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The Graded of Membership (GoM) model is a powerful tool for inferring latentclasses in categorical data, which enables subjects to belong to multiplelatent classes. However, its application is limited to categorical data withnonnegative integer responses, making it inappropriate for datasets withcontinuous or negative responses. To address this limitation, this paperproposes a novel model named the Weighted Grade of Membership (WGoM) model.Compared with GoM, our WGoM relaxes GoM's distribution constraint on thegeneration of a response matrix and it is more general than GoM. We thenpropose an algorithm to estimate the latent mixed memberships and the otherWGoM parameters. We derive the error bounds of the estimated parameters andshow that the algorithm is statistically consistent. The algorithmicperformance is validated in both synthetic and real-world datasets. The resultsdemonstrate that our algorithm is accurate and efficient, indicating its highpotential for practical applications. This paper makes a valuable contributionto the literature by introducing a novel model that extends the applicabilityof the GoM model and provides a more flexible framework for analyzingcategorical data with weighted responses.

WGoM: A novel model for categorical data with weighted responses