Segment Sizes and Discrete Segment Assignment in FIMIX

[Rick M]

I ran FIMIX for a sample of 257. The segment sizes and distributions of discrete segment assignments do not seem to match. Here are the results.

Segment sizes Segment 1- 44.9%, Segment 2 - 32.5%, Segment 3 22.5%

Distribution of Discrete Segment Assignments Segment 1 - 45.91% (n = 118), Segment 2 - 35.02% (n = 90), Segment 3 - 19.07% (n = 49)

The fit statistics indicate that three segments minimize most of the criteria and maximize entropy.

My concern is with the size of segment 3 and the difference in the reported segment sizes and the distribution of discrete segment assignments. Since the minimum sample size for analysis is 50 am I close with 49 in that segment? The path coefficients for the three segments are very different and contribute to understanding of the potential underlying heterogeneity.

Thanks for the help that anyone can provide in resolving the difference and the analysis of three segments.

Rick

[jmbecker]

The segment sizes are based on the FIMIX probabilities of segment membership. The finite mixture approach is a probabilistic approach, the optimal FIMIX solution only provides probabilities of segment membership. The corresponding segment sizes are an aggregation of these probabilities.
In contrast, the discrete segment membership is not an original finite mixture result, but just an additional information that is often provided. It assigns the observations to the segment where it has the highest probability. This assignment must not pertain the FIMIX optimality conditions, but is ideally not far away from it. The better the EN (i.e., the sharper the assignment – the higher the probabilities) the better is also the match between FIMIX solution and discrete assignment.

N=49 is certainly not optimal in terms of number of observations, but you probably have to life with it, when the three segment solution is not only optimal in FIMIX, but also theoretically plausible.