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Difference between Segment Sizes (%) and Total Number of Respondents in Segment

Hi,

I have a question regarding my segments sizes calculated with Latent Class.

I have n=393 respondents and if I choose the 3-group solution the Latent Class analysis displays the following segment sizes:
 
Group 1: 15.3% (15.3% * 393 = 60 respondents)
Group 2:  57.2% (57.2% * 393 = 224 respondents)
Group 3: 27.5% (27.5% * 393 = 108 respondents)

However, when I export the data to SPPS and calculate the frequencies (or even when counting it myself)  I get the following:

Group 1: 13.5 % (53 respondents)
Group 2: 61.3 % (241 respondents
Group 3: 25.2 % (99 respondents)

Is that maybe related to 'average maximum membership probability' = 0.83640?  

Or is there any other possible explanation for this difference?

Thanks for your support!
Stefanie
asked Dec 13, 2019 by Stefanie

1 Answer

0 votes
 
Best answer
Hi Stefanie,

You are correct. Both the group segment sizes and the membership probability numbers are based on each individual's probability of belonging to a group. When we assign respondents to a group, we essentially toss out the uncertainty and assign them with 100% weight to the group to which they are most likely to belong.

As a simple example, suppose we had two respondents and computed their likelihood to belong to two groups. We might end up with individual membership probabilities like this:

          Group 1  Group 2  Assigned Group
R1    0.999          0.001     0.999 > 0.001, so they are assigned to Group 1
R2    0.499          0.501     0.499 < 0.501, so they are assigned to Group 2

Average membership probability:
Group 1 (0.999+0.499)/2 = 74.9%
Group 2 (0.001+0.501)/2 = 25.1%

Average Maximum Membership Probability:
(0.999 + 0.501) / 2 = 75.0%

Assigned Group Membership:
Group 1 - 50% (1 assigned to Group 1 out of  2 respondents)
Group 2 - 50% (1 assigned to Group 2 out of  2 respondents)

--Aaron
answered Dec 13, 2019 by Aaron Hill Gold Sawtooth Software, Inc. (10,995 points)
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