# What regression model should I use for this problem?

I am a lowly undergrad working on a research project with my university. I have only a basic grasp on regression analysis so please bear with me!

We are seeking to find consumers' willingness to pay for different factors of air travel, and especially for carbon.

Our variables are ticket price, carbon emissions, starting airport (SMF or SFO), and number of layovers. SMF is considered a more convenient choice than SFO for this scenario.

We are attempting to fit a logit model to our data. As I understand it, a logit model is useful for independent continuous variables and dependent categorical variables. Carbon emissions, a continuous variable, is directly dependent on number of layovers, a categorical variable. Does this disqualify logit modeling? If so, how should we model our data to determine WTP?

## 5 Answers

If you are trying to estimate if the consumer will pay or not then a logit model would help.

A simple logistic regression model with the set factors should do the trick. The output of the model would be $$P$$(Consumer will pay).

This link should help in understanding multicollinearity in the regressors.

I second the answer above. I'll shoot in that you might also consider a linear probability model (LPM).

LPM uses OLS with a binary dependent variable, and changes in independent variables can be interpreted as probability changes. Some see probability changes as more intuitive to interpret than odds ratios or log odds.

Mood (2010) is often referred to for LPM, and you may also be interested in some arguments for logit over LPM by Allison.

Indeed linear probability model (LPM) could also be used, but I would advise you to stick to logistic regression ("logit" model) as generally more acceptable than LPM (If you want to use LPM, you will have to prove that it is an acceptable approximation of Logit). You might also consider a "Probit" model.

Re your question about predictors - Logit model can handle every type of predictors (continuous, categorical, interaction between continuous and categorical variables).

As already pointed out by Giridhar, with a Logit model you won't be able to compute people WTP - On their probability of being willing to pay for the service (e.g., are women more likely to pay for the service?).

For what I've seen in the description, your problem is one of classification rather than regression. A logistic model is often appropriate unless there is some reason to suspect otherwise.

The main reason to reject a logistic model is having a variable whose relationship with the output is not monotonous (probability of "success" increases up to a point and then decreases), but I cannot find any of those in your data description.

Anyway, Support Vector Machines, Decision Trees and Random Forest classification are also sound alternatives

One issue other answers haven't addressed. You said,

As I understand it, a logit model is useful for independent continuous variables and dependent categorical variables.

This is incorrect - logistic models and linear probability models can handle both categorical and continuous independent variables. They both model probabilities. Now, for the most part, there's little reason to use a linear probability model over a logistic model, given that software can pretty easily fit logistic models these days. One of the arguments for linear probability models raised by the person cited by Allison was computation speed, but this is irrelevant nowadays.

You asked about modeling willingness to pay. That is an econometrics question, and my sense is that most posters here are statisticians rather than econometricians or economists. There may be some other design issues you haven't thought of. You may wish to Google discrete choice models to learn more, but this is not something I can advise on as I haven't ever touched one of these.