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What is the best way to deal with missing data in latent class models?

For example, Latent GOLD can estimate models with missing data (LG technical manual page 51). Simply put, the likelihood contribution is based on the observed indicators only, which means that for an observation with missing data, the likelihood function is maximized with only the remaining data available.

OK-that's fine, but does this mean for the parameters? Am I going to get better classifications because the parameters were estimated with as much information as possible (i.e. if the observation say only has a missing value), or am I going to get worse classifications because of the missing value?

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Your model will be better for including the incomplete data. It will increase your sample size, which is good. But, even better, is that it will mean that your model is assuming the data is Missing At Random (MAR), which is a much safer assumption than Missing Completely At Random (MCAR), which is the implicit assumption you make if excluding incomplete data.

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