Calculating Gini coefficients for each subset (villages) of large data set
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Re: Calculating Gini coefficients for each subset (villages) of large data set
 
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"I am now at a stage where I am considering cutting and pasting a syntax section for each village id since I cannot find a correct way of looping. Any suggestions for syntax in SPSS?"
Yes! I made such suggestions almost TWO weeks ago! Reread the thread and teach yourself about AGGREGATE!
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Re: Calculating Gini coefficients for each subset (villages) of large data set
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/** UNTESTED CODE use at your own risk after testing and verification **/.
/** Simply modified the code you originally pasted to allow a 'break' variable **/. /** Note BREAK on AGGREGATE, SPLIT FILE, BY on RANK... **/. /** These are the "looping" constructs you will want to read up on. **/. * Step 1. SORT CASES BY IDPSU INCOME. * Step 2. AGGREGATE OUTFILE = * / PRESORTED / BREAK = IDPSU INCOME / persons = N . WEIGHT BY persons. * Step 3. AGGREGATE OUTFILE = * MODE ADDVARIABLES / BREAK = IDPSU / suminc = SUM(INCOME). MATCH FILES / FILE * / BY IDPSU / @TOP@=FIRST. * Step 4 . COMPUTE pincome=persons * income. SPLIT FILE BY IDPSU. CREATE cincome=CSUM(pincome). SPLIT FILE OFF. * Step 5 . COMPUTE pcinc = cincome/suminc . * Step 6. RANK VARIABLES=income (A) BY IDPSU / RFRACTION into cdfinc / PRINT=YES / TIES=HIGH . * Step 7. COMPUTE d1 = @TOP@. COMPUTE d2 = @TOP@. * Note that it doesn't matter whether D1 or D2 is the Y variable * in the D1-D2 pair. SPLIT FILE BY IDPSU. * D1 and D2 are identical and are created to allow you to draw a * diagonal line on the graph. GRAPH /SCATTERPLOT(OVERLAY)=cdfinc d2 WITH pcinc d1 (PAIR) /MISSING=LISTWISE /TITLE= 'Lorenz Curve for Income'. * Step 8. * Calculate and print the Gini coefficient(s). * For last case, LAREA is area under the Lorenz curve. DO IF (@TOP@) . + COMPUTE larea = 0. ELSE. + COMPUTE larea = LAG(larea) + (cdfinc - LAG(cdfinc)) * (pcinc + LAG(pcinc))/2 . END IF. IF (cdfinc = 1) gini = (.5 - larea)/.5 . REPORT /VARIABLES gini (VALUES) /BREAK (IDPSU) '' (SKIP(1)) /SUMMARY MAX( gini) SKIP(1) '' .
Please reply to the list and not to my personal email.
Those desiring my consulting or training services please feel free to email me. --- "Nolite dare sanctum canibus neque mittatis margaritas vestras ante porcos ne forte conculcent eas pedibus suis." Cum es damnatorum possederunt porcos iens ut salire off sanguinum cliff in abyssum?" |
Re: Calculating Gini coefficients for each subset (villages) of large data set
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In reply to this post by Mattias
Dear Mattias [+ Richard]
I think I see your problem a bit more clearly now. If your villages are of different sizes, then I can see that the Gini would tend to be biased downwards for smaller villages to an extent which depends on the distribution of income in the population. So any effect of Gini on your outcome variable would be partially confounded by village size. Perhaps you could estimate the extent of the bias by taking a large number of random samples of sizes say 5, 10, 15, or 20 from your population, and calculating Ginis. If sample size has a substantial effect on Gini, you could then correct the empirical Gini for each village by a size factor somehow. Regards Garry -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Mattias Sent: 26 February 2014 14:19 To: [hidden email] Subject: Re: Calculating Gini coefficients for each subset (villages) of large data set Hi Richard and Garry, I think that you both make important points and that the one does not exclude the other as I understand the two of you to be thinking. Garry’s comment makes a lot of sense to me; that it is essentially a question of how representative the (small) sample is. Richard refers to work (e.g. the Deltas (2003) article) which shows that there is a downward bias with sample size for Gini coefficients when samples are small as they are in my data. I asked the question of possible alternative measures that would be more appropriate for small samples