本研究的目的在於應用行列相關模式（the row and column association model by Goodman, 1986, 1991）與潛在分類分析的方法（the latent class analysis, Hagennars,1990），評量學生在多重計分的題目（polytomous items）表現。潛在分類分析與Master’s（1982）部分計分模式（Partial credit model）的聯結也在本文中描述。資料由謝如山（民89）的實證研究來檢視學生在括號概念的使用層次。有關括號概念的題組將被用來分析。使用潛在分類分析有三項優點。第一是學生的學習認知階層可被顯示，如在結合律的題目中，學生在第一層次誤解題意，第二層次只能選出與題意相符的選項，再一層次選擇有括號的題項，最高層次可辨識結合律。不同於項目反應論（Lord, 1980），潛在分類分析假設潛在變項為間斷的，可判定不同層次能力的特徵為何。第二項優點是多重空間的考慮是可行的。如潛在分類分析中可假設兩個以上的潛在變項。第三個優點是無母數估計的分配假設。這在本資料中的假設是相當重要的。因為有部份題項的分配為偏態。研究結果可為認知心理學的統計方法做出些許具體的貢獻。

The aim of the study is to assess children’s performance in the polytomous items via the row and column (RC(M)) association model (Goodman, 1986, 19991) with the latent class analysis approach (Hagenaars, 1990). The connection between latent class analysis and Master’s（1982）partial credit model is described. The empirical example is given by Hsieh’s (1999) study to examine whether children recognize the concept of parentheses. The sets of the parentheses-uses items are discussed. Three advantages were addressed by using the latent class analysis. First is that children’s learning hierarchy can be described such that children in the first latent class misunderstood the problem. The next level is to choose the option which corresponds to the meaning of the questions. And the next, students choose the options that are parentheses related. The highest level is that children are likely to recognize for example, the associative property. Different from the item response theory（Lord,1980）, the latent variable in the latent class analysis is assumed to be categorical. The features of the different levels in the latent variable can be discriminated. Second, the multidimensional approach is applicable. For example, the number of the latent variables can be more than one. The third is that a non-parametric estimation method is assumed in the latent class analysis. This hypothesis is vital because the distributions in some items are skewed. The results made some contribution to the cognitive psychology field.