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Interpreting Relative Chi-Square LC Segmentation Results

Dear Sawtooth Software Team,
I am doing a LC segmentation analysis. Afterwards I want to describe these segments by their demographics.

My results of the relative chi-square is:
(For 2, 3, 4, and 5 groups as well as 10,10, 7, 1 replications)
All other results  of e.g. PctCert and AIC have same behaviour as described in your papers. In the numeric example of your papers the realtive chi-square increases. In my findings, it is decreasing.
So how can I interpret this?
asked Feb 9, 2018 by Liz

1 Answer

0 votes
The Relative Chi-Square is a measure of fit of a latent class solution that attempts to adjust for the number of groups you are using (the number of parameters you are estimating) so you can directly compare different solutions having different numbers of groups.  Higher values of relative Chi-Square would indicate a latent class solution that is better justified by the data than another solution.

Other fit statistics such as CAIC or BIC tend to be more trusted by researchers (and lower is better on these measures), and the BIC and Relative Chi-Square don't always agree.

So, if you are wanting to trust the Relative Chi-Square and if you find that the relative Chi-Square drops as you increase the number of groups from 1 to a larger number (note that you haven't yet run your latent class estimation asking for just 1 group so you can compare the results to 2 groups), then this suggests that the data don't justify segmenting the market along the dimensions of the parameters you included in the model.  In other words, there isn't a stable enough partitioning of the data that leads to a statistically significant  increase in likelihood fit under the assumptions of the latent class multinomial logistical regression model.
answered Feb 9, 2018 by Bryan Orme Platinum Sawtooth Software, Inc. (174,440 points)