# 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?

Stefanie

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 Gold (12,245 points)