s*******e
发帖数: 226 | 1 The reviewer asked us to preform a two-stage regression, for example,
In the first stage, regress Y1 on a series of X1 (firm characteristic
variables). Then in the second stage, use the residual got from the first
stage (let us say Y2) to regresson on a series of time-series variables (X2).
We wonder why we cannot just regress Y1 on X1 and X2 in a single regression.
We know the statistical results will be slightly different, but is there
any material difference between the two-stage method versus the one-step one?
Thank you for your input. | k****i
发帖数: 347 | 2 a series of time-series variables?
举个例子吧，y1, x1, x2都是什么 | l*********s
发帖数: 5409 | | A*******s
发帖数: 3942 | 4 i don't know if it is related to time series.
my understanding is that this two stage regression works like one step
regression on X1, and the part of X2 orthogonal to X1.
X2).
regression.
one?
【在 s*******e 的大作中提到】
: The reviewer asked us to preform a two-stage regression, for example,
: In the first stage, regress Y1 on a series of X1 (firm characteristic
: variables). Then in the second stage, use the residual got from the first
: stage (let us say Y2) to regresson on a series of time-series variables (X2).
: We wonder why we cannot just regress Y1 on X1 and X2 in a single regression.
: We know the statistical results will be slightly different, but is there
: any material difference between the two-stage method versus the one-step one?
: Thank you for your input.
| s*****9
发帖数: 108 | 5 分开做，细节上更好操作吧，如果X2是time series的话。如果放到一起做regression,
residual的distribution的处理上会麻烦一些吧 | w**********y
发帖数: 1691 | 6 想象一个三维空间.x1和x2是两个轴(它们的夹角可能不是直角).Y是三维空间的一个向量..y对x1和x2同时做
regression,就等价于,把y投影到x1和x2张成的平面上的向量,然后这个向量分别向x1,
x2做平行线..这个结构是一个平行四边形
如果分两步,就是先向x1做投影..然后用投影和y的差对x2做投影..这是垂直的,不是平
行的..这个结构是个四边形,有两个角是直角..
只有当x1和x2垂直的时候,这两种才一样..他们夹角越小,也就是correlation越大时,区
别越大. | F****n
发帖数: 3271 | 7 This is a technique normally used to handle collinearity.
If X1 and X2 are highly correlated, the regression coefficients will be
messed up in a model that use them both, i.e. you cannot tell whether the
coefficient on X1 or X2 is the "true" effect.
On the other hand, in your example, you assume (by theory) that X1 always is
the primary effect and will exclusively explain as much original variance
as possible. X2 will only explain the leftovers.
X2).
regression.
one?
【在 s*******e 的大作中提到】
: The reviewer asked us to preform a two-stage regression, for example,
: In the first stage, regress Y1 on a series of X1 (firm characteristic
: variables). Then in the second stage, use the residual got from the first
: stage (let us say Y2) to regresson on a series of time-series variables (X2).
: We wonder why we cannot just regress Y1 on X1 and X2 in a single regression.
: We know the statistical results will be slightly different, but is there
: any material difference between the two-stage method versus the one-step one?
: Thank you for your input.
| D*********2
发帖数: 535 | 8 Re.
Also for better interpretability.
is
【在 F****n 的大作中提到】
: This is a technique normally used to handle collinearity.
: If X1 and X2 are highly correlated, the regression coefficients will be
: messed up in a model that use them both, i.e. you cannot tell whether the
: coefficient on X1 or X2 is the "true" effect.
: On the other hand, in your example, you assume (by theory) that X1 always is
: the primary effect and will exclusively explain as much original variance
: as possible. X2 will only explain the leftovers.
:
: X2).
: regression.
| H**********v
发帖数: 169 | 9 Frisch-Waugh-Lovell theorem explains this well. | s*******e
发帖数: 1385 | 10 Thank you very much!
向量..y对x1和x2同时做
【在 w**********y 的大作中提到】
: 想象一个三维空间.x1和x2是两个轴(它们的夹角可能不是直角).Y是三维空间的一个向量..y对x1和x2同时做
: regression,就等价于,把y投影到x1和x2张成的平面上的向量,然后这个向量分别向x1,
: x2做平行线..这个结构是一个平行四边形
: 如果分两步,就是先向x1做投影..然后用投影和y的差对x2做投影..这是垂直的,不是平
: 行的..这个结构是个四边形,有两个角是直角..
: 只有当x1和x2垂直的时候,这两种才一样..他们夹角越小,也就是correlation越大时,区
: 别越大.
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