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Re: st: fuzzy: calculating coverage and consistency for necessary conditions


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: fuzzy: calculating coverage and consistency for necessary conditions
Date   Thu, 7 Apr 2011 14:06:30 +0100

There was no reply the first time you sent this. If you don't get a
reply to this, I suggest that you contact the authors of the article
you mention directly, as they may well not be members of this list.

Nick

On Thu, Apr 7, 2011 at 1:42 PM, Wolfgang Feudenheim
<wg_feudenheim@web.de> wrote:
> Hello everybody,
> currently I am working on a fuzzy-set analysis. I have, however, found no way to calculate conistency- and coverage-values for necessary conditions.
>
> As laid out by Longest/Vaisey in StataJournal(2008), Number1, pp. 82, the consistency is calculated as
>
> Σmin(x,y)/Σ(x)
>
> From my results I can deduce from the results I get that coverage values are calculated as
>
> Σmin(x,y)/Σ(y)
>
> Unfortunately, these are just the formulas for calculations regarding the included factors as sufficient conditions for the outcome. If one supposes that the factors are necessary, one has to swap the formulas for the two measurements in the following way:
>
> Σmin(x,y)/Σ(y) (consistency) AND Σmin(x,y)/Σ(x) (coverage)
>
> Do you know how this "switch" can be performed. I am adding a little piece of code to exemplify the issue. In the code, we regard how degrees of wealthiness influence the posession of luxury goods (this obviously is a necessary condition since you can only have luxury goods if you have a sufficient amount of money, however, you are not obliged to buy luxury goods just because you are rich). I picked values that should produce a conistency-value of "1". As I have pointed out, however, the program incorrectly produces a coverage-value of "1" and a consistency value of ".739".
>
> *Variables: Wealthiness und Posession of Luxury Goods*
> input wealthy lux_goods
> 0 0
> 1 .8
> .4 .2
> .6 .6
> .4 .4
> .8 .8
> .8 .2
> .6 .4
> end
>
> *calculation of constistency and coverage *
> fuzzy lux_goods wealthy, settest(yvv)
> coverage lux_goods wealth

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