Huge standard errors in latent class analysis using low efficient design

As a pilot, we created a small 3^6 design with 6 choice sets. All attribute levels had a clear ordinal rank order. Due to several reasons we just used one questionnaire version for paper & pencil-interviews. Each level appeared 6 times in the design and 2 times with each other attribute level. We were aware of the warning in the Sawtooth Test Design Report that indicated low design efficiency. But we just wanted to get an idea of the attribute/level importance and the expected standard errors with the simulated data were low. The response rate, however, was great and unexpectedly high. Then we used Aggregate Logit within Sawtooth Analysis Manager and we got what we were looking for. However, with almost 200 respondents we wanted to take a deeper look on the data. We think with Aggregate logit we reached the limit with our small design and as expected with latent class analysis we ran into very huge standard errors. (Using linear coded attribute levels works just fine.)

Even when we didn't want to go there, is there any possibility to get more reliable standard errors in latent class analysis with our design?

Thank you very much!
Andrew

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