回归分析的标准化系数是否可以大于1

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

诸位大侠，想问一下逐步多元回归分析的标准化回归系数是否可以大于1？

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：标准化系数 回归分析 标准化 大于1 多元回归分析 标准化 回归分析 系数

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，你就明白为啥不能大于一了、随便弄一本SPSS教材都可以找到。

Not exactly. Beta CAN be greater than 1, although it usually implies that there might be
a suppressor involved.

FYI:  an abstract:
----------------------
On the Occurrence of Standardized Regression Coefficients Greater Than One
John Deegan, JR
Department of Political Science University of Rochester

For some investigators, the occurrence of standardized regression coefficients greater than one in a model raises questions concerning the legitimacy of such coefficients, and poses serious problems of interpretation (particularly for those employing path analytic procedures). It is demonstrated here that standardized regression coefficients greater than one can legitimately occur. Furthermore, the relationship between the occurrence of such coefficients and the extent of multicollinearity present among the set of predictor variables in an equation is examined. Comments on the interpretation of these coefficients, including a discussion of their interpretation in the context of path analysis, are provided.

Educational and Psychological Measurement, Vol. 38, No. 4, 873-888 (1978)
------------------------

a more technical note from Joreskog in SEM context is also informative: http://www.ssicentral.com/lisrel ... edCoefficientbe.pdf

好像能吧，以前做过因子分析，系统会自己标准化。

不可能大于一

标准数没有大于一的

绝对可以大于1

为什么spss做出大于1的了

In statistics, standardized coefficients or beta coefficients are the estimates resulting from an analysis carried out on independent variables that have been standardized so that their variances are 1. Therefore, standardized coefficients refer to how many standard deviations a dependent variable will change, per standard deviation increase in the predictor variable. Standardization of the coefficient is usually done to answer the question of which of the independent variables have a greater effect on the dependent variable in a multiple regression analysis, when the variables are measured in different units of measurement (for example, income measured in dollars and family size measured in number of individuals).
Some statistical software packages like PSPP, SPSS and SYSTAT label the standardized regression coefficients as "Beta" while the unstandardized coefficients are labeled "B". Others, like DAP/SAS label them "Standardized Coefficient". Sometimes the unstandardized variables are also labeled as "B" or "b".
A regression carried out on original (unstandardized) variables produces unstandardized coefficients. A regression carried out on standardized variables produces standardized coefficients. Values for standardized and unstandardized coefficients can also be derived subsequent to either type of analysis.

Before solving a multiple regression problem, all variables (independent and dependent) can be standardized. Each variable can be standardized by subtracting its mean from each of its values and then dividing these new values by the standard deviation of the variable. Standardizing all variables in a multiple regression yields standardized regression coefficients that show the change in the dependent variable measured in standard deviations.
Advantages
Standard coefficients' advocates note that the coefficients ignore the independent variable's scale of units, which makes comparisons easy.
Disadvantages
Critics voice concerns that such a standardization can be misleading. Since standardizing a variable removes the unit of measurement from its value, a standardized coefficient for a given relationship only represents its strength relative to the variation in the distributions. This invites bias due to sampling error when one standardizes variables using means and standard deviations based on small samples. Furthermore, a change of one standard deviation in one variable is only equivalent to a change of one standard deviation in another predictor insofar as the shapes of the two variables' distributions resemble one another. The meaning of a standard deviation may vary markedly between non-normal distributions (e.g., when skewed or otherwise asymmetrical). This underscores the importance of normality assumptions in parametric statistics, and poses an additional problem when interpreting standardized coefficient estimates that even nonparametric regression does not solve when dealing with non-normal distributions



http://www3.nd.edu/~rwilliam/stats1/x92.pdf

How Large Can A Standardized Coefficient be

KG Jöreskog

http://www.ssicentral.com/lisrel ... edCoefficientbe.pdf