How do I create utility scores from an unequal number of inputs

Question

In my data I have an outcome - "daily satisfaction" - measured on a 1 to 5 scale with 5 representing the respondent was very satisfied with her day and 1 representing the respondent was very unsatisfied with her day. I also have information on what a respondent did that day, e.g., visited a museum, listened to music, washed dishes, spent time with family, mowed the yard, etc. I would like develop estimates for how much each activity contributes to daily satisfaction. I believe that these would be utility scores and maybe estimable by some sort of Bayesian approach, but beyond knowing a little of the jargon, I'm not familiar with this area. Can someone let me know what analyses and terms I should be Googling or point me to some references?

One important consideration is that the respondent may have done a different number of things each day. On one day she may have spent time with her family and mowed the yard. The next day she may have spent time with her family, listed to music, and washed dishes. In other words, this isn't a comparison of 3 sets of attributes that will always be present with different values.

Again, I'm just trying to get a sense of where to start so set aside a few complications for the moment unless they influence which analysis is appropriate:

• The time each activity was done each day will vary and may have an impact on daily satisfaction. E.g., mowing the yard all day probably doesn't have the same effect as just mowing the yard for a few minutes. I don't have time information for each activity so I can't take it into account.
• The absolute number of things done in a day may have an impact on satisfaction. E.g., respondents who completed a lot of things may be more satisfied with their day, but I don't need to take this into account at the moment.
• There may be overlap in activities. E.g., the respondent may have visited the museum with his or her family. Or mowed the lawn while listening to music. For this purpose, assume they are mutually exclusive.

I will be doing these analyses in R. Thanks in advance for your suggestions.

Answer 1

The basic question here is how to translate this substantive question into a regression model.

The model is satisfaction as a function of a bunch of input variables, which sound like they are measured as indicator variables (0 or 1). Assuming you have the data, you simply need to make some decisions about functional form and model specification and this becomes very straightforward in R. Are you willing to treat the outcome as continuous? Consider least squares regression. Do you want to model placement into the outcome as a set of ordered or discrete categories? Then consider ordered logit/probit or multinomial logit/probit. Do you want to make some other assumptions?

You can start with Wikipedia on this: http://en.wikipedia.org/wiki/Discrete_choice#Prominent_Types_of_Discrete_Choice_Models

But you might find some other texts helpful, like:

• Data Analysis Using Regression and Multilevel/Hierarchical Models by Gelman and Hill, for a general introduction to regression modelling
• Regression Models for Categorical or Limited Dependent Variables by J. Scott Long, for a focus on limited dependent variable models
• Discrete Choice Methods with Simulation by Kenneth Train, for a focus on a lot of the assumptions of those models

In terms of executing this in R, you should be able to easily accomplish this (in a classical rather than Bayesian framework) using built-in functions lm and/or glm. If you decide to go with a slightly more advanced model or the Bayesian route, you'll find two CRAN Task Views helpful for summarizing available functions and packages:

• http://cran.r-project.org/web/views/SocialSciences.html
• http://cran.r-project.org/web/views/Bayesian.html