Math Help: How to Calculate Weights for Multiplicative Model with Dummy Variables

#1
Hi Everyone,

My question is how do I calculate weights for Y=W1X1*W2X2*WNXN where N is the number of independent variables.

I could use logarithms to convert this to an additive model, but each of the independent variables are binary/dummy variables. Here is some background.

Assume two independent variables (more in practice). Really this is two sets of dummy variables. The predictive airline market share model looks something like this:

ShareIndex=
[W(ns)D(ns)+W(1s)D(1s)+W(2s)D(2s)] *
[W(wb)D(wb)+W(nb)D(nb)+W(rj)D(rj)+W(tp)D(tp)]

W for weights, D for binary dummy variables
ITINERARY CONNECTIVITY (ns=nonstop, 1s=connection, 2s=doubleconnection)
AIRCRAFT TYPE (wb=widebody, nb=narrowbody, rj=regionaljet, tp=turboprop)

For each record, the there is one AIRCRAFTTYPE dummy variable with a value of 1; all others 0.

For each record, the there is one ITINERARY dummy variable with a value of 1; all others 0.

So basically the model is ShareIndex=W(aircrafttype)*W(itinerarytype)

The dependent variable in the actual data is SHARE (market share). However, the model might produce a ShareIndex where each record's SHAREINDEX / (sum SHAREINDEXES all records that market)=market share

For example if a market has 10 records each with 10% market share. MS(record1)=W(AircraftType)*W(ItineraryType)/

How do I calculate the coefficients/weights?

Thanks!!!
 
#2
Re: Math Help: How to Calculate Weights for Multiplicative Model with Dummy Variable

Here is some more info...

Looking for to calculate the weights/coefficients. Not sure how to regress this model. (This model is more complex than any I have worked with due to multiplicative function AND use of ShareIndex while the data only includes Market share.)

MarketShare = ℎ() / (∑_(=1)^▒(ℎ()) )

My data array looks something like this...

i,Market,Share,Dns,D1s,D2s,Dwb,Dnb,Drj
1,IAHORD, 0.205 ,1,0,0,0,1,0
2,IAHORD, 0.158 ,1,0,0,0,1,0
3,IAHORD, 0.299 ,1,0,0,0,1,0
4,IAHORD, 0.181 ,1,0,0,0,1,0
5,IAHORD, 0.157 ,1,0,0,0,1,0
1,AUSGIG, 0.250 ,0,1,0,1,0,0
2,AUSGIG, 0.219 ,0,1,0,1,0,0
3,AUSGIG, 0.048 ,0,0,1,0,1,0
4,AUSGIG, 0.020 ,0,0,1,0,1,0

13,AUSGIG, 0.018 ,0,0,1,0,1,0

Thanks again for your help.