基於半參數化潛在曲線模型之成長曲線分析

Analysis of Growth Curves Based on the Semiparametric Latent Curve Model

鄭澈(Che Cheng)

指導教授 ： 江金倉

國立臺灣大學/理學院/應用數學科學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202002033

摘要

發展心理學中，刻劃成長曲線是具挑戰性的課題。然而，既有研究常使用參數化模型來研究成長軌跡，這類模型亦可能過度簡化成長軌跡的形狀；再者，常被使用的潛在曲線模型則需要假設每一個參與者在每一波當中收案的年齡都相同，但由於每個小孩的出生日期皆有差異，這類模型可能會過度簡化了成長軌跡的形狀。

本研究建立半參數潛在軌跡模型以及延伸至資料具有時間不變共變量之情況，且建立兩個模型對應之參數估計方法以及交叉驗證帶寬選擇。並將該方法應用於分析NLSY79資料庫中小孩之不安全依戀於24至83個月之成長曲線。最後模擬該資料的設定進行蒙地卡羅模擬，以檢視迴歸係數之有限樣本性質。

關鍵字

半參數化潛在曲線模型 ； 成長曲線 ； 交叉驗證帶寬選擇 ； 不安全型依戀

並列摘要

Characterizing the growth curves of children is a challenging task in the field of developmental psychology. However, in this field, several of commonly used models assume that the shape of the growth curves is of a specific parametric form, which might over-simplify the shape of the growth curves. Moreover, the widely used latent growth curve model unrealistically assumed that children's observations are taken at the same age.

We consider the semiparametric latent curve model and an extension of it by incorporating time invariant covariates. The estimators and cross-validation bandwidth selection methods are constructed. The proposed methodology is applied to analysis the development of insecure attachment from 24 to 83 months in the child sample of NLSY79. Then we consider a simulation study based on the data to assess the finite sample performance of the estimator of the regression coefficients.

並列關鍵字

Semiparametric latent curve model ； growth curve ； cross-validation bandwidth selection ； insecure attachment

參考文獻

Curran, P. J., Bauer, D. J., Willoughby, M. T. (2004). Testing Main Effects and Interactions in Latent Curve Analysis. Psychological Methods, 9(2), 220–237. https: //doi.org/10.1037/1082-989X.9.2.220

Del Giudice, M. (2019). Sex differences in attachment styles. Current Opinion in Psychology, 25, 1–5. https://doi.org/10.1016/j.copsyc.2018.02.004

Fan, J., Huang, T., Li, R. (2007). Analysis of Longitudinal Data With Semiparametric

Estimation of Covariance Function. Journal of the American Statistical Association, 102(478), 632–641. https://doi.org/10.1198/016214507000000095

Huang, M. Y., Chiang, C. T. (2017). An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model. Journal of the American Statistical Association, 112(519), 1296–1310. https : / / doi . org / 10 . 1080 / 01621459 . 2016 . 1215987