Welcome back. If you viewed the previous lesson of this course you've seen that

the examples we've use so far were such that the dependent variables were continuous.

In many cases, however,

marketing outcomes are not continuous and are instead

discrete like donating money or not to a charity.

By the end of this lesson,

you'll be able to discuss methods for analyzing how

marketing factors affect discrete consumer decisions.

First, let's look at the decision when the outcome is one or zero.

In this case, what you want to do is something called LOGIT or

logistic regression where the dependent variable

is going to be the logarithm of P over one minus P,

and the model is going to be A plus B1X1 plus B2X2 and so on.

So what is P here?

P refers to the proportion of people who decided to,

let's say, buy a house within a given period or not.

Another example could be the proportion of

people who decided to give blood within a market area.

You can see here that P and one minus P are going to be proportion that you'll use

to do the regression that measures the impact

of each of the variable on this proportion or probabilities.

In marketing, you often have situations

where what you observe are discrete decisions by customers or households.

Let's say that you have two brands in

the marketplace and customers can either buy brand A or brand B.

The first two observations relate to the same households for two purchase occasions.

That is, this household decided to buy a brand A.

The second household decided to buy brand B at two purchase occasions.

And household three decided to buy brand A in two purchase occasions.

The question is can I predict these choices and, most importantly,

can I understand how prices and

other marketing variables impact those choice probabilities?

If I decrease the price of B,

how likely am I going to observe someone switching from brand A to brand B?

And similarly, if brand A were to decrease its price,

can I predict the switching behavior of someone from brand B to brand A?

In such marketing model,

the question is what is the dependent variable and what are the independent variables?

It's a bit tricky because what we want to understand is

the impact of different marketing variables on the utility of consumers.

The assumption is that a given customer is going to choose brand A over brand B

if his or her utility for brand A is higher than for brand B.

The problem here is that utilities are

a latent construct that usually come from economic theory.

So that means that it's not directly observed by the marketing researchers.

It actually doesn't exist in reality.

So what we need to do is a way to indirectly measure the utility of the customer.

Formally, it means that you are going to say that

individual I has a utility of consuming product A.

That is a function of an intersect Alpha A plus Beta A times XI where

Beta A is going to be a vector of

all the parameter values that corresponds to the independent variable XIs.

Similarly, Alpha B is going to be the intersect

of customer I utility function for brand B.

And so we can see that Alpha A and Alpha B

could be some measure of brand values in the marketplace.

That would be the value that brand command

irrespectively of all the variables of choice prices.

From here, HN and AI and HN and BI are going to be

some error terms to which we are going to impose some parity distribution functions.

That is an assumption about how they evolve.

Long story short, what you want to do is work out the math to

find out what is the probability based on

the data that someone is going to choose brand A over brand B.

This particular function will be given by this last equation.

So here the point of this is for you to know how you

would do this analysis and what this analysis would mean.