mu013rer | 5279 .6541012 1.263232 0 7 mu014rer | 5277 .8609058 1.300107 0 7 mu015rer | 5286 .2415815 .845546 0 7 mu016rer | 5260 5.615399 2.289262 0 7 mu017rer | 5279 .9414662 1.532823 0 7 mu018rer | 5281 5.207726 2.239078 0 7 mu019rer | 5261 .6565292 1.325413 0 7 mu020rer | 5286 1.393681 1.819465 0 7 mu021rer | 5278 .6661614 1.124079 0 7 mu022rer | 5277 .8487777 1.292901 0 7Examine Items0 1 2 3 4Density0 2 4 6 8# of Days Can't Shake off Blues0 1 2 3 4Density0 2 4 6 8# of Days Bothered by Things0 1 2 3 4 5Density0 2 4 6 8# of Days Thinking Life was Failure0 .5 1 1.5 2Density0 2 4 6 8# of Days Felt HappyHistograms of Items 1-4:Data Source: The Wisconsin Longitudinal StudyChecking Correlations Among ItemsCES-D1 CES-D2 CES-D3 CES-D4CES-D1 1CES-D2 0.5569 1CES-D3 0.5570 0.3938 1CES-D4 -0.3864 -0.2748 -0.3618 10 .01 .02 .03 .04 .05Density0 50 100 150Total Score of CES-DHistogram of Total CES-D ScoreIndex as a Weighted Mean•If we wish to give certain items more importance than other items, we use weights:•Index = wi * scorei / wi,•A typical weighted index is GPA.•Two assumptions are involved:–Interval scale. (A - B = B – C)–Equal importance for each credit hour. •GPA = (credit hoursi*gradesi) / credit hoursiAssign Scores for Responses•Decide the desirable range of the index scores.•Some items may need be “reverse-coded” before being added up.•Decide whether to give each item in the index equal weight or different weights.Ways to Handle Missing Data in Index Construction•Exclude cases with missing data from the construction of the index and the analysis. (We lose observations.)•Treat missing data as one of the available responses (usually as “no” or “neutral”).•Assign the variable average to missing cases. •Analyze missing data to interpret the meaning.Segregation IndexNeighborhoodsCity A City B City C1 0.2 0.05 0.12 0.2 0.1 0.143 0.2 0.17 0.184 0.2 0.25 0.245 0.2 0.8 0.56Total 0.2 0.274 0.244Percent white population in the neighborhoodNeighborhoodsCity A City B City C0 0 0 01 0.2 0.04 0.082 0.4 0.11 0.203 0.6 0.23 0.344 0.8 0.42 0.545 1 1 1Cumulative white population in the first X neighborhoodAssuming that there are only 5 neighborhoods in each city and all neighborhoods have the same number of residents.Segregation Index•Index of
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