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Class 8

Class 8. Indexes and Scales. Class Outline. Indexes versus Scales Guttman Scale Index Construction CES-D (measure of depression) Segregation index. Index and Scale. Similarities: Both are composite measurements, i.e., measurements based on multiple items.

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Class 8

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  1. Class 8 Indexes and Scales

  2. Class Outline • Indexes versus Scales • Guttman Scale • Index Construction • CES-D (measure of depression) • Segregation index

  3. Index and Scale Similarities: • 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.

  4. Index and Scale Difference: • 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.

  5. Index and Scale Why do we need them? • 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. • 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)

  6. Guttman Scale Response Patterns The difficulty levels of the five math problems follow a clear pattern.

  7. Bogardus Social Distance Measure Response Patterns

  8. Constructing an Index • Select items for a composite index. • Examine empirical relationships. • Assign scores for responses. • Handle missing data.

  9. An Example: Clinical Measure of Depression--the CES-D Scale • 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] • 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] • 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] • On how many days during the past week did you feel happy? [0, 1, 2, 3, 4, 5, 6, 7] • On how many days during the past week did you feel that people were unfriendly? [0, 1, 2, 3, 4, 5, 6, 7] • …

  10. Examine Items . 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 7

  11. Histograms of Items 1-4: Data Source: The Wisconsin Longitudinal Study

  12. Checking Correlations Among Items

  13. Histogram of Total CES-D Score

  14. Index as a Weighted Mean • If we wish to give certain items more importance than other items, we use weights: • Index = S wi * scorei / S wi, • A typical weighted index is GPA. • Two assumptions are involved: • Interval scale. (A - B = B – C) • Equal importance for each credit hour. • GPA = S(credit hoursi*gradesi) / S credit hoursi

  15. Assign 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.

  16. 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.

  17. Segregation Index Percent white population in the neighborhood Cumulative white population in the first X neighborhood Assuming that there are only 5 neighborhoods in each city and all neighborhoods have the same number of residents.

  18. Segregation Index • Index of dissimilarity is calculated as D= 0.5 S |Pig/Pg-Pih/Ph| • Pig is the population of group g in census tract i • Pih is the population of group h in census tract i • Pg is the total population of group g and • Ph is the total population of group h • Interpretation of D: the (minimum) proportion of group g or h that needs to be moved to different neighborhoods in order for the city to be evenly distributed.

  19. Segregation Index

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