Constructing Common Factors from Continuous and Categorical Data
回顾了通过Procrustes问题求解主成分的方法，并将其扩展到分类数据，发现无需量化即可直接从分类数据精确估计因子空间，但可能需要更多因子来补偿信息损失。
The method of principal components is widely used to estimate common factors in large panels of continuous data. This article first reviews alternative methods that obtain the common factors by solving a Procrustes problem. While these matrix decomposition methods do not specify the probabilistic structure of the data and hence do not permit statistical evaluations of the estimates, they can be extended to analyze categorical data. This involves the additional step of quantifying the ordinal and nominal variables. The article then reviews and explores the numerical properties of these methods. An interesting finding is that the factor space can be quite precisely estimated directly from categorical data without quantification. This may require using a larger number of estimated factors to compensate for the information loss in categorical variables. Separate treatment of categorical and continuous variables may not be necessary if structural interpretation of the factors is not required, such as in forecasting exercises.