attractivenss multiplier

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"Andy Ford"
Junior Member
Posts: 10
Joined: Fri Mar 29, 2002 3:39 am

attractivenss multiplier

Post by "Andy Ford" »

This is Andy Ford responding to Daniel Jaroshs inquiry about "common
practice" for simulating choice among multiple products with several
attributes such as price, color, etc. When facing discrete choices among
alternatives with differing attributes (which can not all be translated into
equivalent monetary terms), we will do well to turn to the discrete choice
literature, especially the pionerring work of Daniel McFadden. Discrete
choice can be simulated with mulit-nominal logit models whose parameters may
be estimated from either state preference data or reveal preference data.
An example (implemented in Stella) for choice among 5 types of motor
vehicles with 6 different attributes is shown on page 265 of my text on
"Modeling the Environment" (Island Press 1999).

Andy Ford
Professor
Program in Environmental Science and Regional Planning
Washington State University
Pullman, WA 99164-4430

FordA@mail.wsu.edu
(509) 335-7846
http://www.wsu.edu/~forda
Tom Fiddaman
Senior Member
Posts: 55
Joined: Fri Mar 29, 2002 3:39 am

attractivenss multiplier

Post by Tom Fiddaman »

If you surf the web for "random utility maximization" "discrete choice"
"LOGIT" "generalized extreme value" "MCI market share" and similar terms
youll find a lot of references to this. Ill save you the trouble by
listing three comprehensive online books:

http://elsa.berkeley.edu/books/choice2.html
http://164.67.167.7/MCI_Book/introduction.htm
http:/
oso.epfl.ch/mbi/papers/discretechoice/paper.html

These are all pretty industrial-strength. I suspect the first would be most
helpful; I havent looked at it for a while but the author does plenty of
work including noneconomic input variables. All of the above have a
statistical estimation flavor, and the restricted functional forms employed
should be used with caution, for robustness reasons Ill outline below.

There is a common practice in SD often called Us/(Us+Them), in which
share[us] = attractiveness[us]/SUM(attractiveness[all options])
attractiveness[us] = F(price[us],quality[us],service[us],...)
this is typically extended by a total market demand, so that
demand[us] = share[us]*total demand
total demand = G(SUM(attractiveness[all options]))
note that using the average instead of the total attractiveness to drive
total demand - a seemingly innoccuous choice - can have pervers effects, so
you have to be a bit careful.

If people were consistent and measurements were perfect, youd expect all
share to go to the single most attractive item. In reality of course people
are different and you cant measure everything, so share gets smeared out
over various items due to the influence of diversity in preferences for
unmeasured attributes. In one extreme, exchange rate spreads across markets
are extremely small because price is the only thing that matters,
information is pervasive, buyers are hightly price sensitive, etc. In the
other extreme, market share of fat and lean remains 50-50 regardless of
price, as Jack Sprat can eat no fat, and his wife can eat no lean.

The big choice here is the form of the attractiveness function -
multiplicative weighting is common (yielding an MCI model):
attr[us] = price[us]^e * quality[us]^k * service[us]^r ...
Obviously all these inputs should be normalized so that this is
dimensionally consistent.
Exponential is also common (yielding logit or MNL):
attr[us] = EXP( e*price[us] + k*quality[us] + r*service[us]
The nice thing about both of the above is that they can be linearized for
easy estimation.

However, you should be suspicious of anything thats easy. Often the right
form of the attractiveness function will be some blend of expressions
thats not linearizable. Reality checks or thought experiments about
extreme conditions are a good way to verify this - e.g. what happens if
price goes to 0 (probably not 100% or infinite share)? what happens if
advertising goes to infinity (again probably not 100% share)? what happens
if advertising goes to 0 (not 0 share)?

