ISSN 0439-755X
CN 11-1911/B
主办:中国心理学会
   中国科学院心理研究所
出版:科学出版社

心理学报 ›› 2014, Vol. 46 ›› Issue (9): 1400-1412.doi: 10.3724/SP.J.1041.2014.01400

• 论文 • 上一篇    

多阶段混合增长模型的影响因素:距离与形态

刘源1,2;骆方1;刘红云1   

  1. (1北京师范大学心理学院应用实验心理北京市重点实验室, 北京 100875) (2香港中文大学教育心理系, 香港)
  • 收稿日期:2013-08-07 发布日期:2014-09-25 出版日期:2014-09-25
  • 通讯作者: 刘红云, E-mail: hyliu@bnu.edu.cn
  • 基金资助:

    国家自然科学基金(31100759)、全国教育科学“十二五”规划教育部重点课题(GFA111001)、教育部人文社会科学研究青年基金项目(11YJC190016)、北京市与中央在京高校共建项目(019-105812)资助。

Factors of Piecewise Growth Mixture Model: Distance and Pattern

LIU Yuan1,2; LUO Fang1; LIU Hongyun1   

  1. (1 Beijing Key Laboratory of Applied Experimental Psychology; School of Psychology, Beijing Normal University, Beijing 100875, China) (2 Department of Educational Psychology, The Chinese University of Hong Kong, Hong Kong, China)
  • Received:2013-08-07 Online:2014-09-25 Published:2014-09-25
  • Contact: LIU Hongyun, E-mail: hyliu@bnu.edu.cn

摘要:

通过模拟研究, 考察潜类别距离和发展形态等因素对多阶段混合增长模型的模型选择和参数估计的影响:(1)潜类别距离越大, 模型选择和分类效果越好。(2)混合模型的选择, 应以一定样本量(至少200)为前提, 首先考虑BIC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)多阶段的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影响。(4)潜类别距离和样本量越大, 参数估计精度越高。(5)在判断分类准确性的指标中, ARI的选择更偏向于真实的模型。

关键词: 多阶段混合增长模型(PGMM), 潜类别增长分析(LCGA), 潜类别距离(SMD), 发展形态

Abstract:

The piecewise growth mixture model (PGMM) has been a very popular analytical approach in recent studies of longitudinal data. PGMM builds on the piecewise growth model (PGM) and the growth mixture model (GMM). It is used to locate the turning point of growth trajectory as well as to identify the latent class of the population. It is particularly useful in detecting the non-continuous growing trend in a heterogeneous population. A simplified version of the model, the latent class growth analysis (LCGA), has also been often used with a restriction on the variance of PGMM. Understandably, factors affecting PGM and GMM will affect the estimates and performance of PGMM. These factors may include the change of the slope, the distance of latent classes, and the sample size. PGMM being developed from the two growth-related models (PGM, GMM) also attempts to analyze the growth pattern in latent growth trajectory as a special and newly emerged issue. Even for models with the same distance, their different slopes can be combined to form different patterns. This issue has not been fully explored in previous literature. Yet in empirical studies, factors such as the distance of the latent classes, the growth pattern, the existing criteria of model fit indices, and the precision of parameter estimates are well worth examining issues. In the present simulation study, a two-class-two-period model was adopted. The three simulation conditions being considered were: the sample size, the distance of latent class, and the pattern of the growth trajectory. The sample size was set to be 100, 200 and 500. The distance of the latent classes was defined as the squared Mahalanobis distance (SMD), with 1.5, 3 and 5 being used to represent the small, medium and large distance of latent classes respectively. Four different types of growth pattern were selected to represent one parallel and three non-parallel patterns. Finally, the LCGA was selected as the reference model to see whether PGMM could be further simplified or not. The results showed that: (1) the distance between the latent classes (SMD) was a crucial factor that influenced the model selection and parameter estimation. Large distance would lead to consistent BIC and entropy when the right models were selected; while small distance (SMD = 1.5) would not. (2) When mixture modeling was taken into consideration, it was suggested that a sample size of at least 200 should be used. BIC index should be the preferred choice to be used for model selection; the entropy, ARI and other indices were also recommended to further reference. (3) The pattern of the growth trajectory would affect model selection; specifically, non-parallel patterns of the trajectory would help model selection (higher entropy and higher total hit ratio) for medium distance (SMD = 3) and medium sample size (N = 200) conditions. However, as compared to LCGA, the pattern of the growth trajectory had little influence on PGMM. (4) Parameter estimation was affected by the sample size and distance of latent classes. Parameter estimates would become more precise as the sample size and the distance increased. (5) ARI was a reasonably good index belonging to the recovery indices family. ARI was highly correlated with the total hit ratio and thus would lead to recommendations of models closer to the true model.

Key words: piecewise growth mixture modeling (PGMM), latent class growth analysis (LCGA), distance of latent classes (SMD), pattern of the growth trajectory