具ARMA效果一般性潛伏成長模型之研究

Abstract

針對大量受測者之樣本而且有限重複測量時點之縱橫斷面資料(panel data)分析，潛伏成 長模型(Latent Growth Model，簡稱LGM)扮演著重要的角色。本研究結合LGM with ARMA for response variables 以及LGM with ARMA for level-1 errors 兩種既有模式，提 出一個具一般性的擁有更強大配適與預測功能的成長模型GCAR(p*)-EARMA(p, q)，並 解決該模型階數鑑定問題。該模型之假定為LGM 之 level-1 errors 須具穩態性，若穩 態性不克滿足時，本研究提出GCAR(p*)-HECM 模型，亦提供鑑定HECM 型態的程 序。我們採蒙地卡羅模擬評估所提模型之估計與預測效能以及模型設定錯誤對成長 參數推論上的衝擊效應。所提模型可延伸為二階GCAR(p*)-EARMA(p, q)以及二階 GCAR(p*)-HECM 模型以利從事構念之成長趨勢分析，二階模型之效能與模型誤設的 衝擊效應亦採蒙地卡羅模擬評估之。我們預期本研究在方法上具突破性貢獻，具學術 價值；在管理實證上則具應用價值。

Latent growth models (LGM) are useful in analyzing panel data with repeated-measures at finite time points for many subjects. In this study, a general latent growth model with ARMA effects is proposed. The model, called GCAR(p*)-EARMA(p, q), combines LGM with ARMA for response variables and those for level-1 errors, and is more powerful in goodness of fit and prediction. The model assumes that the level-1 error process is stationary. The GCAR(p*)-HECM model is recommended when the assumption is violated. Procedures to identify the models proposed are given. Monte Carlo simulation will be used to assess the effectiveness of the models and the effects of model misspecification. The models can be extended to be the second-order GCAR(p*)-EARMA(p, q) and the second-order GCAR(p*)- HECM, used for the analysis of change over time with respect to constructs. Assessment for the second-order models will be conducted by using Monte Carlo simulation as well. We believe the study will provide contribution in methodology and for empirical applications