There are a number of common extensions of this framework. The most
frequent are hierarchy - e.g. users first choose whether to fly or drive,
then choose an airline or a type of car - and correlation structure (i.e.
stocks) in the attractiveness components or shares - e.g. due to experience
effects, inertia, perception delays, etc. A fancier approach (detailed in
the first book) measures the diversity of users (as described by
distributions of the e, k, r ... parameters describing their choices).

As far as I know these methods fall apart when you introduce limited
supply. I can think of two typical examples:

First, if you think of a product like telecom services, there are hard
service area boundaries that restrict the competitive set available to
potential subscribers - some have no choice, some have one choice, and some
may have two or three. This creates separate unserved, protected, and
competitive niches for the various carriers, which may need to be addressed
separately (I think in theory this could be handled by brute force
application of many simple models or an appropriate GEV model - see the
first book). The problem is that with many actors there will be zillions of
permutations.

Second - and more intractable - is the case of limited capacity or
stockouts (airline seats, cans of soup, cellular calls). These limits break
the assumption that consumer choices are independent, since you cant buy
something if Ive just bought the last one. Vensims ALLOCATE BY PRIORITY
function solves this problem, but with less-satisfying assumptions about
the random component of choice. An LP can also be used for allocation in
such cases, but is even less attractive as it assumes no randomness -
winner takes all up to capacity limits. Other strategies for solution
include taking orders for choices that exceed capacity, backlogging the
excess, and using the backlog as a component of attractiveness. All of the
above have problems so I keep hoping someone will do a dissertation on
discrete choice subject to capacity constraints (or point me to the right
paper).

Interestingly the allocations that come out of all this are quite similar
to what you get with aggregate production functions (try searching the web
for "cobb douglas" "constant elasticity of substitution" or "translog"). On
the surface the stories are a little different but a lot of the fundamental
assumptions can be reduced to the same thing.

Hope this helps.

Tom

****************************************************
Thomas Fiddaman, Ph.D.
Ventana Systems http://www.vensim.com
8105 SE Nelson Road Tel (253) 851-0124
Olalla, WA 98359 Fax (253) 851-0125
Tom@Vensim.com http://home.earthlink.net/~tomfid
****************************************************
"George Backus"
Member
Posts: 23
Joined: Fri Mar 29, 2002 3:39 am

attractivenss multiplier

Post by "George Backus" »

Daniel inquired about utility functions to define choices:

I maintain a fetish for the Qualitative Choice Theory (QCT) of Daniel
McFadden.(Won the Nobel Prize in 2000 for this work). It seems completely
compatible with good SD in that it accepts perceptions, includes
uncertainty, is statistically rigorous, is compatible with economics and
psychology, and the terms of the function have a real-world causal
correspondence. It is excellent for modeling essentially any decision
process. We have used QCT for over 25 years with and it has stood up to
many a skeptics beating unscathed. Some good references are:

McFadden, D., "Qualitative Response Models," in Advances in Econometrics,
Ed. Werner Hildenbrand, Cambridge University Press, New York, 1982
McFadden, D., (1986), "Econometric Model of Probabilistic Choice," in
Structural Analysis of Discrete data with Econometric Applications, ed. C.F.
Manski and D. McFadden, Cambridge, MA, MIT Press.

Ben-Akiva, M., Discrete Choice Analysis: Theory and Applications, MIT
Press, Cambridge, MA, 1985.



McFadden, D., "Conditional Logit Analysis of Qualitative Choice Behavior,"
in Frontiers in Econometrics, Ed. P. Zarembka, New York, Academic Press,
1974.



Train, K., Qualitative Choice Analysis, MIT Press, Cambridge, MA, 1986.

For logic to help define the preferences (choice variables) see

Keeney, R. L. and Raiffa, H., Decisions with Multiple Objectives, John Wiley
& Sons, New York NY, 1976.

