Instructions:

This assignment aims to make you familiar with the use of Logit models to study choice decisions of consumers. This type of analysis is commonly called as brand choice analysis or product choice analysis. The data consists of a panel of consumers choosing between different types of (Dannon) yogurt over a 52 week period. Read in the datasets using SAS and study it to familiarize yourself with the variables. The data consists of the following files, which for your convenience, has been converted to SAS datasets - Products, Prodchars, Panel.

The SAS Documentation for Proc MDC will be found under SAS/ETS in the help files. The following sections of the documentation will be helpful to complete this assignment.

1. Details: MDC Procedure
2. Syntax: Proc MDC
3. Syntax: Model Statement and CHOICE, NCHOICE. TYPE options
4. Examples: Conditional Logit and Data

In this exercise you will setup and estimate a logit model without an outside good. The exercise will walk you through the typical steps in setting up, estimating and interpreting a logit model. The first few steps involves assembling the choice sets and formating the data for input to Proc MDC.

1. The first step in any data analysis is to understand the data. Begin by looking at the contents of each dataset using Proc Contents. Write the SAS code to list out the contents of each file and run it. Report what you observe about the data.

2. Use the panel dataset to compute the share of each included product. The colupc variable indicates the product that was bought by the panelist on that shopping occasion. How would you define the market size M for this analysis?

Hint: There is no outside good in this analysis.

3. Identify how many products are included in the data from the products dataset. Use this information to define the total number of product J in the choice set. Write a data step to create and assign a unique id called JID to each product. Hint: JID=1,2,3...J. Use the information in products and prodchars datasets to describe the product space that your are analyzing and the decision that you are going to model.

4. Generate summary statistics for product characteristics. Describe your observations and what can you infer?

5. The next step is to assemble the choice set for each week. Use the product and prodchar dataset to create a choice set for each week. The choice set for a week should contain all products and their attributes in that week. Note that some attributes might/could change weekly while others do not. Create alternative specific intercepts for each alternative in the choice set. How many intercepts do you need? Write out a matrix where the rows correspond to the alternatives and columns correspond to the intercepts. Write a data step to include the intercepts in the choice set dataset. Merge the weekly choiceset data to the panel dataset and introduce a binary dummy variable bought to indicate the chosen product in the choice set. Note this is a many-to-many merge - while it can be done using a data step, using Proc SQL is easier. How many data rows should the merged file have?

6. Now you are ready to start estimation. Specifying a condition logit model in Proc MDC with only the alternative specific intercepts in the utility function. Estimate the model and interpret the results.

7. Add price as a covariate in the utility function and repeat the analysis. Comment on your results.

8. Add the display variable to the model. Estimate the model and comment on your results.

9. Add the feature variable to the model. Estimate the model. Is SAS able to estimate the model correctly? Go back to the data and investigate why Proc MDC is unable to estimate the coefficient for feature. Report what you find.

10. Assemble a table with the loglikelihood, AIC and BIC values for the three models. Which model would you choose for subsequent analysis and why?

11. Using the model chosen in Qtn 10, compute the own and cross price elasticity of demand for each product. What can you conclude from the elasticity measures.

12. Assume the the product manager of Daimon had given you this data with the hope that you would help him understand the market. Based on your analysis so far what would you report about the product and market place to the manager?