Hi,
I really don't understand what you mean. Multicollinearity is a mathematical
problem, not statistical. If, as limit, X2=k*X1, the model matrix (X'X)^(-1)
is not invertible, and the algorithm should fail or report not reliable
results (coeff and St.Err very HUGE). Also, if X2 is approx k*X1 you obtain
estimates with huge coefficient of variation.
Then the St.Err are "correct" for any design matrix X: "they are well-able
to understand the structure of your data",
This is valid for any regression model;
Hope that helps you,
best,
vito
Dear list,
I would like to know the impact of concurvity , the non-parametric
>analogue of
multicollinearity, on the standard error of coeffients when we use GAM. I
wonder if the standard errors produced by summary.glm in S-plus can be
smaller than the true standard errors of the estimated parameter. For
example,
the model is
fit_ gam(mortality ~ lo(time) + pollution, .......)
where time and pollution are higly correlated. Do I need to worry that the
estimated standard errors are too small when multicolinearity exists?.
Can standard errors from summary.glm lead one to conclude that the effect
of pollution is statistically significant when in fact it is not? If the
standard errors
from summary.glm are not good estimates of the true standard errors, is
there
any other way to get the correct standard errors?
Thank you very much.
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