because I also found the Deltas (2003) article you mention which by the way also argues that “The small sample bias is especially relevant when [..] the Gini is used to compare income inequality across sub-populations, some of which may have very small sample sizes”. Delta suggests a ‘small sample adjusted’ Gini instead when samples are small. At the same time, the Wiki on income inequality measures also describes the property of population independence as one of four properties any measure on inequality should fulfil in the following way: “the income inequality metric should not depend on whether an economy has a large or small population. An economy with only a few people should not be automatically judged by the metric as being more equal than a large economy with lots of people. This means that the metric should be independent of the level of population” I have spent most of my time being what you call a subject specialist, for example through conducting surveys and by doing field work in village India. It is indeed of particular substantive interest to investigate village level inequality because the village is a social unit of specific importance in India. In this project, however, I am working on secondary data from a large scale survey and this is the first time I use an inequality measure so I am trying to find my way and as such I am anxious to understand the limitations of for example the Gini and also reluctant to use unconventional “adjusted” Gini measures such as that suggested by Deltas (2003). As for how to actually calculate Gini coefficients for villages - which was my original question - I am still looking for a way to do this in terms of syntax. Jon's suggestion to use an R plug in is exhausted for now since it appears I will need special technical assistance to install things properly. I am now at a stage where I am considering cutting and pasting a syntax section for each village id since I cannot find a correct way of looping. Any suggestions for syntax in SPSS? Mattias -- View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Calculating-Gini-coefficients-for-each-subset-villages-of-large-data-set-tp5724495p5724639.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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In reply to this post by David Marso
Got it working after a few minor adjustments and have calculated Gini's. Will verify now.
Learned something important about @TOP@ in the process.
Gesendet: Mittwoch, 26. Februar 2014 um 16:35 Uhr
Von: "David Marso [via SPSSX Discussion]" <[hidden email]> An: Mattias <[hidden email]> Betreff: Re: Calculating Gini coefficients for each subset (villages) of large data set /** UNTESTED CODE use at your own risk after testing and verification **/.
/** Simply modified the code you originally pasted to allow a 'break' variable **/. /** Note BREAK on AGGREGATE, SPLIT FILE, BY on RANK... **/. /** These are the "looping" constructs you will want to read up on. **/. * Step 1. SORT CASES BY IDPSU INCOME. * Step 2. AGGREGATE OUTFILE = * / PRESORTED / BREAK = IDPSU INCOME / persons = N . WEIGHT BY persons. * Step 3. AGGREGATE OUTFILE = * MODE ADDVARIABLES / BREAK = IDPSU / suminc = SUM(INCOME). MATCH FILES / FILE * / BY IDPSU / @TOP@=FIRST. * Step 4 . COMPUTE pincome=persons * income. SPLIT FILE BY IDPSU. CREATE cincome=CSUM(pincome). SPLIT FILE OFF. * Step 5 . COMPUTE pcinc = cincome/suminc . * Step 6. RANK VARIABLES=income (A) BY IDPSU / RFRACTION into cdfinc / PRINT=YES / TIES=HIGH . * Step 7. COMPUTE d1 = @TOP@. COMPUTE d2 = @TOP@. * Note that it doesn't matter whether D1 or D2 is the Y variable * in the D1-D2 pair. SPLIT FILE BY IDPSU. * D1 and D2 are identical and are created to allow you to draw a * diagonal line on the graph. GRAPH /SCATTERPLOT(OVERLAY)=cdfinc d2 WITH pcinc d1 (PAIR) /MISSING=LISTWISE /TITLE= 'Lorenz Curve for Income'. * Step 8. * Calculate and print the Gini coefficient(s). * For last case, LAREA is area under the Lorenz curve. DO IF (@TOP@) . + COMPUTE larea = 0. ELSE. + COMPUTE larea = LAG(larea) + (cdfinc - LAG(cdfinc)) * (pcinc + LAG(pcinc))/2 . END IF. IF (cdfinc = 1) gini = (.5 - larea)/.5 . REPORT /VARIABLES gini (VALUES) /BREAK (IDPSU) '' (SKIP(1)) /SUMMARY MAX( gini) SKIP(1) '' .
