摘要
實務上，連續型資料與滿意度資料可能以順序尺度方式取得，而傳統上這些有序資料(ordinal)常被視為等距(interval)資料進行統計分析，有其不適當之處。因此，過去也有許多文獻探討有序資料的分析方法。而探討有序資料的因素分析方法，可分成二類：(1)先將有序資料量化後，再將之視為連續型資料進行傳統因素分析；(2)結合有序資料的因素分析方法進行因素分析。為了了解各方法於因素分析結果的差異，因此本文試圖比較分析不同的有序資料量化法：(1)等距法、(2)多變量有序量化法、與(3)多變量類別量化法三種方法結合傳統因素分析的結果，與兩種直接進行有序資料的因素分析方法：(1)最小化殘差法、與(2)完全資訊最大概似法之因素分析結果共五種因素分析方法進行比較分析。 透過模擬分析與個案的實證分析對本文所提的五種方法之因素分析結果進行比較分析。模擬分析旨在了解連續型資料或滿意度資料以各種不同的順序資料尺度取得時，採用這五種因素分析方法，何者的因素分析結果與原來的連續型資料之分析結果最接近，以反應不同順序尺度資料蒐集資料方式。模擬分析的步驟：(1)首先模擬兩組相關係數不同的連續型資料做為原始資料，此原始資料為後續有序資料的轉換來源因素，也是因素分析結果之比較基準；(2)接著將原始資料利用不同的方式轉換為有序資料後；(3)比較分析有序資料使用這五種方法進行因素分析結果與原始連續型資料進行因素分析結果之接近度。在因素分析結果之比較，以各方法之因素分析結果的解釋變異比例、因素負荷值及殘差值做為比較基礎進行比較分析。為了反應這些方法在實務應用的成效，另以兩個實際調查資料個案進行因素分析比較。 模擬結果發現最小化殘差法在各種模擬情境下皆可得到較佳的因素分析結果；而若欲將有序資料先行量化再進行因素分析，則以多變量類別量化法結合最大概似法因素分析結果較接近原始資料的因素分析結果。實證結果發現完全資訊最大概似法與最小化殘差法解釋變異比例較高。整體而言，模擬分析與實證分析結果皆顯示有序資料不適用以等距量化的因素分析；而其他因素分析方法在模擬分析與實證分析上各有其優劣。基本上，兩種直接進行有序資料的因素分析方法之解釋變異比例相對較高，其中以最小化殘差法的因素分析結果最好，如果只討論有序資料量化的方法，以多變量類別量化法的因素分析結果較好。此外，有序資料經量化後得到的連續型資料，可結合其他多變量方法進行多變量分析。
並列摘要
In practical survey, continuous data might be collected by ordinal scale, while satisfaction level might be ordinal data measured with Likert scale. The ordinal data usually treated as interval data for statistical analysis that have some inadequacies. Some quantification methods and data analyses have been proposed to deal with ordinal data in previous studies. The factor analysis methods with ordinal data can be simply classified into two ways: (1) conducting quantification for the ordinal data first and then using traditional factor analysis with the quantified ordinal data, (2) directly using factor analysis of ordinal data for the ordinal data. In order to see the performance of the various factor analysis methods on ordinal data, five methods of factor analysis are proposed for comparison in this thesis. In which, three of them employ traditional factor analysis with quantified ordinal data by three different quantification methods, namely, equal interval method, multivariate quantification method of ordinal data, and multivariate quantification method of categorical data. The other two directly use factor analysis of ordinal data for the ordinal data which includes minimize residual method and full information maximum likelihood method. A simulation approach is used to see the performance of the five factor analysis with various ordinal data as the continuous data or satisfaction level were collected by ordinal scale. An empirical analysis is used to see the practical performance of the five factor analysis methods based on two survey data sets. The simulation steps include: (1) first, two data sets of three continuous variables with different correlation coefficients among variables are generated as original data sets, (2) transfer the continuous variables of the original data sets into ordinal data by different ways to obtain different ordinal data sets, which represent various data collecting ways of ordinal scale, (3) compare the results of the five factor analysis methods with simulated ordinal data sets to the results of the factor analysis with the original continuous data set to see the performance of the five factor analysis methods based upon proportion of variation explained, factor loadings, and residuals. Simulation results show that the minimal residual method performs better than others in any case; while for the methods of traditional factor analysis with quantified ordinal data, the multivariate quantification method of categorical data performs better than others because its results close to that of the original continuous data set. The empirical study results show that full information maximum likelihood and minimum residual method have larger proportion of variation explained. In summary, the equal interval quantification method is improper to quantify ordinal data for factor analysis; while the other four factor analysis methods have their advantage and disadvantage to be used with ordinal data. The ordinal data analysis directly using factor analysis of ordinal data has relative higher proportion of variation explained; while the ordinal data analysis using traditional factor analysis with quantified ordinal data has its advantage, because the quantified ordinal data could be analyzed with any multivariate analysis methods.