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題 名 | 邏輯斯迴歸模式與對數線性模型之比較=A Comparison between Logistic Regression and Log-Linear Model |
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作 者 | 林正祥; | 書刊名 | 中國統計學報 |
卷 期 | 35:3 1997.09[民86.09] |
頁 次 | 頁249-269 |
分類號 | 319.51 |
關鍵詞 | 邏輯斯迴歸模式; 對數線性模型; 適合度檢定; Logistic regression model; Log-linear model; Good-ness of fit; |
語 文 | 中文(Chinese) |
中文摘要 | 邏輯斯迴歸模式和對數線性模型間之關係由來已久,惟二者間之適用範圍及其 關係之更進一步探討則鮮有被提及。本研究利用了幾組類別數據深入的探討有關此二者間 之關係,結果發現二者在理論上互通之模式以實際數據分析時會有某些程度的差異,故乃 針對此找出其間互通之規則,並就其實際應用層面提出以下建議:在變數較少時(四個變 數以下),對數線性模型提供了比邏輯斯迴歸模式較多的訊息;惟當變數增多時,則由於 對數線性模型所探討者為變數間之交互作用,因而可能產生共線性之問題而無法估出參數 ;然邏輯斯迴歸模式則較適用於變數較多之情形,並且在某些自變數為連續變數之情形下 亦能適用,這是對數線性模型無法達成的。因此,我們建議在變數有限的情形下,可以對 數線性模型來解釋,若變數增多,則邏輯斯迴歸模式當優先考慮。另外,我們亦對此二類 模式進行適度檢定,結果發現某些無相對應邏輯斯迴歸模式之對數線性模型亦能配適資料 。此一結果再次驗證了在變數較少的情況下,就類別資料言,對數線性模型有較為寬廣的 範圖來詮釋數據。 |
英文摘要 | Logistic regression model and log-linear model are very popular in the field of public. health, social science, and behavior science, etc. Under some circumstances both models are equal. However, there are few papers mentioning about their differences. In this study, we attempt to scrutinize both models and provide some examples to illustrate the differences. We find that one to one correspondence between those two models does not always exist in practical applications. When the correspondence exists, a rule connecting both models is established. The log-linear model provides more information than logistic regression when the variables are not more than 4. Once the number of variables increases, the log-linear model, which deals with the interaction among the variables, can not handle the problem of collinearity and a large number of parameters. On the contrary, with fewer parameters in the model, logistic regression can handle problems with more variables. Furthermore, it can also be applied when categorical and continuous variables are present at the same time. From the standpoint of practical application of categorical data analysis, log-linear model is a good choice when the number of variables is not greater than 4, and the logistic regression should be adopted once the number of variables is bigger. In addition, we use goodness-of-fit to test these two models and find that the loglinear models without corresponding logistic regression models can also fit the data very well. This confirms that the loglinear model is more flexible in explaining the data under the circumstances of fewer variables. |
本系統中英文摘要資訊取自各篇刊載內容。