CowboyBear (06-26-2013), noetsi (06-26-2013)
We're trying to limit the variation that is left unexplained. Increasing the variation in the predictor actually decreases the standard error of the parameter estimates. If that's hard to get your head around then maybe a concrete example will help.
In both of these plots I simulated 30 values using: Y = 2 + 3*X + e where e~N(0,1). The only thing that is different is the range of x values I used.
Hopefully you'll believe that in the case where the range of x goes from 0 to 100 we will have much lower standard errors on our parameter estimates!
Odds ratios don't say much about the actual raw increase in the probability of success for a unit increase in the predictor.
So an increase in the probability of success from .001 to .0039 gives an odds ratio of 4. Increasing the probability of success from .5 to .6666 only gives an odds ratio of 2. The second one has a lower odds ratio but increases the raw probability of success by a much greater amount.Code:> (0.003988036/(1-0.003988036)) / (.001/(1-.001)) [1] 4 > (0.6666667/(1-0.6666667)) / (.5/(1-.5)) [1] 2
I don't have emotions and sometimes that makes me very sad.
CowboyBear (06-26-2013), noetsi (06-26-2013)
Thanks dason.
"Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995
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