Multivariate Analysis of Multiple Response Data
针对调查中常见的多项选择题数据，提出多元二项式probit模型，通过潜变量方法探索响应间关系，并开发高效估计算法，适用于大量选项的市场数据。
Multiple response questions, also known as a pick any/J format, are frequently encountered in the analysis of survey data. The relationship among the responses is difficult to explore when the number of response options, J, is large. The authors propose a multivariate binomial probit model for analyzing multiple response data and use standard multivariate analysis techniques to conduct exploratory analysis on the latent multivariate normal distribution. A challenge of estimating the probit model is addressing identifying restrictions that lead to the covariance matrix specified with unit-diagonal elements (i.e., a correlation matrix). The authors propose a general approach to handling identifying restrictions and develop specific algorithms for the multivariate binomial probit model. The estimation algorithm is efficient and can easily accommodate many response options that are frequently encountered in the analysis of marketing data. The authors illustrate multivariate analysis of multiple response data in three applications.