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Re: st: exponential extrapolation


From   Austin Nichols <[email protected]>
To   [email protected]
Subject   Re: st: exponential extrapolation
Date   Tue, 1 Mar 2011 12:21:18 -0500

Nick,
Yes, the extrapolation based on 2 points is by design, but obviously
that can be improved on to the extent that a more global model
predicts well out of sample. Out of sample prediction like this is
always tricky--just ask the space shuttle Challenger engineers, or the
US CBO. Here are 4 ways to implement the bad idea, compared:

clear
input genomes csf
1       2045
2       1793
3       1715
4       1665
5       1637
6       1613
7       1596
8       1579
9       1566
10      1554
11      1539
12      1527
13      1516
14      1511
15      1497
16      1486
17      1480
end
set obs 100
g lc=ln(csf)
replace gen=gen[_n-1]+1 if mi(gen)
ipolate lc gen, gen(ilc) e
g ic=exp(ilc)
qui poisson csf gen
predict c1hat
g lng=ln(gen)
qui poisson csf lng
predict c2hat
qui poisson csf lng if gen>10
predict c10hat
sc c10hat c1hat c2hat ic csf gen if gen<35

On Tue, Mar 1, 2011 at 12:00 PM, Nick Cox <[email protected]> wrote:
> The extrapolation here is linear in the logarithms. That being so, it is an extrapolation based on the last known line segment (16, log(1486)) (17, log(1480)) only. No other information is used.
>
> Nick
> [email protected]
>
> Austin Nichols
>
> ipianah nic <[email protected]>:
> One way to implement the bad idea:
>
> clear
> input genomes csf
> genomes csf
> 1       2045
> 2       1793
> 3       1715
> 4       1665
> 5       1637
> 6       1613
> 7       1596
> 8       1579
> 9       1566
> 10      1554
> 11      1539
> 12      1527
> 13      1516
> 14      1511
> 15      1497
> 16      1486
> 17      1480
> end
> set obs 100
> g lc=ln(csf)
> replace gen=gen[_n-1]+1 if mi(gen)
> ipolate lc gen, gen(ilc) e
> g ic=exp(ilc)
> sc ic c gen
>
>
> On Tue, Mar 1, 2011 at 4:03 AM, Nick Cox <[email protected]> wrote:
>> In fact a look at the archives shows that you asked essentially the
>> same question on 11 February, and unsurprisingly got a very similar
>> answer from Maarten Buis and myself.
>>
>> So, what is going on? Perhaps you need to find someone in your
>> institution who can talk you through these things.
>>
>> Incidentally, a plot of these data suggests to me that exponential
>> decline is not the right model. There is curvature not taken out by
>> looking at the data on log scale. Extrapolating the wrong model over
>> more than 5 times the range of the observation strikes me as a bad
>> idea, unless there is a compelling biological argument to the
>> contrary.
>>
>> Nick
>>
>> On Tue, Mar 1, 2011 at 8:27 AM, Nick Cox <[email protected]> wrote:
>>> This looks more as if you have an exponential decline, not an
>>> exponential distribution.
>>>
>>> As with your previous questions, fit an appropriate model using one or
>>> more of -regress- after transformation, -glm- with log link, or -nl-.
>>> Then use -predict-.
>>>
>>> Nick
>>>
>>> On Tue, Mar 1, 2011 at 7:00 AM, ipianah nic <[email protected]> wrote:
>>>
>>>> my data set  exhibits an exponential distribution.how  can I
>>>> extrapolate my data set as in the case below where i have genomes and
>>>> csf..help please
>

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