In clinical research, it is sometimes desirable to dichotomize a continuous variable so that the information expressed using a dichotomous variable is more straightforward for clinicians to interpret and communicate. The distribution of a continuous variable can differ between two populations defined by the case status. Under such a scenario, the dichotomization process can be based on distributions of the continuous variable in two distinct populations. The resulting dichotomous variable can be used as an endpoint in future studies. Even though dichotomization has not been extensively studied, dichotomization has been commonly carried out in clinical trials. We developed a methodology on dichotomization based on maximizing the correlation between the two populations and the dichotomous variable. We have investigated several commonly assumed distributions (e.g., normal, log-normal and gamma distribution) of the continuous variable for the two populations and developed a numerical algorithm for the proposed method to determine the optimal cutoff point. The two populations can differ in form and/or parameters. The proposed method of finding the optimal cutoff was also extended to adjust for covariates. In real world scenarios where the two samples from the two populations are not completely identified, we recommended using the EM method to first estimate the parameters associated with the two populations before applying the proposed method to find the optimal cutoff point. The performance of the proposed method with the numerical algorithm and the EM method has been studied for several theoretical distributions and using simulated data. These methods were also applied to a varicella vaccine example. / Statistics

銀行在面對借款人以不動產申請抵押貸款時，產生對住宅擔保品估價之需求，以為債權之確保。然銀行的估價過程與一般估價最大不同，肇因於其估價前，擔保品本身已先產生一組買賣契約價格。過去研究指出，估價會嘗試以某些較易取得的價格資訊作為定錨點(anchor)，藉以調整並成為最後的價格。而我國不動產交易價格資訊不透明，契約價格往往由借款人提供的情況下，銀行內部估價人員可能因資訊不易取得、定錨效果，在擔保品的鑑估結果上受到契約價格影響，倘有心人士欲藉此獲得高額貸款、牟取不法利益，將損及銀行債權，即使採用自動估價系統降低人為影響因素，因資料來源不佳，只會產生所謂「garbage in garbage out」的結果。據此，如何分辨契約價格是否具有參考力變成為關鍵，亦為本文欲補足的研究缺口。 本文採用國內某銀行臺北市不動產擔保品8,348筆估價資料為樣本，建立以挑選契約價格是否具有參考力的機率預測模型，尋求影響能判定契約價格是否具有參考力的主要因素，並研究在最適的機率界限下，篩選出具有參考力的契約價格樣本。而研究結果所建立的模型，其預測並篩選出的契約價格樣本均較未經模型篩選者，對擔保品價格之估計有顯著提升。因此本研究所建立的契約價格篩選模型確能提升銀行估價準確性，使不動產擔保品鑑估價格的形成過程中，獲得更多可靠的參考資訊，降低人為操縱的空間，並在成交價格資訊不足的情況下，提升估價人員對契約價格的辨識能力。 / In the face of the borrower to apply for a mortgage of real estate, financial institutions have estimated the price of the collateral requirements to protect the debt claim. However, the biggest difference with the general valuation and that of financial institutions, valuation of its causes before the collateral itself has produced a first sale contract price. In the past research that one attempts to estimate the price of some greater access to information act to anchor in order to adjust and become the final price. Because financial institutions are not easy to obtain price information on real estate transactions in Taiwan, price information is often provided by the borrower. A small number of loans borrower deliberate fraud to forgery or false irrigation Contract price sale and purchase agreement in order to obtain high credit. Even with the automatic valuation system to reduce the human impact factor, due to poor data sources, it will only produce so-called "garbage in garbage out" of the results. Accordingly, how to tell whether the contract price to a reference force becomes critical, and also in this article want to complement the research gap. We adopt 8,348 estate collateral valuation data in Taipei City of a domestic bank for the sample to establish a binary logistic regression model. And we try to seek the main factors that determine whether the contract price of the reference force, and find out the optimal cutoff point, filter out of a sample of the contract price of the reference force. The results confirm the model in this paper. The selected samples of the contract price is estimated that the price of collateral significantly improved compared with those without filtering. Therefore, the model established in this study can really improve the accuracy of bank valuation. Enhance the recognition ability of the bank's internal appraisers on the contract price in the lack of transaction price information.

住宅為兼具消費及投資之雙重功能財貨，因此若從購屋動機劃分購屋族群，可以分為自住者及投資者，近年來受到國內房市呈現生氣蓬勃之景象及利率持續走低等總體經濟因素影響之下，出現越來越多以投資為主要目的之投資型購屋者，對於金融機構之購屋貸款業務來說，投資者之還款行為相較於自住者是比較不穩定的。故本文之研究目的即藉由探討自住者及投資者之購屋特徵異同，建立投資者之機率預測模型，預測某購屋者成為投資者之機率，提供一較為客觀之機率預測模型，供作金融機構放貸參考準則。接著進一步探討在不同機率界限（cutoff point）下之預測準確率，找出預測準確率最高之機率界限值，提高本模型之預測準確度；並探討金融機構在不同經營方針下之較適機率界限值。 / 本文使用台灣住宅需求動向季報之已購屋者問卷，建立二元羅吉特模型。研究結果顯示，區位在中心都市、高單價、小面積產品及大面積產品、預售屋及拍賣屋市場屬於投資型產品，而搜尋時間短、搜尋間數少、年齡較長、男性、無固定職業及家庭平均月收入較高者成為投資者之機率較高。接著，運用貝氏定理計算出預測準確率最高之機率界限值，結果當機率界限值為0.70時預測準確率最高，投資者達72.22%，自住者達80.07%。此外，並使用2007Q4的資料作樣本外驗證，投資者命中率為65.52%，自住者命中率為84.51%。最後，為提供金融機構運用，本文模擬兩種預測誤差在不同權重下對於金融機構所造成的損失，找出損失最少的機率界限值，結果皆是以0.70為最適機率界限值。 / Housing is dual function goods, consumption and investment, so if we separate the home buyers by their motives, they can be defined as two groups, owner-occupiers and investors. Recently, because the housing market is vigorous inland and the rates are fairly low, there are more and more home buyers buying houses for investment. To financial institutions, their payment behaviors are more instable, compare to owner-occupiers. So this article is aim to build a probability predictive model of housing investors by discussing the different home buying characters between owner-occupiers and investors. Therefore we can provide financing institutions a more objective method evaluating if they should lend money to the home buyers. Then we discuss the predictive accuracy with different cutoff points, finding the cutoff point with highest predictive accuracy, therefore we can elevate the model`s predictive accuracy. Besides, we also discuss the most optimal cutoff point for financial institutions under different administration principles. / This article builds binary logit model by the data of “Housing Demand Survey in Taiwan”. Our results suggests that if the houses in downtown、high unit price、big and small acreage、presale and court auction housing market belong to investing houses. And short search duration、few search items、older、male、non-constant job、higher income are getting higher probability to be housing investors. Then, we use Bayesian Theorem to figure out the cutoff point with highest predictive accuracy, and Our results suggests that 0.70 cutoff point with highest predictive accuracy , at that time, investor predictive accuracy is 72.22%, owner-occupier is 80.07%. Besides, we also do the out-sample test by the 2007Q4 data, the investor`s hit-rate is65.52%, the owner-occupier`s hit-rate is 84.51%. At the end, in order to provide financial institution to use, we give two predictive deviation different weights, to find the smallest loss cutoff point, the result all suggest that 0.70 is the most optimal cutoff point.