鑑於台灣高等教育整合資料庫資料的有限揭露，除了利用科系進行多層次分析外，本研究介紹另一種分析模式：交叉分類模型，示範解決部分資料違反獨立性假設的情況。資料來自於2005年所抽樣調查具有完整研究變項的46,961位大一新生，本研究利用揭露的112個科系與10種學校類型，進行大一新生運用數學來解決實際問題的能力的巢套與交叉分類邏吉斯迴歸的分析比較。在科系、學生兩層結構的巢套模式下，就「男生」、「對運用數學來解決問題的興趣愈高」及「高一、二曾補過數學」等研究變項之分析結果發現，可提升其運用數學來解決實際問題的能力。而在學校類型與科系的交叉分類模式，高一、二補過數學則變為不顯著。在隨機效果方面，興趣對能力的影響存在科系間差異，學校類型間的差異則不顯著。最後提出交叉分類邏吉斯迴歸軟體操作與應注意事項，以及本研究的結論、建議與限制。

Because of the restricted release of departmental and university codes in the Center for Higher Education Research database, a full, hierarchical departmental structure is not nested within the universities. In this study, we used a different hierarchical, linear, cross-classified random effects model (i.e., HCM) to demonstrate this method for determining the effect of the mathematical problem-solving capability of freshmen on the restricted data. We used department type as an upper-group-level row and university type as a group-level column to develop a 2-level model (i.e., HLM) for comparing the results of the logistic regressions of freshmen nested within the departments. Although some results differed between the HLM and HCM models, the 2 models similarly showed that male freshmen and students interested in higher mathematical problem solving exhibited more ability and that the contextual variable of departmentally aggregated mathematical problem-solving interest showed a negative moderating effect on the positive relationship between student interest and student ability. Finally, this paper describes the software operations and precautions, with a discussion, the study limitations, and recommendations being presented in the conclusion.