F****n
发帖数: 3271 | 1 理想状态下，IVs应该是 uncorrelated, 但实际上他们或多或少的会有一些相关性，当
相关性并不强或multicollinearity在可忍受范围内时，常常直接MODEL。但在弱相关的
情况下，IVs的Coeff显然受顺序的影响。比如
Y =b1X1 + b2X2 + b0 算出来的coefficients 和
Y =b2X2 + b1X1 + b0 不一样 (OLS)。
假设X1, X2 each accounts for 40% of Y variation when modeled separately, but
when modeled together only account for 70% (as indicated by R square). So:
1) Can we say there is 10% (80%-70%) of Y variation explained jointly by X1,
X2?
2) If so can we say b1 actually is calculated to reflect 40% variability of | F****n
发帖数: 3271 | 2 Moreover, for
Y = b1X1 + b2X2 + b0
is it possible to create
Y = b1X1 + b2X2' + b0
where X2' is a variable totally independent of X1, and only accounting for
the part of variance independently explained by X2? i.e. "strip away" the
part of X2 correlated with X1?
but
X1,
of
【在 F****n 的大作中提到】
: 理想状态下，IVs应该是 uncorrelated, 但实际上他们或多或少的会有一些相关性，当
: 相关性并不强或multicollinearity在可忍受范围内时，常常直接MODEL。但在弱相关的
: 情况下，IVs的Coeff显然受顺序的影响。比如
: Y =b1X1 + b2X2 + b0 算出来的coefficients 和
: Y =b2X2 + b1X1 + b0 不一样 (OLS)。
: 假设X1, X2 each accounts for 40% of Y variation when modeled separately, but
: when modeled together only account for 70% (as indicated by R square). So:
: 1) Can we say there is 10% (80%-70%) of Y variation explained jointly by X1,
: X2?
: 2) If so can we say b1 actually is calculated to reflect 40% variability of
| l***a
发帖数: 12410 | 3 PCA
【在 F****n 的大作中提到】
: Moreover, for
: Y = b1X1 + b2X2 + b0
: is it possible to create
: Y = b1X1 + b2X2' + b0
: where X2' is a variable totally independent of X1, and only accounting for
: the part of variance independently explained by X2? i.e. "strip away" the
: part of X2 correlated with X1?
:
: but
: X1,
| F****n
发帖数: 3271 | 4 Sorry, no PCA. I explained that multicollinearity was regarded as tolerable
(small correlation) and also PCA makes interpretation hard.
Basically I am looking for a method that can sequentially "strip away"
correlation from an IV to previous IVs. My questions actually are:
1) Whether such methods exist;
2) If no, can we interpret the coefficients as in my original post, e.g.
b1 is based on X1, b2 is based on X2 minus the correlated part with X1. My impression is probably yes, because OLS coeffs
【在 l***a 的大作中提到】
: PCA
| s*r
发帖数: 2757 | 5 coefficient should be the same
type I ss will be different
type 3 ss will be the same | l*********s
发帖数: 5409 | 6 How can coef change at all? OLS estimate shall be unique.
but
X1,
of
【在 F****n 的大作中提到】
: 理想状态下，IVs应该是 uncorrelated, 但实际上他们或多或少的会有一些相关性，当
: 相关性并不强或multicollinearity在可忍受范围内时，常常直接MODEL。但在弱相关的
: 情况下，IVs的Coeff显然受顺序的影响。比如
: Y =b1X1 + b2X2 + b0 算出来的coefficients 和
: Y =b2X2 + b1X1 + b0 不一样 (OLS)。
: 假设X1, X2 each accounts for 40% of Y variation when modeled separately, but
: when modeled together only account for 70% (as indicated by R square). So:
: 1) Can we say there is 10% (80%-70%) of Y variation explained jointly by X1,
: X2?
: 2) If so can we say b1 actually is calculated to reflect 40% variability of
| o****o
发帖数: 8077 | 7 regress your X2 on the residuals from Y=b0+b1*X1
use the projected X2 from that auxilary regression to your original model
besides, I don't think the ordering matters in OLS, check the linear algebra
tolerable
impression is probably yes, because OLS coeffs and confidence intervals are
computed sequentially, but I am not sure about it at all.
【在 F****n 的大作中提到】
: Sorry, no PCA. I explained that multicollinearity was regarded as tolerable
: (small correlation) and also PCA makes interpretation hard.
: Basically I am looking for a method that can sequentially "strip away"
: correlation from an IV to previous IVs. My questions actually are:
: 1) Whether such methods exist;
: 2) If no, can we interpret the coefficients as in my original post, e.g.
: b1 is based on X1, b2 is based on X2 minus the correlated part with X1. My impression is probably yes, because OLS coeffs
| h****s
发帖数: 16779 | 8 coefficients should be unique: \hat{beta} = (X'X)^{-1} X'Y
but
X1,
of
【在 F****n 的大作中提到】
: 理想状态下，IVs应该是 uncorrelated, 但实际上他们或多或少的会有一些相关性，当
: 相关性并不强或multicollinearity在可忍受范围内时，常常直接MODEL。但在弱相关的
: 情况下，IVs的Coeff显然受顺序的影响。比如
: Y =b1X1 + b2X2 + b0 算出来的coefficients 和
: Y =b2X2 + b1X1 + b0 不一样 (OLS)。
: 假设X1, X2 each accounts for 40% of Y variation when modeled separately, but
: when modeled together only account for 70% (as indicated by R square). So:
: 1) Can we say there is 10% (80%-70%) of Y variation explained jointly by X1,
: X2?
: 2) If so can we say b1 actually is calculated to reflect 40% variability of
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