“The Standard Errors are usually smaller than they would be in the absence of Heteroskedasticity/Multicollinearity” I would assumed this would have been the opposite? (I am looking at the graph on pg 194 of book2) Would anyone be able to help my little brain out?
i remember getting confused by that. there was a whole post awhile back here that you might want to look for. but the cliffs notes version is that when heteroskedasticity is present, the standard errors are smaller than without, because they are ARTIFICIALLY TOO SMALL. you get a bad measure of standard error, it should be higher. so it makes the results look too good when the relationship isnt actually there hope this helps
Heteroskedasticity/Multicollinearity caused the standard errors to be artificially smaller. You cannot trust these small standard errors. One way to correct for Heteroskedasticity/Multicollinearity is to increase the standard errors (the way one would do that is not in the CFA curricullum, IMHO).
The Joey Notes version thinks that’s BS - Heteroscedasticity - Can have either effect on standard errors (which ought to seem reasonable because there are some infinite number of patterns of heteroscedascity). For example, in simple linear regression, a butterfly shape of residuals makes estimate standard error of slope too small while football shaped (Go Eli) residuals make estimated standard error too big. Multicollinearity - Always makes standard errors bigger than they would be without multicollinearity. The reason for this is that s.e. is about how well you are doing estimating a parameter - a small s.e. means you have a fine estimate of a parameter. If there are two or more collinear variables, they are clouding up the effects of each other.
wow Joey just when I thought i couldn’t like you more after all of your great answers you show that you are a giants fan… now i have even a bigger man crush!
I’m also, gulp, a Jets fan…
{joeyD just fell a notch or two}