| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 96 === We often use the attitude amount form to understand interviewees’ opinion in questionnaire survey, and use ordinal scale to measure the observations. Under the continuous latent factors assumption, we often use factor analysis to extract common latent factors from observable variables. If the original data is omitted too much, there are some mechanisms behind, for example, missing at random, the missing data, so that the person with a certain characteristic apt to become omitting value, the estimation based on the observed data will twisted the dependence between variables. Therefore, the factors obtained from that analysis may completely different from the real factor. The researcher had shown that high proportion of missing may cause significant bias in certain statistical analysis.
In this study, we extend Wang’s (2007) result and relies mainly on the data of attitude about high school students’ psychological health from the education tracks database. We focus on ordinal data and investigate the data having various missing proportions to find out the critical proportion of missing that may cause significant bias on the estimation of covariance matrix. We also investigate susceptibility of factor analysis on the proportion of missing data and find out the difference on the number of common factors and the estimation of factor loading. According to the original missing mechanism, we construct datasets of several missing proportions, say 6%~40%. Under the assumption of normality, we find that starting from 16% missing proportion, the estimation of covariance matrix will be biased significantly. Base on the original missing mechanism, we consider the complete part as baseline to find out the effects on the ways of handling the missing data in factor analysis. We use polychoric correlation to run the factor analysis. The result shows that the list-wise deletion method works fine in low missing proportion (< 34%). MCMC method performs good in most of the missing proportions. The available case method is the worse among 4 methods.
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