Odds ratio and probabilities

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  • #903

    Hi,

    I’m facing some difficulties in interpreting the results of a logistic regression.

    The dependent variable is “carrying cash to the restaurant”.

    The odds ratio for Constant : 4.16

    The odds ratio for Budget: 1.38

    The article states:

    ‘Constant’ reflects the odds if all predictors have value ‘0’. In that case, according to the seventh line, the odds that a participant takes cash to the restaurant is ‘4.16 is to 1’, which means that there is four times as much chance to take cash to the restaurant than nót to take cash. If the predictor ‘budget’ changes from high to low (coded as 1), the chance that cash is taken to the restaurant increases with 1.38 (exp(B)). This means that the chance goes from 1.38*4.16= ‘4.7 is to 1’. If the budget is low, the chance to take cash is almost five times as high as not to take it.”

    I understand the reasoning about the Constant, I can interpret the Odds ratio but what about the last 2 sentences :

    This means that the chance goes from 1.38*4.16= ‘4.7 is to 1’. If the budget is low, the chance to take cash is almost five times as high as not to take it.

    Why do they multiply the odds ratio of the  Constant with the odd ratio of the Budget?

    And how would I express it in % ?

    Would it be:

    1.38 / (1+1.38) = 0.5798 so if the budget is low, the chance to take cash to the restaurant increases with 58 % ?

    Is that correct?

    Thank you so much for helping me out!

    #905
    Stephen Gorard
    Participant

    I think what you are reading is probably nonsense. It does not make sense either in maths or English.

    The Exp(B) is a simple multiplier. So 1.38 means (all other things equal) the dependent variable is 1.38 times more likely to be ‘true’ if Budget is ‘true’. Or 38% more.

    If Budget is ‘true’ then the odds of carrying cash become 5.75 (as opposed to the former 4.16).

    However, given the constant it seems they have a very unbalanced dependent variable (less than 20:80 in observed outcome frequency). Logistic regression only works well with near 50:50 splits in observed outcomes. My guess would be that this model explained very little extra variation. Imagine betting whether someone carries cash. I just always bet they do and I will be right over 80% of the time. You are told about the Budget variable. How much more often will you be right (over the more than 80% that I am right). My guess not much. This is the definition of a poor model. Did the authors even quote the amount of extra variation explained? Many do not (but imagine not citing the R value for linear regression!).

    #904

    Thank you for your comments!

    I will contact the authors of that paper because in statistical sense their interpretation indeed doesn’t make sense.

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