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# Decomposition for log-linear model

Hi,

I have estimated a log linear regression model using SAS with the following functional form:

lnY = a + XB1 + Xb2 + Xb3 + Xb4

The dependent variable is in log form, the independent/explanatory variables in linear form.

With the equation I can estimate/forecast the linear value of Y by taking the antilog/exponent of the forecast from the equation so that I can see the value in the orginal Y values instead of the logs. This is fine.

But I also want to decompose the forecast/estimate by the respective explanatory X variable.

For example if the total forecast in log form = 5, then the anti log/exponent of that gives me a forecast of 148 in the original Y series. Now of that 148, what I need to calculate is how much is X1, X2 etc is worth, e.g

a = 2
X1 = 45
X2 = 15
X3 = 25
x4 = 61

Total = 148

Does anyone know how to do this?

Thanks,

Biswajit

Views: 801

### Replies to This Discussion

Dear Biswajit,
Good evening. Your statement has ambiguity. If you are building regression equation using independent variables to find dependent variable then you'll have the value and proportion of each factor playing role in it. Also, SAS will give you coefficient value too. Apart from this if you require forecasted value of independent variables to forecast dependent then use time series. I hope, I'd answered your question. If I misunderstood then please give little more clarity about your purpose.

Regards,
Sagar.

Hey Bishu!! Long time.. I was pretty much looking for something similar since I ended up doing log-linear for a market mix project.

As far as I can tell, there's no easy way to land at decompositions for a log-linear model. Log transformed models lose all relations to the original variable, and the multiplicity of the explanatory vars end up making it difficult to say what % of something caused something. Elasticities are available ofcourse.

There's 2 approx. methods though that I came across that might help - 'Purging Method' and 'Delta Method' that help approximate the % contribution.

(And I can tell the other person who commented has no idea what you're asking! Lol.)

Best,

Arun (let's see if you recognize who this is!)