Test for Additional Information and Variable Selection in Quantification Method Type II

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  • Kan Tamio
    Faculty of Science and Engineering, Chuo University, Esumi Co., Ltd., Tokyo

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  • 数量化２類の追加情報の検定と変数選択
  • スウリョウカ 2ルイ ノ ツイカ ジョウホウ ノ ケンテイ ト ヘンスウ センタク

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Abstract

Quantification methods which consist of types 1, 2, 3, 4 are basic for statistical analysis of qualitative data such as questionnaires data, etc. Upon quantifying qualitative data by introducing dummy variables of 0 and 1, Type 1 and 2 may be regarded as regression analysis and discriminant analysis respectively. In this paper we propose a test statistic for additional information in Type 2, based on sample scores. It is shown that the test statistic is essentially the same as the ones for additional information in regression analysis and discriminant analysis. Therefore, it may be noted that the validity of F-approximation for the test statistic in Type 2 can be examined by checking a normal approximation of residuals in regression analysis and by this, we will numerically validate the fit of test statistic's F approximation. Also, in Type 2, we will reflect sequential variable selection method using additional information test and variable selection methods based on model selection criteria, which have been established in regression analysis, and try to numerically validate these.

Journal

  • Ouyou toukeigaku

    Ouyou toukeigaku 38 (1), 1-18, 2009

    Japanese Society of Applied Statistics

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