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Re: Aw: Re: Calculating Gini coefficients for each subset (villages) of large data set
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There is nothing special about @TOP@.
It is simply a variable (0/1) created on the MATCH (FIRST function) so we know to reinitialize the accumulation. I tend to flank such variables with @ to avoid collisions. Please post the new code with 'minor adjustments' so the list has it available as a future resource. You can see there are numerous techniques for 'looping' (SPLIT FILE, BY on AGGREGATE and RANK). MACRO also has the !DO, the transformation language has DO REPEAT and LOOP. ---------
Please reply to the list and not to my personal email.
Those desiring my consulting or training services please feel free to email me. --- "Nolite dare sanctum canibus neque mittatis margaritas vestras ante porcos ne forte conculcent eas pedibus suis." Cum es damnatorum possederunt porcos iens ut salire off sanguinum cliff in abyssum?" |
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In reply to this post by Mattias
Here is suggested syntax for computing Gini coefficients for each subunit (IDPSU) based on INCOME provided by David Marso and slightly adjusted by me. Be aware that, as discussed above, these Gini coefficients are subject to downward bias when samples are small and that this problem is not addressed in this syntax.
* Step 1. SORT CASES BY IDPSU INCOME. * Step 2. AGGREGATE OUTFILE = * / PRESORTED / BREAK = IDPSU INCOME / persons = N . WEIGHT BY persons. * Step 3. AGGREGATE OUTFILE = * MODE ADDVARIABLES / BREAK = IDPSU / suminc = SUM(INCOME). MATCH FILES / FILE * / BY IDPSU / FIRST=@TOP@. * Step 4 . COMPUTE pincome=persons * income. SPLIT FILE BY IDPSU. CREATE cincome=CSUM(pincome). SPLIT FILE OFF. * Step 5 . COMPUTE pcinc = cincome/suminc . * Step 6. RANK VARIABLES=income (A) BY IDPSU / RFRACTION into cdfinc / PRINT=YES / TIES=HIGH . * Step 7. COMPUTE d1 = @TOP@. COMPUTE d2 = @TOP@. * Note that it doesn't matter whether D1 or D2 is the Y variable * in the D1-D2 pair. SPLIT FILE BY IDPSU. * D1 and D2 are identical and are created to allow you to draw a * diagonal line on the graph. GRAPH /SCATTERPLOT(OVERLAY)=cdfinc d2 WITH pcinc d1 (PAIR) /MISSING=LISTWISE /TITLE= 'Lorenz Curve for Income'. * Step 8. * Calculate and print the Gini coefficient(s). * For last case, LAREA is area under the Lorenz curve. DO IF (@TOP@) . + COMPUTE larea = 0. ELSE. + COMPUTE larea = LAG(larea) + (cdfinc - LAG(cdfinc)) * (pcinc + LAG(pcinc))/2 . END IF. IF (cdfinc = 1) gini = (.5 - larea)/.5 . REPORT /VARIABLES gini (VALUE) /BREAK = IDPSU (SKIP(1)) '' /SUMMARY MAX( gini) SKIP(1) '' . |
Re: Calculating Gini coefficients for each subset (villages) of large data set
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At 05:21 AM 2/28/2014, Mattias wrote:
>Here is suggested syntax for computing Gini coefficients for each >subunit (IDPSU) based on INCOME provided by David Marso and slightly >adjusted by me. I did a little numerical experimentation, with three constructed distributions: A. Four quartiles, with income (from low to high) 0.4, 0.8, 1.2, and 1.6 times the mean; true Gini coefficient 0.250 B. Half the income distributed evenly among 10% of the population, the other half evenly among the other 90%; true Gini = 0.40 B. Half the income distributed