無母數多層次潛在類別分析在分類方法上的應用：以TEDS-M小學數學教師學習機會為例

Application of Nonparametric Multilevel Latent Class Analysis to Opportunity to Learn (OTL) Classification of Future Mathematics Teachers in the TEDS-M Dataset

隨著機器學習近年來的快速發展，分類方法不斷地推陳出新，不論是估計方法的微調，或是模式的改變，非監督式學習所涵蓋的種類浩繁，從研究者熟知多變量分析中的主成分分析，至集群分析（cluster analysis）及其變化形式，皆為現今被推廣使用的分類方法，並已廣泛應用於資料採礦、文字探勘等領域。儘管機器學習以及資料採礦在統計分析上被廣泛使用，在教育以及心理分析方法上之應用卻遠不及於行銷分析、搜尋引擎開發等領域，歸納其主要原因有二：一為對於測驗誤差的考量，二為對於教育現場中巢式結構資料的顧慮。有鑑於分類方法需考量教育資料的獨特性，本文擬介紹Vermunt（2003）所提出的無母數多層次潛在類別模式，並於文末以TEDS-M數據庫中小學數學教師學習機會，163個師資培育單位及10,721位小學師資培育生為例，做一應用案例的呈現，以供對分類方法有興趣的研究者參考。

Classification methods have developed considerably in recent years, with improvements in both estimation methods and model selection. Researchers can now make use of principal component analysis among other alternatives, and have applied them to tasks such as data mining and text mining. However, these methods’ applications in the fields of education and psychology have generally been limited. The reasons for this may include two features of educational datasets: (1) measurement error of the latent construct, (2) nested-data structures. Accordingly, the purpose of the present research is to test the applicability of nonparametric multilevel latent class analysis (NP-MLCA) (Vermunt, 2003) in the context of such data, and to review the latest model-specification and model-selection procedures. Specifically, NP-MLCA is applied to the TEDS-M dataset’s opportunity to learn (OTL) questions, which were administered to 10,721 future mathematics teachers enrolled in 163 teacher-preparation programs in 17 countries.