【作者】 刘源； 刘红云； 侯杰泰；

【Author】 LIU Yuan~(1,2) LIU Hongyun~2 HAU Kit-Tai~1 1 Faculty of Education,The Chinese University of Hong Kong 2 School of Psychology,Beijing Normal University

【机构】 香港中文大学教育学院； 北京师范大学心理学院；

【摘要】 多阶段混合增长模型(Piecewise growth mixture modeling,PGMM)可以同时考察发展趋势不连续和发展群体不同质的问题,在实际研究中具有特殊作用。通过模拟研究,考察潜类别距离和发展形态等因素对模型选择和参数估计的影响,得到以下结论:(1)潜类别距离影响模型选择和分类效果。潜类别间距离较大时,BIC、熵值表现出一致性,均能选出正确的模型,得到正确的分类结果;但当潜类别问的距离很小(SMD=1.5),不分类的模型比分类模型更好拟合数据,即便使用GMM强行分类,分出来的类别也可能是错误的。(2)关于混合模型的选择,研究者应充分考虑模型的拟合与分类结果确定性之间可能存在的相悖关系,在满足一定样本量(至少200)的前提下,首先考虑BIC指标选出正确的分类模型,再通过熵值、ARI等选择分类确定性较高的模型。(3)多阶段发展形态对正确模型的选择和分类的确定性均有一定程度的影响,潜类别间距离中等(SMD=3)样本量较小时(N=200),平行发展形态正确模型选择的比例和熵值均低于非平行形态。形态的差异对参数估计结果的影响相对较小。(4)模型的参数估计精度受到类别间距离和样本量的影响,类别间距离越大,参数估计精度越高;样本量越大,参数估计精度越高。(5)ARI是一个较为优良的指标,不仅和总命中率高度相关,且采用ARI的模型选择更偏向于真实的模型。更多还原

【Abstract】 The use of the longitudinal studies has rapidly increased in numerous areas among education, psychology,sociology and other sciences over the past years.This approach aims at the development of the traits and behaviors of both individuals and groups,permitting the use of growth curve modeling.Up to now,newly developed statistic model,latent growth modeling(LGM) for example,which has become popular among researchers to solve the growth issues,can detect the growth trajectory as well as the variance of the individuals.In special case,that is,if there is knot in the trajectory or unobserved heterogeneity in population,piecewise growth modeling and growth mixture modeling can be used respectively.Or being combined of the two,i.e.piecewise growth mixture modeling(PGMM),can be used to solve the heterogeneous population and the turning point simultaneously in practice. Using the simulation study,a two-class-two-period model,as well as several simulation conditions was considered: the sample size,distance of latent class and the pattern of the growth trajectory.The distance of the latent classes was the most important factor which could influence the model selection and parameter of the mixture modeling according the previous reference,so the SMD was used to represent the distance,where 1.5,3 and 5 represented for the small,mediate and large distance of latent classes respectively.Pattern of growth trajectory was another special case considered in the PGMM,where even with the same distance,difference slopes can be combined to form the PGMM modeling.Four different types of pattern were chosen to represent one parallel and three unparallel patterns. it can be illustrated from the results that:(1) the distance between the latent classes(SMD) was a crucial factor that can influence the model selection and parameter estimations.Large distance will led to consistent results of BIC and entropy,where the right model would be selected;while small distance(SMD=1.5) would not,where the results preferred to the general LGM.(2) When mixture modeling was taken into consideration,it was suggested that the sample size of 200 should be guaranteed.BIC index should be the prior option to select models,and the entropy,ARI and other indices were recommended to further decisions.(3) The pattern of the growth trajectory influenced model selection to some extent,where the unparallel patterns of the trajectory led to better model estimations when moderate distance(SMD=3) with relatively small sample size(N=200) was considered. However,pattern of the trajectory influenced little to parameter estimations of PGMM.(4) Parameter estimations were affected by the sample size and distance of latent classes.The larger the sample size as well as the distance became,the better the parameter estimations would be.(5) ARI was a good index which belonged to the recovery indices family.ARI was highly correlated with the total hit ratio,and the selected models based on it were preferred to the true model.更多还原