Developmental cascade models最先由Masten & Cicchetti 2010系统性提出。中文翻成“发展级联模型”，要是能翻译成“发展瀑布模型”该多有趣。

最近写论文要用，所以读了些论文，为了防止忘记后将来有一天又要用，写个笔记存档。问题是自己概括的，方便找信息。中文解释是自己的随意阐发，如果想看正经的话，请参考英文以及文后给的文献，这些成段出现的英文直接出自Racz et al., 2017，懒得加引号了。概念上的笔记欢迎看另一篇http://blog.sina.com.cn/s/blog_70fa07fd0102yl0y.html

是什么？

发展级联模型的特殊之处：展示“变量间跨领域和跨时间的关联”。跨领域没有什么特别的，就是类似一个是认知性的变量（比如智商）一个是社会性变量（比如合作行为）。

统计模型上也很简单：控制变量A的stability effect和A与另一个变量B在同一时间点上的相关，对模型中的所有变量都作此操作。如果不用潜变量，就直接用路径分析（path analysis）。具体变量个数和时间点没有限制，不过通常都是3个变量，追踪3次或更多，像是高级版的cross-lag model.

Developmental cascade models are conservative, multivariate, longitudinal models that allow for the examination of the direction, specificity, and ordering of effects among domains, while simultaneously controlling for stability and covariation (Bornstein et al. 2010, 2013; Masten and Cicchetti 2010). Controlling for stability and covariation is crucial in longitudinal studies, given that the strength of these effects likely reduces the availability of unique, predictable variance (Burt et al. 2008). Cascade models isolate and identify specific cross-domain cross-time relations and allow for the prediction of change in constructs over time.

有啥用？

证明发展就是个“牵一发而动全身的状态”，或者说有多米诺骨牌效应。比如，这一段时间内变量A影响了变量B，下一段时间内变量B又影响了变量C。Developmental cascades demonstrate that changes in one domain trigger system-wide, spreading effects into other domains, resulting in dynamic longitudinal interactions (Lansford et al. 2010; Masten et al. 2005).

帮研究者找出问题行为更早的“罪魁祸首”以及它出现的时间点，证明该研究的实用价值These progressive effects are therefore positioned to identify early pathways that could be targeted to prevent future developmental difficulties.

展示我们使用了少有人使用的模型（所以很牛），这个基本上就是在论文里“自吹”了Despite their methodological and theoretical advantages, cascade models remain largely underutilized in psychological research.

模型怎么搭？

首先，把主要的变量按照自己的示意图弄好。有的人是一次就把所有路径都弄好，把不显著的路径去掉(Racz et al., 2007)；有的则是逐步加路径看各个nested model哪个model 最简洁fit最好（Vaillancourt et al., 2013, Liu et al., 2017，后者讲得更清楚一些）。通常用maximum likelihood robust (MLR) estimation。Mode fit参考指标CFI, TLI, RMSEA, SRSR, AIC, 而做模型比较经常用的是Satorra–Bentler scaled chi-square difference test。

其次，加入协变量（更方便提高显著关联的可信度）；或者看性别差异，还有自己关心的几个不同sub-group间的差异。

被试之间互相关联怎么办？Huber-White adjustment of the standard errors to account for non-independence

要不要管multilevel问题？如果group level sample size低于50且ICC很小，不用管（Hox & Maas, 2001）

如果要管的话，怎么管？在MPlus可以用TYPE=COMPLEX然后cluster option

Hox, J. J., & Maas, C. J. (2001). The accuracy of multilevel structural equation modeling with pseudobalanced groups and small samples. Structural Equation Modeling, 8, 157-174.

Liu, J., Bullock, A., Coplan, R. J., Chen, X., Li, D., & Zhou, Y. (2018). Developmental cascade models linking peer victimization, depression, and academic achievement in Chinese children. British Journal of Developmental Psychology, 36, 47-63.

Masten, A. S., & Cicchetti, D. (2010). Developmental cascades. Development and Psychopathology, 22, 491-495.

Racz, S. J., Putnick, D. L., Suwalsky, J. T., Hendricks, C., & Bornstein, M. H. (2017). Cognitive abilities, social adaptation, and externalizing behavior problems in childhood and adolescence: specific cascade effects across development. Journal of Youth and Adolescence, 46, 1688-1701.

Vaillancourt, T., Brittain, H. L., McDougall, P., & Duku, E. (2013). Longitudinal links between childhood peer victimization, internalizing and externalizing problems, and academic functioning: Developmental cascades. Journal of abnormal child psychology, 41, 1203-1215.