Detection of Abnormal Items using Likelihood Ratio Test when Mixed Categorical and Continuous Variables are Observed

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  • 離散変量と連続変量が混在する場合の尤度比検定法による異常検出
  • リサン ヘンリョウ ト レンゾク ヘンリョウ ガ コンザイ スル バアイ ノ ユウ ドヒ ケンテイホウ ニ ヨル イジョウ ケンシュツ

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Detection of abnormal items is discussed when both continuous and categorical variables are observed. Assuming the location model where continuous variables are multivariate normally distributed with common covariance matrix when categorical variables are observed, the problem of detecting abnormal items is formulated as a hypothesis testing problem. When all parameter values of the distribution for the normal group of items are known, it is shown that the distribution of the likelihood ratio test statistic is a mixture of shifted x^2 distributions. Based on this result, a detection method is constructed as a hypothesis testing procedure with exact significance level. For the case when only one dichotomous variable is included, some basic properties are shown on the conditional rejection probabilities for normal items. Further, a comparison is made with some other detection methods such as the modified Mahalanobis distance method which uses the Mahalanobis distance based on all variables. From the numerical evaluation of the power functions of the methods, it is observed that the proposed method performs better than the other ones for a wide range of parameter values.

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