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I want to see how many profiles (latent classes) can be differentiated based on respondents’ patterns of responses to four binary variables (accepting or rejecting four different immigration policies).

In order to explore how many profiles are there, I ran several latent class analyses, asking for different number of classes. I used the poLCA package in R. Whenever I asked for more than 3 classes, there was a warning that residual degrees of freedom are negative. What does it mean?

Can I still use the model with negative df if the classes intuitively make sense? Is it possible to compare the model with negative df to other models to see which one better fits data?

Since I do not have any experience with the LCA, your help would be very much appreciated.

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According to the documentation by Lanza et al http://www.methodology.psu.edu/ra/lca/model-faq/: A model will have negative degrees of freedom when the model is trying to estimate more parameters than it is possible to estimate. If you have negative degrees of freedom, reduce the number of latent classes or latent statuses, or add parameter restrictions to reduce the number of parameters being estimated. I do not think you can make intuitive sense of negative degrees of freedom in this case

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