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Thread: Article on logistic regression - don't understand logic of statement.

  1. #16
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    Re: Article on logistic regression - don't understand logic of statement.




    Quote Originally Posted by noetsi View Post
    I would think so since the standardized coefficient in all the models he presents use the standard deviation of the predictor to standardize that predictor. I am not sure why a study would deliberately increase variation - usually you are trying to limit that I thought to limit standard errors
    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!


    Quote Originally Posted by noetsi View Post
    While I am at it, I have never understood why the following is true (because the metric for odds ratios is exactly the same for every coefficient - the liklihood of being in a given level of Y for a change in X). I know it is true, but I don't understand the logic of why - if X1 has an odds ratio of 2 and X2 has an odds ratio of 4 why isn't X2 having more impact on Y than X1 would?
    Odds ratios don't say much about the actual raw increase in the probability of success for a unit increase in the predictor.
    Code: 
    > (0.003988036/(1-0.003988036)) / (.001/(1-.001))
    [1] 4
    > (0.6666667/(1-0.6666667)) / (.5/(1-.5))
    [1] 2
    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.
    I don't have emotions and sometimes that makes me very sad.

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  3. #17
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    Re: Article on logistic regression - don't understand logic of statement.


    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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