Ridge-type regularization method for questionnaire data analysis

In questionnaire studies for evaluating objects such as manufacturing products, evaluators are required to respond to several evaluation items for the objects. When the number of objects is large, a part of the objects is often assigned randomly to each evaluator, and the response becomes a matrix with missing components. To handle this kind of data, we consider a model by using a dummy matrix representing the existence of the missing components, which can be interpreted as an extension of the GMANOVA model. In addition, to cope with the case where the numbers of the object and evaluation items are large, we consider a ridge-type estimator peculiar to our model to avoid instability in estimation. Moreover, we derive a C p criterion in order to select the tuning parameters included in our estimator. Finally, we check the validity of the proposed method through simulation studies and real data analysis.