Attractiveness Multiplier
Posted: Sun Apr 08, 2001 2:32 pm
Bill Braun and Jim Hines are talking about different things, I think. Jim
refers to attractiveness indicators being used to model market shares. He
offers one formulation, but a better one (Id claim) is based on formal
utility theory, and predicts shares using either a logit or probit model.
The logit model gives the probability that product A is chosen out of n
alternatives as exp(UA)/ sigma( exp(Ui)), where UA is the utility
("attractiveness") of alternative A etc. The utility expression is some
function of the product attributes, commonly linear additive. In practice
it is similar to Jims formulation but uses the exponential of the
attractiveness terms. Its advantage is that it is grounded in utility
theory, and the utility parameters can - usually - be calibrated, using
specialised survey techniques.
The original question was about something rather different. The Urban
Dynamics model calculated attractiveness multipliers for each of several
attributes of the city, and then multiplied them together. The product
(or a lagged version of it) was then applied multiplicatively to one or more
rates, such as migration rate, or construction rate. I have been trying to
use this recently, and have problems with it, mostly to do with calibration.
First, using a product of multipliers has its attractions, but it obscures
the implied tradeoffs between different attributes. For instance, an
increase in land availability of X% will necessarily have the same modelled
effect on construction rates as a change in one of the other multipliers,
vacancies, say, by some other amount, y%. These equivalences are a useful
cross check when testing the credibility of model, but are not explicit in
the formulation and are awkward to tease out.
The second thing is relating the scale of the multipliers to rates of
activity. It seems to be hard for people to think in terms of the effect of
attractiveness on a rate of activity, such as construction. To be credible
to many people - certainly the audience I work to - some evidence or
calibration would be needed, however rough, to demonstrate that credible
orders of magnitude are used for these multipliers, but it is hard to see
how this could be achieved. The original book simply asserted some values -
very bold but not an approach that is easy to sell.
Two ideas occur to me that might improve things. One is to formalise the
notion of attractiveness a little more, probably by tying it in to the
economic notion of utility. The second is to tease out the mechanism linking
attractiveness to activity rates rather more fully, in the hope that
intermediate steps can be identified that can plausibly be
measured/calibrated.
John Swanson
From: "Swanson, John" <J.Swanson@sdgworld.net>
refers to attractiveness indicators being used to model market shares. He
offers one formulation, but a better one (Id claim) is based on formal
utility theory, and predicts shares using either a logit or probit model.
The logit model gives the probability that product A is chosen out of n
alternatives as exp(UA)/ sigma( exp(Ui)), where UA is the utility
("attractiveness") of alternative A etc. The utility expression is some
function of the product attributes, commonly linear additive. In practice
it is similar to Jims formulation but uses the exponential of the
attractiveness terms. Its advantage is that it is grounded in utility
theory, and the utility parameters can - usually - be calibrated, using
specialised survey techniques.
The original question was about something rather different. The Urban
Dynamics model calculated attractiveness multipliers for each of several
attributes of the city, and then multiplied them together. The product
(or a lagged version of it) was then applied multiplicatively to one or more
rates, such as migration rate, or construction rate. I have been trying to
use this recently, and have problems with it, mostly to do with calibration.
First, using a product of multipliers has its attractions, but it obscures
the implied tradeoffs between different attributes. For instance, an
increase in land availability of X% will necessarily have the same modelled
effect on construction rates as a change in one of the other multipliers,
vacancies, say, by some other amount, y%. These equivalences are a useful
cross check when testing the credibility of model, but are not explicit in
the formulation and are awkward to tease out.
The second thing is relating the scale of the multipliers to rates of
activity. It seems to be hard for people to think in terms of the effect of
attractiveness on a rate of activity, such as construction. To be credible
to many people - certainly the audience I work to - some evidence or
calibration would be needed, however rough, to demonstrate that credible
orders of magnitude are used for these multipliers, but it is hard to see
how this could be achieved. The original book simply asserted some values -
very bold but not an approach that is easy to sell.
Two ideas occur to me that might improve things. One is to formalise the
notion of attractiveness a little more, probably by tying it in to the
economic notion of utility. The second is to tease out the mechanism linking
attractiveness to activity rates rather more fully, in the hope that
intermediate steps can be identified that can plausibly be
measured/calibrated.
John Swanson
From: "Swanson, John" <J.Swanson@sdgworld.net>