查詢結果分析
來源資料
頁籤選單縮合
題 名 | Fitting Non-linear Models with AR(1) Structure: A Marginal Likelihood Approach=擬合AR(1)結構之非線性模式:邊際概似法 |
---|---|
作 者 | 邱曉婷; | 書刊名 | 嘉南學報 |
卷 期 | 26 2000.11[民89.11] |
頁 次 | 頁153-167 |
分類號 | 360.13 |
關鍵詞 | 縱貫性數據; 非線性模式; 生長曲線; 邊際概似法; Restricted最大概似法; 胎兒基底高度; Longitudinal data; Non-linear models; Growth curves; Marginal likelihood; AR(1); Restricted maximum likelihood; Fundal height; |
語 文 | 英文(English) |
中文摘要 | 估計生長模式時有兩個主要問題:(一)它們通常為非線性(non-linear),(二)誤差為連續相關(serial correlated)。Lindstrom和Bates(1990)提出的混合模式法(the mixed model methods)已發展出自身相關誤差(auto-correlated errors)之非線性模式的方法學。但這些方法主要用於短期觀察所得數據,以估計其母群體平均生長曲線(population averages of growth)。這篇文章所提供之方法則是用於對長時間觀察的數據,在固定效用結構下(fixed effect structure),以AR(1)(first order auto-regressive)誤差來估計個體特有(individual specific)非線性生長曲線。 邊際概似法(the marginal likelihood method)將邊際概似之估計過程以quasi-概似法分為兩部份,以減少繁雜之計算。此方法以多次式近似非線性模式後,求得只含AR(1)參數的邊際概似並估計AR(1)的唯一參數。當AR(1)參數為已知後,則進一步估計非線性模式中的參數。 電腦模擬(simulations)則用於探討邊際概似估計法之性質,並測試以多次式近似非線性之有效性。此方法亦於模擬中與1977與Harvill提出以混合模式結構為主的restricted最大概似法相比較。 最後,將邊際概似法應用於研究母子健康護理領域之二組相關數據。也就是以邊際概似法分析這些胎兒基底高度(fundal height)數據,且同時與其他方法之分析結果相比較。 |
英文摘要 | In the estimation of growth models the two main problems are a) they are often non-linear and b) the errors are serially correlated. Methodology for non-linear growth models with serially correlated errors using the mixed models approach are available in the literature (Lindstrom and Bates (1990)). These methods are mainly useful for estimating population averages of growth from data that are observed over short time periods. In this dissertation a method for estimating individual specific non-linear growth curves under first order auto-regressive (AR(1)) error structure for data that are observed over a long period of time is presented. In order to reduce the computational complexity the maximum likelihood estimation procedure is separated into two parts using a quasi-likelihood method called here the marginal likelihood method. In this method the AR(1) 'nuisance' parameter is estimated from a marginal likelihood that contains the AR(1) parameter alone, under a polynomial approximation of the non-linear model. Then the non-linear model parameters are estimated by assuming the AR(1) parameter to be known, where he known value is the estimate. Simulation results are presented to discuss the properties of the marginal likelihood estimation method and to test the validity of the polynomial approximation. The method is also compared with the Restricted Maximum Likelihood Estimation (REML) proposed under a mixed model structure by Harville (1977). The method is applied to two data sets from maternal and child health studies. These data on fundal heights are analyzed using the marginal likelihood approach and compared with other approaches. |
本系統中英文摘要資訊取自各篇刊載內容。