George Backus
Policy Assessment Corporation
14602 West 62nd Place
Arvada, CO 80004
Bus: 303-467-3566
Fax: 303-467-3576
Email:
George_Backus@ENERGY2020.com
Alan Graham
Member
Posts: 27
Joined: Fri Mar 29, 2002 3:39 am

attractivenss multiplier

Post by Alan Graham »

Hi Daniel,

As usual, there are at multiple approaches to modeling utility in dynamic
models:

1. The traditional way is attractiveness multipliers that are the product
of many input multipliers. Described in, e.g. Forresters Urban Dynamics or
my (and Louis Alfelds) Introduction to Urban Dynamics, and Im sure the
usual texts as well. This is an easy and quick approximation. It doesnt
create an explicit value of utility, but does give behavioral results.

2. Explicit utility functions, supported by conjoint analysis of some form,
can drive action within a model. There are probably a few more published
applications (in addition to the commercial and unpublished ones
PA/Pugh-Roberts has done), but the one I know is: Markus Schmidt and Shayne
Gary "Combining system dynamics and conjoint analysis for strategic
decision-making with an automotive high-tech SME" in SDR 18(3) Fall 2002,
pp. 359-379. A public sector utility function was used, briefly mentioned
and referenced in Mayo, Callaghan and Dalton, "Aiming for restructuring
success at London Underground" SDR 17(3) Fall 2001, pp. 261-289. That seems
to be based on work by a branch of the UK government, and so may be
accessible online.

3. In for-profit settings or non-profit settings where the benefits
straightforwardly translate into cash flows, there is of course Net Present
Value. While NPV is often calculated over the course of a simulation to
assess, e.g. the efficacy of a strategy, sometimes a modeler will actually
want a perceived NPV and some consequences to drive decision-making at every
point during the simulation. PA (and doubtless others) does this big-time
for energy market models, but the only published example that comes to mind
is Jim Hines MIT PhD thesis deriving corporate investment functions
explicitly in terms of NPV maximization (and apologies if my memory isnt
precise on the contents).

cheers,

alan

Alan K. Graham, Ph.D.
PA Consulting Group

Alan.Graham@PAConsulting.com
One Memorial Drive, Cambridge, Mass. 02142 USA
Bill Braun
Senior Member
Posts: 73
Joined: Fri Mar 29, 2002 3:39 am

attractivenss multiplier

Post by Bill Braun »

The best example in practice that I know of is Urban Dynamics, by Jay W.
Forrester. It is priceless in its application of the attractiveness
multiplier, and quite useful for a host of other reasons as well. A good
addition to your library. I consider it a staple in mine.

Bill Braun
From: Bill Braun <medprac@hlthsys.com>
"Roderick Brown"
Junior Member
Posts: 6
Joined: Fri Mar 29, 2002 3:39 am

attractivenss multiplier

Post by "Roderick Brown" »

Several eminent folk have already replied to Daniel Jaroschs query
about common practice in modelling the attractiveness of products or the
utility of services in non-profit settings and I couldnt attempt to
better the references and advice cited. However, it does strike me that
logit-type choice models, be they additive, multiplicative, exponential
or so on, could be improved a little by we dynamic folk through
recognising more often that consumer preferences themselves change over
time. That is, the weightings today are not necessarily the same as
weightings tomorrow and consumer assessed product values (stated or
observed) will shift in face of changing (rising?) market standards.
The qualities of a bulky 1982 Ericsson mobile "house brick" phone,
though highly ranked 20 years ago, are not qualities that would score so
well in 2003. Capturing shifting standards is a further refinement of
preference modelling and probably especially important in public sector
choice models that may play out over longer timescales than in
commercial applications - though not necessarily! In short, we should
consider greater use of levels to define US and THEM market factors and
do better than pure statistical functions. This also raises interesting
questions about the "half-life" of market standards and the
(corresponding?) pace of innovation. To think about anyway.

Kind regards,

Rod.

Roderick Brown
Strategy Dynamics Solutions
Cupola House
15 Alfred Place
LONDON
WC1E 7EB
ENGLAND
Mobile: +44 (0)7980 597 412
Office: +44 (0)207 467 9336
rod@strategydynamics.com
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