Martin (and Dan) .....
I clearly didn't read the question as Martin did. I took Dan's expression
'inverse relationship' to mean 'inverse correlation'.
That is, f(x) is a function mapping [0, +inf) to [0,1] such that f(0)=1 and
f(+Inf)=0 ... or strictly, f(x)->0 as x->+Inf
This is satisfied by f(x)=exp(-x) and so this is the transformation that Dan
requires.
..... Andre Francis
On 22 July 2011 15:58, Martin Holt <[log in to unmask]> wrote:
> Hi,
>
> I sent the following answer to the SPSS list in error, so am now forwarding
> it on to ALLSTAT.
> >Hi Dan,
> >Tentatively, because playing with infinities and 0 is risky, so using a
> calculator:
> >If first variable = 0, then exp0 = 1 and then 1/exp0 = 1.
> >If first variable = 20, say, then exp20 = 485165195.4 and 1/exp20 =
> 0.000000009
> >So, as first variable 'x' increases towards +Inf, the function 1/exp(x)
> tends towards 0 and does not go below 0.
> >So, if x=0, 1/exp(0) =1 and if x=+Inf, 1/exp(+Inf) = 0 as required.
> >This assumes that x lies between 0 and +Inf: you'd need to check with any
> potential -ve x's as to whether the function does what >you want it to.
> >HTH
> >Martin Holt
> >Medical Statistician
>
> ----- Forwarded Message -----
> From: Martin Holt <[log in to unmask]>
> To: Dan Abner <[log in to unmask]>; "[log in to unmask]" <
> [log in to unmask]>
> Sent: Thursday, 21 July 2011, 20:29
> Subject: Re: Transformation Question XXXX
>
>
> Hi Dan,
>
> Tentatively, because playing with infinities and 0 is risky, so using a
> calculator:
>
> If first variable = 0, then exp0 = 1 and then 1/exp0 = 1.
>
> If first variable = 20, say, then exp20 = 485165195.4 and 1/exp20 =
> 0.000000009
> So, as first variable 'x' increases towards +Inf, the function 1/exp(x)
> tends towards 0 and does not go below 0.
>
> So, if x=0, 1/exp(0) =1 and if x=+Inf, 1/exp(+Inf) = 0 as required.
>
> This assumes that x lies between 0 and +Inf: you'd need to check with any
> potential -ve x's as to whether the function does what you want it to.
>
> HTH
>
> Martin Holt
> Medical Statistician
>
> From: Dan Abner <[log in to unmask]>
> To: [log in to unmask]
> Sent: Thursday, 21 July 2011, 7:27
> Subject: Transformation Question XXXX
>
> Hello everyone,
>
> I have a variable that ranges from
> 0 to +Inf and need to map it to a space
> from 0 to 1 with an inverse relationship with the original variable (in
> other words, 0 of the new variable corresponds with max(old variable) and 1
> of new variable corresponds with min(old variable).
>
> Can anyone suggest a transformation?
>
> Thank you!
>
> Dan
>
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