偏最小二乘为什么适用于少的样本量以及样本量如何确定

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最近毕设论文用到了偏最小二乘（PLS），发现诸多文献都说PLS适用于小样本的情况（即在小样本情况下，依旧稳定），求原理，能甩一个文献更好。。。还有样本容量如何确定？

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关键词：偏最小二乘 最小二乘 样本量 样本容量 PLS 如何 论文 样本

这篇文献，还有之后的引用，你可以找找
http://www.cnblogs.com/jerrylead/archive/2011/08/21/2148625.html

yangyuzhou 发表于 2015-5-26 09:45 http://www.cnblogs.com/jerrylead/archive/2011/08/21/2148625.ht ...

谢谢，步骤很清晰，很容易读懂。

自己用google 搜索到了一个答案，觉得说的还挺有道理。复制上来给大家看看。

提问如下：（也是问PLS的样本问题的）
sample size of PLS

[size=1em]by Myst_Vearn » Tue Oct 08, 2013 7:28 am

hello everyone,
I just use smart PLS, so I dont know clearly about it.
Can I ask you some questions.
1. how about the sample size to use PLS?
Because my sample size is small (about 50 observations), so i am afraid I cant use PLS or the it can affect to the significant of the model
2. as far as I know I can take t-statistic through bootstrap and then, compute P-value by using excel function TDIST.
TDIST= (T-statistic, DF, Tailed)
I dont know what is DF and how can i take it.
Thanks for your help.


















回答如下：（运用G-POWER软件进行计算样本容量）




1) Sample size:
1.1)A priori = How big should my sample be?
- Look for the latent variable (LV) with the bigger number of arrows that arrive (could be from structural model ou from the formative measurement model). Use this number as "number of predictors"
- Download G*Power3 from (http://www.psycho.uni-duesseldorf.de/ab ... d-register)
- Install and open G*Power3
- Tests/Correlation../Linear Multipl... R2 deviation from zero.
- A priori
-f2 = 0.15 (medium)
- alpha = 0,05
- Power = 0.8
- Predictors = max number of arrows arriving in a LV
- Calculate --> n

1.2) Post-hoc
I already colected my data, Were they enough?
- If t > 1.96 = the relations are significant and Power ok (you have not type II error)
- if t < 1.96 = Doubt! [relations = zero] or [sample size too small]?
test the Power using Post hoc test in G*Power 3, if Power > 0.8, you could conclude that the sample was enough and relations = 0 (in the population).

2) If you ru bootstrap with 1000 resamples, the DF = 999.
DF = resamples - 1



回答中还涉及了一些参考文献，具体到页数，可以去查一下：



Here is some references:

CHIN, W. W. The partial least squares approach for structural equation modeling. In: G. A. Marcoulides (Ed.); Modern methods for business research. p.295–336, 1998. New Jersey: Lawrence Erlbaum Associates, Inc.

CHIN, W. W.; NEWSTED, P. R. Structural equation modeling analysis with small samples using partial least squares. In: R. H. Hoyle (Ed.); Statistical strategies for small sample research. p.307–341, 1999. Thousand Oaks, CA: Sage Publications. p.326-327

HAIR JR., J. F.; HULT, G. T. M.; RINGLE, C. M.; SARSTEDT, M. A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM). Thousand Oaks, CA: Sage Publications, Inc., 2014. p.20-21