Latent Class Analysis with Arbitrary-Distribution Responses

The latent class model has been proposed as a powerful tool in understanding human behavior for various fields such as social, psychological, behavioral, and biological sciences. However, one important limitation of the latent class model is that it is primarily applied to data with binary responses or categorical responses, making it fail to model real-world data with continuous or negative responses. In many applications, ignoring the weights throws out a lot of potentially valuable information contained in the weights. To address this limitation, we propose a novel generative model, the arbitrary-distribution latent class model (adLCM). Our model enables the generation of data's response matrix from an arbitrary distribution with a latent class structure. When compared to the latent class model, our adLCM is both more realistic and general. To our knowledge, our adLCM is the first model for latent class analysis with any real-valued responses, including continuous, negative, and signed values, thereby extending the classical latent class model beyond its traditional limitation to binary or categorical outcomes. We investigate the identifiability of the model and propose an efficient algorithm for estimating the latent classes and other model parameters. We show that the proposed algorithm enjoys consistent estimation. The performance of our algorithm is evaluated using both computer-generated data and real-world personality test data.