evenly among 1% of the population, the other half evenly among the other 99%; true Gini = 0.49. I randomly drew samples of 5, 10, and 20, with 20 'villages' for each distribution and sampling level -- 180 'villages' all told. Here's what it looked like; this is the result of AGGREGATE over the combinations of distributions and per-village sample sizes: |-----------------------------|---------------------------| |Output Created |03-MAR-2014 21:14:50 | |-----------------------------|---------------------------| [Summary] Distrib PerVillg TrueGini Villages GiniMean GiniSD GiniMin GiniMax A 5 .250 20 .202 .076 .042 .300 A 10 .250 20 .238 .033 .192 .291 A 20 .250 20 .234 .040 .146 .292 B 5 .400 20 .210 .241 .000 .492 B 10 .400 20 .223 .232 .000 .494 B 20 .400 20 .364 .119 .000 .500 C 5 .490 20 .000 .000 .000 .000 C 10 .490 20 .041 .183 .000 .817 C 20 .490 20 .120 .292 .000 .817 Number of cases read: 9 Number of cases listed: 9 Roughly as expected: the mean Gini coefficient was low in every condition, although for distributions A and B, the observed range of estimated Gini coefficients always spanned the true value. (I wrote in an earlier post about distribution C, with half the income concentrated in 1% of the population. That is a very intractable distribution for estimating the Gini coefficient from empirical data, and that shows, above.) And larger sample sizes matter: it looks like a Gini estimated from sample of size 5 can't be trusted; Ginis from samples of sizes 10-20 are at least broadly reasonable estimates. However, if the true distribution of income shows a high concentration in a small proportion of the population, empirical Gini coefficients can be wildly unreliable. I append the full code, with should allow anyone to reproduce or extend these results. It divides roughly into three sections: a long INPUT PROGRAM to generate the data; code to calculate the empirical Gini coefficients; and a section to summarize and report the results. The code to calculate empirical Gini coefficients is essentially a streamlined version of that in the post I'm responding to; it's by David Marso, Mattias, and an unknown earlier author. In streamlining it, I've . Taken out code to plot each empirical Lorenz curve, and to print the final values . Taken out an initial AGGREGATE to collapse all cases with the same income into a single record -- it's not necessary, probably costs more than it saves in most cases, and isn't likely to be of use with empirical data . Rather than using CREATE and RANK to calculate cumulative values for population and income, I've included code to do that in the transformation program that calculates the Lorenz-cure integral and the Gini coefficient. -Live long and prosper (in the higher percentiles!), Richard Ristow =================== APPENDIX: Test code =================== * C:\Documents and Settings\Richard\My Documents . * \Technical\spssx-l\Z-2014\ . * 2014-02-28 Mattias- . * Re Calculating Gini coefficients for each subset.SPS . * In response to posting . * Date: Fri, 28 Feb 2014 02:21:49 -0800 . * From: Mattias <[hidden email]> . * Subject: Re: Calculating Gini coefficients for each subset . * (villages) of large data set . * To: [hidden email] . * ................................................................ . * ................. Test data .................... . SET RNG = MT /* 'Mersenne twister' random number generator */ . SET MTINDEX = 4718 /* Boston, MA telephone book */ . NEW FILE. INPUT PROGRAM. . STRING IDPSU (A6). . NUMERIC TrueGini(F6.3). . NUMERIC SampSize(F3). . LEAVE IDPSU TrueGini SampSize. . NUMERIC Person (F3). . NUMERIC Income (DOLLAR9.2). . VAR WIDTH IDPSU (6). . VAR WIDTH TrueGini SampSize Person Income (8). * The number of 'villages' to generate for each combination of . * distribution (A-C) and sample size: . . NUMERIC #VlgPss (F3). . COMPUTE #VlgPss= 20. * Distribution A: . * Mean income is 1,000. . * Income in 1st quartile = 400 . * Income in 2nd quartile = 800 . * Income in 3rd quartile = 1,200 . * Income in 4th quartile = 1,600 . * Actual Gini coefficient = 0.25 . . COMPUTE TrueGini = 0.25. . LOOP #Stype = 1 TO 3. . RECODE #Stype (1 = 5) (2 = 10) (3 = 20) INTO SampSize. . LOOP #Village = 1 TO #VlgPss. . COMPUTE IDPSU = CONCAT('A', STRING(SampSize,N2), '.', STRING(#Village,N2)). . LOOP Person = 1 TO SampSize. . COMPUTE #IncRank = RV.UNIFORM(0,1). . RECODE #IncRank (0.00 THRU 0.25 = 400) (0.25 THRU 0.50 = 800) (0.50 THRU 0.75 = 1200) (0.75 THRU 1.00 = 1600) INTO Income. . END CASE. . END LOOP. . END LOOP. . END LOOP. * Distribution B: . * Mean income is 1,000 . * 1/2 of total income is to top 10%, evenly: . * I = (1,000/2)/0.1 = 5,000 . * 1/2 of total income is to bottom 90%, evenly: . * I = (1,000/2)/0.9 = 555.56 . * Actual Gini coefficient = 0.40 . . COMPUTE TrueGini = 0.40. . LOOP #Stype = 1 TO 3. . RECODE #Stype (1 = 5) (2 = 10) (3 = 20) INTO SampSize. . LOOP #Village = 1 TO #VlgPss. . COMPUTE IDPSU = CONCAT('B', STRING(SampSize,N2), '.', STRING(#Village,N2)). . LOOP Person = 1 TO SampSize. . COMPUTE #IncRank = RV.UNIFORM(0,1). . RECODE #IncRank (0.00 THRU 0.90 = 555.56) (0.90 THRU 1.00 = 5000.00) INTO Income. . END CASE. . END LOOP. . END LOOP. . END LOOP. * Distribution C: . * Mean income is 1,000 . * 1/2 of total income is to top 1%, evenly: . * I = (1,000/2)/0.01 = 50,000 . * 1/2 of total income is to bottom 99%, evenly: . * I = (1,000/2)/0.9 = 505.05 . * Actual Gini coefficient = 0.49 . COMPUTE TrueGini = 0.49. . LOOP #Stype = 1 TO 3. . RECODE #Stype (1 = 5) (2 = 10) (3 = 20) INTO SampSize. . LOOP #Village = 1 TO #VlgPss. . COMPUTE IDPSU = CONCAT('C', STRING(SampSize,N2), '.', STRING(#Village,N2)). . LOOP Person = 1 TO SampSize. . COMPUTE #IncRank = RV.UNIFORM(0,1). . RECODE #IncRank (0.00 THRU 0.99 = 505.05) (0.99 THRU 1.00 = 50000.00) INTO Income. . END CASE. . END LOOP. . END LOOP. . END LOOP. END FILE. END INPUT PROGRAM. EXECUTE /* to avoid some DATASET glitches */. DATASET NAME TestData WINDOW=FRONT. DATASET COPY Process. DATASET ACTIVATE Process WINDOW=FRONT. *--F0r testing, select a small subset of the data . *--SELECT IF SUBSTR(IDPSU,1,1) EQ 'A' AND SampSize EQ 20 AND NUMBER(SUBSTR(IDPSU,5,2),F2) LE 5. * ................................................................ . * ................. Test code .................... . * Step 1. SORT CASES BY IDPSU INCOME. * Step 2, combining all subjects with the same income into ... . * a single summary record, omitted in this version ... . * Step 3: Total income (and population) for each group ... . * ... If there is a variable giving the number of persons at ... . * ... each income level, replace "#Persons" by that variable, ... . * ... globally, and delete the following declaration and ... . * ... COMPUTE. ... . . NUMERIC Persons (F4). . VAR LABEL Persons 'How many persons the record represents'. . COMPUTE Persons = 1. COMPUTE GrpPop = Persons. COMPUTE GrpInc = Persons * income. AGGREGATE OUTFILE = * MODE =ADDVARIABLES OVERWRITE=YES / BREAK = IDPSU / GrpPop 'Total persons in sub-sample or group' = SUM(GrpPop) / GrpInc 'Total income in sub-sample or group' = SUM(GrpInc). FORMATS GrpPop (F5) GrpInc (DOLLAR11.2). * Steps 4-8: Cumulative population & income; cumulative ... . * fractional population & income (X and Y values on ... . * the Lorenz curve), and cumulative Lorenz integral. ... . MATCH FILES / FILE * / BY IDPSU / FIRST=@TOP@. NUMERIC /* Cumulative, at or below this income level: */ #CPersons (F5) /* Total persons */ #CIncome (F11.2) /* Total income */. NUMERIC CDFpers CDFinc Gini #PvCDFpers #PvCDFinc (F6.3) @LArea (F8.4). VAR LABELS CDFpers 'Fraction of population at or below this income level' CDFinc 'Fraction of income to persons at or below this level' Gini 'Gini coefficient'. * Descriptions for scratch variables: . * #PvCDFpers Previous value of "CDFpers"' . * #PvCDFinc Previous value of "CDFinc"' . * @LArea Area under the Lorenz curve, to this level' . LEAVE @LArea. DO IF @TOP@. . COMPUTE #CPersons = 0. . COMPUTE #CIncome = 0. . COMPUTE #PvCDFpers = 0. . COMPUTE #PvCDFinc = 0. . COMPUTE @LArea = 0. END IF. * Steps 4-6: ... . * Cumulative total population and income: ... . COMPUTE #CPersons = #CPersons + Persons. COMPUTE #CIncome = #CIncome + Persons*Income. * Cumulative FRACTIONS of population and income: ... . COMPUTE CDFpers = #CPersons / GrpPop. COMPUTE CDFinc = #CIncome / GrpInc. * Step 7 (graph of Lorenz curve) omitted from this version ... . * Step 8: Cumulative area under the Lorenz curve, ... . COMPUTE @LArea = @LArea + (CDFinc + #PvCDFinc)*(CDFpers-#PvCDFpers)/2. * and Gini coefficient: ... . IF #CPersons EQ GrpPop GINI = 1 - 2*@LArea . * Save current cumulative fractions of population and income, ... . * for the next step in the Lorenz integration: ... . COMPUTE #PvCDFpers = CDFpers. COMPUTE #PvCDFinc = CDFinc. * ................................................................ . * ................. Output code .................... . EXECUTE /* to avoid some DATASET glitches */. DATASET COPY Output. DATASET ACTIVATE Output WINDOW=FRONT. SELECT IF NOT MISSING(Gini). NUMERIC MeanInc (DOLLAR9.2). VAR LABEL MeanInc 'Sample mean income'. COMPUTE MeanInc = GrpInc / GrpPop. LIST CASES=5 /VAR=IDPSU TrueGini SampSize MeanInc Gini. ADD FILES /FILE=* /RENAME=(SampSize=PerVillg /KEEP=IDPSU TrueGini PerVillg MeanInc Gini. STRING Distrib (A1). COMPUTE Distrib = SUBSTR(IDPSU,1,1). VAR LABEL Distrib 'Which of the constructed underlying distributions'. VAL LABEL Distrib 'A' 'Tractable, four quartiles' 'B' 'Half of income to top 10%' 'C' 'Half of income to top 1$'. DATASET DECLARE Summary. AGGREGATE OUTFILE=Summary /BREAK = Distrib PerVillg /TrueGini 'Gini for constructed income distribution' = MAX(TrueGini) /Villages 'Number of "villages" drawn' = NU /GiniMean 'Mean of sample Ginis' = MEAN(Gini) /GiniSD 'Std deviation of sample Ginis' = SD(Gini) /GiniMin 'Smallest Gini coefficient in sample' = MIN(Gini) /GiniMax 'Largest Gini coefficient in sample' = MAX(Gini). DATASET ACTIVATE Summary WINDOW=FRONT. FORMATS GiniMean GiniSD (F6.3). LIST. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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