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研究生:劉宜萍
研究生(外文):LIU YI-PING
論文名稱:探討混合型驗證因素分析參數估計的影響因子之模擬研究
論文名稱(外文):A Monte Carlo study exploring factors effecting parameter estimates in mixture confirmatory factor analysis
指導教授:林定香林定香引用關係
指導教授(外文):LIN TING-HSIANG
學位類別:碩士
校院名稱:國立臺北大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:55
中文關鍵詞:結構方程模型混合型驗證性因素分析蒙地卡羅模擬法均方根誤差
外文關鍵詞:structural equation modelingmixture confirmatory factor analysisMonte CarloRMSE
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結構方程模型(structural equation modeling; SEM)常使用在行為科學,心理學與社會科學的量化分析上,它將研究學者所蒐集到的資料,利用因素分析抽取出數個因素,而模型便能將由依變數與自變數所抽取出的因素,進一步的探討變數間的因果或相關。以往運用結構方程模型都只使用觀察變數與潛在變數為連續的假設,但是在現實中所蒐集的資料並不僅只為連續型的變數,也有許多類別型或排序型的變數,所以近年來也衍生了許多觀察變數或潛在變數具有連續型與類別型的混合模型。
本研究所探討的混合型結構方程模型是包含非連續型的類別變數與連續型的變數,利用因素分析所擷取的因素決定每個樣本應屬於哪個分組(class);本研究將使用Muthén等人(1998)所提出的混合型驗證性因素分析模型(confirmatory factor analysis;CFA),並使用蒙地卡羅模擬法(Monte Carlo),在考慮樣本個數、觀察指標個數與潛在變數個數比、因素負載量、潛在變數個數、潛在變數間的相關係數等五個因子的相互組合情況下,重複次數都為1000次,模擬資料再利用EM演算法(EM-algorithm),估算出最大概似估計值(ML estimator)。我們將利用估計偏誤(bias)與均方根誤差(root mean square error;RMSE),來評斷不同因子下的影響效用。
在結果部份,五個因子或多或少都與bias、RMSE呈現負向相關,當樣本數、觀察變數個數與潛在變數個數比、連續型潛在變數個數、因素負載量係數與因素間的相關係數越大時,參數估計的bias與RMSE就會越小。以參數的bias與RMSE做為依變數的多元迴歸分析發現樣本數對各個參數的bias與RMSE具有顯著的影響效用,而連續型潛在變數個數則對各個參數的bias與RMSE就較少有顯著的效用。
由結果發現,在潛在變數為非連續型變數的情況下,以上五個因子對參數估計的影響,與一般連續型的結構方程模型無太大的差異。
Structural equation modeling (SEM) is a very popular statistical technique used in social sciences, behavioral sciences and psychology. It uses factor analysis to extract factors from data, and this model uses factors that are extracted exploring the causal relation and correlation of the latent variables. Traditionally, SEM uses the continuous dependent variables and independent variables, but the data often include both categorical and ordinal. Therefore, the recent developed mixture models combine continuous and categorical variables.
This study used mixture model that include continuous factor and categorical latent classes, and decides the class of each observed variable by factor analysis. Monte Carlo simulation of this study used the confirmatory factor analysis (CFA) proposed by Muthén, and there are five effects:sample size、ratio of the number of the indicators and the number of the latent variables、factor loading、number of latent variables and correlation coefficient of the factor. We used EM algorithm to get the MLE to evaluate the bias and RMSE, and we compared the effect under different effects.
In the results, the five effects more or less have negative relationship with the bias and RMSE, when sample size、ratio of the number of the indicators and number of the latent variables、factor loading、number of latent variables and correlation coefficient of the factor are larger, the bias and RMSE are smaller. By conducting a regression analysis using bias and RMSE as dependent variables, we found sample size has significant effect on the bias and RMSE, but the number of the latent variables has least significant effect.
From the result, the effects of the five effects do not different from the continuous structural equation modeling on parameter estimation.
目錄
表目錄
圖目錄
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的 3
第三節 研究貢獻 3
第二章 文獻探討 4
第一節 結構方程模式 4
第二節 混合型結構方程模型 14
第三節 影響變數的相關文獻探討 21
第三章 研究方法 23
第一節 理論模型 23
第二節 影響變數 26
第三節 模擬流程 29
第四節 分析計畫 31
第四章 研究分析 33
第一節 模擬研究之結果 33
第二節 多元迴歸分析結果 43
第五章 結論與建議 50
第一節 主要的研究發現 50
第二節 研究建議、限制與未來的研究方向 52
參考文獻 53
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