[R] Sensibility analysis

Micheall Taylor pols1oh at bestweb.net
Wed Jul 18 15:32:10 CEST 2001

I believe the english term you are looking for is sensitivity analysis -
sometimes also called a stress analysis. 

I'll have to leave it to others to discuss the R portion as I am pretty new
to that, but may help some in the other areas.

There are no rules concerning the parameters and and step variances that
should be used in this form of analysis. 

The parameters that you chose to vary are those that you are concerned may
1) vary in the "real-world" 2) affect outcomes.  For example, modeling
elections in the U.S. one may "stress" the model with a variances in
weather as bad weather will cause Americans to stay home and vote in fewer
numbers.  One would be less tempted to do so in France as the french voter
tends to vote in elections (compared to Americans) and weather isn't quite 
as varied as in the U.S. (I would imagine - milder climate - smaller 
geography, etc)

What step to use?  What level of precision to you want?  There is no right
and wrong. Being sort of a data guy, I tend to you smaller steps to create
more granular precision - the resulting graphs look better :)

Your vary-one-parameter-hold-others-constant is a fine strategy most of the
time. One word of caution.  If you are doing a nonlinear mixed-effects
model, following such a technique may not show you the real sensitivity of
the model.  You might want to consider a model in which all parameters are
allowed to vary randomly within a known and fixed distribution. This sort
of model is much harder to intrepret in the end, but can produce facinating
spikes in model outcomes that can be very informative.

I've built such a model for "stressing" investment models. The non-linear
and joint "stresses" produce radically different outcome contours than
single variable variances.  These outcome contours better match reality. 

Michaell Taylor, PhD
Chief Economist, Reis, Inc., New York
Professor of Political Science, NTNU, Trondheim, Norway
Adjunct Professor, UofD, South Africa

On Wed, 18 Jul 2001 11:50:14 +0200 (MEST) brunels at free.fr wrote:

> Hi everyone,
> i'm actually working on a nonlinear mixed-effects model, and beginning the 
> study of its sensibility.
> It takes 35 input and gives a n*35 matrix of output as it's a growth model (n 
> is the number of days of the growth period).
> Well, I have to analyse the variation of the output in relation to the 
> variation of the parameters of this models (first univariate then multivariate 
> variation)  :  it's a sensibility analysis ( a french word-by-word 
> translation ). 
> So, I choose one parameter, increase its value, do it one more time and again, 
> and for each of the 10 responses I have a curve of sensibility which i have to 
> calculate numerically the derivative.
>  I have read some books but none of them treated this scope in detail, so i 
> wonder : 
>     - what are the numeric differentation methods available in this case. Are 
> they available on R?
>     - which criteria to choose for the variation step of the parameters ?
>     - do you have any reference of books i may consult ?
> I'd be glad to receive any help from you all. Thanks.
> the student i am bless your mailing-list
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