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Consider a dataset from 1990 to 2017 that contains the crime rate per 100,000 people in some cities from Latin America.

I want to measure which city is more complex according to this data and other indicators. I'm using The analytic hierarchy process proposed by Saaty.

Consider this example:

city_code  r1990  r1991 r1992 r1993 r1994 r1994
  12345     120     80    91   110   105   99
  23456      10     15    16    12     7   11
  34567      90     91    85    75    77   65

According to my question, I want to sum each rate in each year, and then get for each year the mean of each rate based on the total.

Based on the example above:

city_code  total
  12345     605
  23456      71
  34567     483

city_code  mean1990  mean1991 mean1992 mean1993 mean1994 mean1994
  12345      0.20      0.13     0.15     0.18     0.17     0.16
  23456      0.14      0.21     0.23     0.17     0.10     0.15
  34567      0.19      0.19     0.18     0.16     0.16     0.13

So, is this a good practice? I couldn't find an example following this method? Any orientation about this subject will be appreciated.

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  • $\begingroup$ What do you mean by 'which city is more complex'? What does crime rate have to do with complexity? $\endgroup$
    – kingledion
    Feb 21 '18 at 14:48
  • $\begingroup$ No, I mean in which city occurs more crimes than and other, for not saying which city is more dangerous. I think the concept complex could lead to confusion. I wll edit. Thanks. $\endgroup$
    – estebanpdl
    Feb 21 '18 at 15:28
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This can be fairly good if you deal with few years.

In general it's not a good practice, since asymptotically will lead you to have almost the same fraction of crimes per all the considered years. But unless you have data from the last 10000 years, you can simply ignore the asymptotic behavior a continue the way you are doing.

Otherwise, you can normalize the data to a reference value, say the maximum number of crimes on the series. This is more robust.

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  • $\begingroup$ Thanks a lot for the orientation. I will follow your recommendation. $\endgroup$
    – estebanpdl
    Feb 21 '18 at 15:29

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