A factor analysis method for contingency table data with unlimited multiple choice questions

Hideki Toyoda, Reina Haiden*, Saori Kubo, Kazuya Ikehara, Yurie Isobe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The purpose of this study is to propose a method of factor analysis for analyzing contingency tables developed from the data of unlimited multiple-choice questions. This method assumes that the element of each cell of the contingency table has a binominal distribution and a factor analysis model is applied to the logit of the selection probability. Scree plot and WAIC are used to decide the number of factors, and the standardized residual, the standardized difference between the sample, and the proportion ratio, is used to select items. The proposed method was applied to real product impression research data on advertised chips and energy drinks. Since the results of the analysis showed that this method could be used in conjunction with conventional factor analysis model, and extracted factors were fully interpretable, and suggests the usefulness of the proposed method in the study of psychology using unlimited multiple-choice questions.

Original languageEnglish
Pages (from-to)535-544
Number of pages10
JournalShinrigaku Kenkyu
Issue number6
Publication statusPublished - 2015


  • Binomial distribution
  • Contingency table
  • Factor analysis
  • Unlimited multiple choice method

ASJC Scopus subject areas

  • Psychology(all)


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