Opinion of users expressed in the form of observed ratings can influence an individual's view of an item. However, the true quality of an item is often obfuscated by user biases, and it is not obvious from the observed ratings the importance users place on different aspects of an item. In this paper, we propose a probabilistic modeling of the observed aspect ratings to infer (i) each user's aspect bias and (ii) latent intrinsic quality of an item. We model multi-aspect ratings as ordered discrete data and encode the dependency between different aspects by using a latent Gaussian structure. We handle the Gaussian-Categorical non-conjugacy using a stick-breaking formulation coupled with recently developed Polya-Gamma auxiliary variable augmentation for a simple, fully Bayesian inference. On two real world datasets, we demonstrate the predictive ability of our model over state-of-the art baselines and its effectiveness in learning explainable user biases to provide insights towards a more reliable product quality estimation.
@cite_18: Questions that use a discrete ratings scale are commonplace in survey research. Examples in marketing include customer satisfaction measurement and purchase intention. Survey research practitioners have long commented that respondents vary in their usage of the scale: Common patterns include using only the middle of the scale or using the upper or lower end. These differences in scale usage can impart biases to correlation and regression analyses. To capture scale usage differences, we developed a new model with individual scale and location effects and a discrete outcome variable. We model the joint distribution of all ratings scale responses rather than specific univariate conditional distributions as in the ordinal probit model. We apply our model to a customer satisfaction survey and show that the correlation inferences are much different once proper adjustments are made for the discreteness of the data and scale usage. We also show that our adjusted or latent ratings scale is more closely related to ...
@cite_14: This article presents a Bayesian latent variable model used to analyze ordinal response survey data by taking into account the characteristics of respondents. The ordinal response data are viewed as multivariate responses arising from continuous latent variables with known cut-points. Each respondent is characterized by two parameters that have a Dirichlet process as their joint prior distribution. The proposed mechanism adjusts for classes of personalities. The model is applied to student survey data in course evaluations. Goodness-of-fit (GoF) procedures are developed for assessing the validity of the model. The proposed GoF procedures are simple, intuitive, and do not seem to be a part of current Bayesian practice.
@cite_20: Abstract A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are developed using the idea of data augmentation. The general approach can be summarized as follows. The probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data. Values of the latent data can be simulated from suitable truncated normal distributions. If the latent data are known, then the posterior distribution of the parameters can be computed using standard results for normal linear models. Draws from this posterior are used to sample new latent data, and t...
In contrast, most statistical approaches handle ordinal data using an ordinal probit model @cite_20 @cite_18 @cite_14 . Although they allow a Bayesian inference but it necessitates using truncated Gaussian distributions and forced ordering of cut-off points. This leads to complicated and even sub-optimal inference.