# Probability Means

Hello,

In other software systems I see the possibility to get an output of what they call "ProbMeans".  This shows that for example a person that chooses A instead of B is most likely to be in segment 1 (instead of 2).

Is this also something I can get with Sawtooth?
I hope to hear from you soon. Many thanks in advance.
asked Feb 23, 2017

+1 vote

We don't offer that calculation automatically, but you can compute it pretty easily.

First, you compute the prior likelihood that a person belongs to the segments.  That's simply equal to the size of the segments.  For example, if:

Segment 1 has 50% of respondents
Segment 2 has 30% of respondents
Segment 3 has 20% of respondents

...then those are the prior likelihoods of a person belonging to the segments, before we see any data (any choice data from that respondent).

Next, we compute the likelihood that each segment chooses concept A instead of Concept B in a choice task.  You can do that via aggregate logit, or any other technique (e.g. latent class or HB) that allows you to build a model with a subsequent market (choice) simulator to predict the likelihood that respondents in each segment choose A or B.  Let's imagine that we build a model (a market simulator) that predicts the likelihood of respondents in each segment picking concepts A vs. B and the results are:

Segment 1: A=50%, B=50%
Segment 2: A=20%, B=80%
Segment 3: A=70%, B=30%

Now, imagine we observe a new respondent who picks A when given that same choice between A and B.  What's the likelihood that she belongs to segment A, B, or C?  It's proportional to the prior likelihood times the likelihood of picking A given the segment membership, or:

Segment 1: (0.5)(0.5) = 0.25
Segment 2: (0.3)(0.2) = 0.06
Segment 3: (0.2)(0.7) = 0.14

...but those three posterior probabilities don't sum to 1.0, so we need to normalize them to sum to 1.0 by dividing each by the sum (0.25+0.06+0.14) = 0.45, leading to...

Probability of a person who picks A in the set {A, B} belonging to each segment:

Segment 1: 0.25/0.45 = 0.55555
Segment 2: 0.06/0.45 = 0.13333
Segment 3: 0.14/0.45 = 0.31111
Sum = 1.000

This is called a Naive Bayes classifier and it is the same approach that we use with our MaxDiff Typing Tool, which generates a small number of "golden" MaxDiff questions to ask respondents to assign them with high accuracy to an existing segmentation scheme.
answered Feb 23, 2017 by Platinum (154,205 points)
edited Feb 23, 2017

I don't completely understand what you're saying here:
"Next, we compute the likelihood that each segment chooses concept A instead of Concept B in a choice task.  You can do that via aggregate logit, or any other technique (e.g. latent class or HB) that allows you to build a model with a subsequent market (choice) simulator to predict the likelihood that respondents in each segment choose A or B.  Let's imagine that we build a model (a market simulator) that predicts the likelihood of respondents in each segment picking concepts A vs. B and the results are:"

I figured out how to make a choice simulator and how to get the percentages, but only for all my respondents together, but I want to have the different percentages for my 2 segments. Is there something I should check or do in the simulator to get these for 2 groups separately? I got the results with my Logit model.

I hope you can explain this, thank you very much!
If you are using aggregate logit to run the utility estimation and to build your market simulator, then to create a segmentation (say, males vs. females) you need to go back to utility estimation under Logit and create two separate utility runs: one for males and one for females.  Our Logit program lets you choose which respondents to include in the estimation via filters.

However, if you are using HB utilities, you don't have to re-run HB separately for males vs. females.  You can just choose in the market simulator to filter the market simulation scenario results by males or female.  That's another plus for using HB estimation for building market simulators!
I'm not sure if I understand you correctly. My wish is to say that a person who chooses level A over level B is most likely to be in segment 1. With segment I meant the 2 groups I made with a Latent Class analysis. I do not see where in the market simulator I can tell the program to split up the results among these 2 classes. I hope to hear from you soon!
You can apply the same Bayesian logic that I earlier gave you regarding a respondent picking Concept A or Concept B.  Just now, the only thing different about the concepts is that one concept is defined as having only level A of a given attribute and the other concept is defined as only having level B.  You hold all other attributes constant (at zero utility).  So, the utility for Concept A is the utility for level A and the utility for Concept B is the utility for level B.

Regarding getting segment membership from latent class analysis into the market simulator as a segmentation variable, this question is probably best answered by our technical support team.  But, my quick guidance is (if using Lighthouse Studio) to open the Data Management area and to add a new variable to the data table, where the new variable is the assigned (most likely) segment membership for each respondent.  Then, when you use the market simulator within Lighthouse Studio, you can create "Segments" and use the Segment builder to refer to that new variable that you have merged into the data table.  If these instructions don't work for your situation, please contact our technical support team at support@sawtoothsoftware.com or call them at +1 801 477 4700.