回归分析的标准化系数是否可以大于1

IBSM SPSS Technote (troubleshooting)

Problem(Abstract)
I have run a linear regression (Analyze->Regression->Linear) with several predictors in SPSS/PASW Statistics. I was surprised to see that the standardized coefficients, labelled BETA, for some predictors had values which exceeded the bounds of (-1,1). Are standardized coefficients outside these bounds valid?
Resolving the problem
If there is a single predictor or multiple predictors that are uncorrelated, then the Beta values will be confined to the bounds of (-1,1). However, if there are 2 or more predictors that are correlated, positively or negatively, then the Beta values may exceed those bounds.

Deegan, J.Jr. (1978). On the Occurrence of Standardized Regression Coefficients Greater Than One. Educational and Psychological Measurement, 38, No. 4, 873-888.

The topic is discussed in the context of structural equation modeling by Karl Joreskog at http://www.ssicentral.com/lisrel/advancedtopics.html . Click the link for "How Large Can a Standardized Coefficient be?"

strongyanwei 发表于 2009-7-4 09:01
任何标准化的系数 都不能大于一，标准回归系数也一样，你先去弄弄明白标准化回归系数 是干啥的，怎么用的， ...

互生的系数不应该大于1,应为系数的总和应该是1

ReneeBK 发表于 2014-3-14 22:48
How Large Can A Standardized Coefficient be
KG Jöreskog

您好，抱歉时隔多年打扰您，这个链接过期了，请问您可以提供一下新的下载地址吗

是有这个可能的，但你的这系数本身是有问题的，超出合理范围了，检查模型设定等问题，在看看情况。
标准化回归系数(也称为标准误差)是衡量回归模型拟合程度的一种度量。它表示预测值与实际观测值之间的差异，通常用标准差来衡量。标准化回归系数的计算公式为：

β̄ = ∑(xi - x̄)(yi - ȳ) / (σ^2(n - 1))

标准化回归系数的范围在 -1 到 1 之间。当标准化回归系数大于 1 时，这意味着模型对观测数据的拟合程度要优于随机猜测。然而，这种情况在实际应用中是非常罕见的，因为大多数情况下，模型的拟合程度会接近 0 或者小于 0。

可以通过SPSSAU进行回归分析得到标准化回归系数

标准化回归系数一般小于1吧