Statistical Analysis of Questionnaire Data via Cumulative Logistic Regression Model

Based on a real questionnaire data, we build a cumulative logistic model to deal with the mutual relationship of the variables in the data. Aiming at the problem of too much designed variables, we apply statistical method to select those important ones and delete the useless ones without losing too much information. We also provide the analysis results for the data by the software SAS, and give some suggestions for the design of questionnaire. Our analysis also shows that the model built in paper can fit the questionnaire data very well, and it has higher preciseness rate of forecasting. Introduction With the incessant development of statistics, the method of logistic regression analysis attracts more and more attention [1,2]. However, as an important component part of logistic regression, the cumulative logistic regression is fairly less concerned in factual researches [3,4]. In 2013, to achieve the optimization configuration of human resource, a questionnaire about the service conduct situation of higher leaders in some direct-units of Heilongjiang province was carried out. Because too much problems and trivial content are designed in the questionnaire, it will bring bigger error if the usual method is used to analyze the data [5]. In this paper, the cumulative logistic regression is employed to integrate and analyze the data, which reduces some unnecessary variables. Then we use the model we built to perform some statistical forecasting, and the results are satisfactory. There are 7 direct-units concerned in the survey, and 20675 questionnaires were sent out and collected. Two parts of content are designed: a. personal information of attendee; b. detail items on the service conduct situation, where 28 problems are included. Attendees can answer each problems based the factual situations of testing object (Rank: A, B, C, D). For the convenience of studying, we use variables xi (i=1,...,28) to denote the scores to the 28 questions, with values 1, 2, 3 and 4, where variables xi (i=1,...,27) are the specific evaluations on the service conduct to a testing object, and variable x28 is an integrative evaluation to the testing object.