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本研究之目的旨在探討成就測驗中，學生的不完整作答反應是否能利用插補法，對不完整作答反應資料進行彌補。研究者藉由試題參數與受試者能力參數的分析討論，期望能獲得支持插補技術應用於成就測驗的結論。研究欲探討的問題有三：（一）利用統計插補法所估算之替代值與實際作答反應之間是否有差異存在；（二）受試者之部分答題反應組型在經過插補後，與完全作答反應組型之分析結果是否有差異存在；（三）能否將統計插補技術應用於成就測驗模式中。 本研究程序包含兩部分，一為模擬資料（N=1000，3000，5000，l0000；缺失比例為5%，10%，15%，30%，50%）的分析，模擬研究主要作為實證研究結果的驗證與推論；另一個則為實證資料的分析與討論。針對不完整作答反應，基於IRT的強假設前提，以及成就測驗作答反應的資料型態，研究者選擇熱卡插補法(HOt Deck imputation method)的統計插補技術，分別對於實證資料與模擬資料中之各類樣本數，與不同缺失比率下的作答反應作插補。另又以EM插補法作對照分析。 根據研究結果與討論，提出以下幾點歸納結論：（一）當缺失比例不大時，能符合原本的資料分佈假設，但隨著缺失比例愈高，高至30%以上時，已漸不符合原本假設；（二）當缺失比例愈高時，各項參數之估計標準差值幾乎是最大的；若忽略未作答反應之受試者的表現時，其分析所得的參數估計值亦並未是最佳的，反而是將所有受試者的作答反應進行插補估計後，所得的參數估計標準差值才是最小、最佳的；（三）本研究中，主要以熱卡法為插補方法，而EM插補法並不符合本研究資料之性質，故若採用此法進行插補，則所得的估計標準差會是最大的；（四）經過模擬研究與實證資料的分析後，證明熱卡法所推估的未作答反應，與直接刪除未作答反應或不處理未作答反應的確有差異存在，且經過插補所產生的替代值，對於受試者的能力表現能提供更穩定有效的解釋力。 關鍵詞：熱卡插補法、不完整作答反應、成就測驗 / This purpose of this study is to infer the feasibility if examinees' non response could be made up, by using imputation method in non response or missing value of achievement test. The research design contains two procedures: one is simulation research (setting sample sizes are 1000, 3000, 5000, and 10000; percents of non response are 5%, 10%, 15%, 30%, and 50%), and the other is pragmatic research. Hot deck imputation method is the main concern method in this research. To test if this method fits to achievement test, EM method is used for comparison with the Hot deck imputation method. The results are as follows: 1. The distribution of below 30% percent non response data after imputated is the same as the original data, but following the higher percents of non response, the distribution is not match what we expected. 2. Applying Hot Deck imputation method to the achievement test with different sample size and different percents of non response, the researcher found that following the higher percents of non response in any sample size, the higher standard deviation happened. Besides, ignoring or deleting these non responses is not a good way to deal with this test response pattern. Imputating an appropriate answer for the non response by Hot Deck imputation method, we could get the least standard deviation of the test and ability parameters estimation, and get largest test information for examinees. 3. We found the Hot Deck imputation method is suitable for the data pattern of achievement test than EM method. There are different outcomes between Hot deck imputation method and EM method. Hot Deck imputation method also has accuracy parameter estimation. 4. Based on above discussions, this study suggested that Hot deck imputation method could cope with non response in achievement test pretty well. Key Words: Hot Deck imputation method, Non response, Achievement test

有賴電腦的輔助，企業或組織內部所存放的資料量愈來愈多，加速資料量擴大的速度。但是大量的資料帶來的未必是大量的知識，即使擁有功能強大的資料庫系統，倘若不對資料作有意義的分析與推論，再大的資料庫也只是存放資料的空間。過去企業或組織只把資料庫當作查詢系統，並不知道可以藉由資料庫獲取有價值的資訊，而其中資料庫的內容完整與否更是重要。由於企業所擁有的資料庫未必健全，雖然擁有龐大資料庫，但是其中資訊未必足夠。我們認為利用資料庫加值方法：插補方法、抽樣方法、模型評估等步驟，以達到擴充資訊的目的，應該可以在不改變原始資料結構之下增加資料庫訊息。 本研究主要在比較不同階段的資料經過加值動作後，是否還能與原始資料結構一致。研究架構大致分成三個主要流程，包括迴歸模型、羅吉斯迴歸模型與決策樹C5.0。經過不同階段的資料加值後，我們所獲得的結論為在迴歸模型為主要流程之下，利用迴歸為主的插補方法可以使加值後的資料庫較貼近原始資料，若想進一步採用抽樣方法縮減資料量，系統抽樣所獲得的結果會比利用簡單隨機抽樣來的好。而在決策樹C5.0的主要流程下，以類神經演算法作為插補的主要方法，在提增資訊量的同時，也使插補後的資料更接近原始資料。關於羅吉斯迴歸模型，由於間斷型變數的類別比例差異過大，致使此流程無法達到有效結論。 經由實證分析可以瞭解不同的配模方式，表現較佳的資料庫加值技術也不盡相同，但是與未插補的資料庫相比較，利用資料庫加值技術的確可以增加資訊量，使加值後的虛擬資料庫更貼近原始資料結構。 / With the fast pace of advancement in computer technology, computers have the capacity to store huge amount of data. The abundance of the data, without its proper treatment, does not necessary mean having valuable information on hand. As such, a large database system can merely serve as ways of accessing and storing. Keeping this in mind, we would like to focus on the integrity of the database. We adapt the methods where the missing values are imputed and added while leaving the data structure unmodified. The interest of this paper is to find out when the data are post value added using three different imputation methods, namely regression analysis, logistic regression analysis and C5.0 decision tree, which of the methods could provide the most consistent and resemblance value-added database to the original one. The results this paper has obtained are as the followings. The regression method, after imputation of the added value, produced the closer database structure to the original one. And in the case of having large amount of data where the smaller size of data is desired, then the systematic sampling provides a better outcome than the simple random sampling. The C5.0 decision tree method provides similar result as with the regression method. Finally with respect to the logistic regression analysis, the ratio of each class in the discrete variables is out of proportion, thereby making it difficult to make a reasonable conclusion. After going through the above studies, we have found that although the results from three different methods give slight different outcomes, one thing stands out and that is using the technique of value-added database could actually improve the authentic of the original database.

Several studies have shown that prices differ across regions and affect standards of living substantially. This thesis investigates whether they cause the differential impact of minimum wage on employment and hours of work across the European Union NUTS 2 regions. Based on the existing regional price estimates of 7 European Union countries and publicly available aggregate regional data, estimates of regional price levels for another 11 European Union countries with minimum wage are obtained. The method that was used for this purpose (multiple imputation) enables to use the resulting estimates as an explanatory variable in another regression as it takes into consideration using imputed instead of observed values by correcting the variances of parameter coefficients. The impacts of minimum wage are investigated for 3 groups of people who are at risk of being affected by its increase - young adults (15-19 years), low-educated individuals and low-skilled individuals. The results indicate that the minimum wage has a negative impact on employment that is higher in regions with higher price levels. The negative effect of minimum wage on hours of work was not confirmed.