I am testing a relationship between a continuous predictor and a binomial 0-1 outcome variable. My hypothesis is that the smaller the value of the predictor the more likely it is to fall into group 0 of the outcome variable.

My question is - How can I measure this specific relationship? I ONLY want to see if smaller numbers are more likely to fall into 0 category, and disregard the cases where higher numbers may fall into 0 category as well.

So far I was using the Binomial Logistic Regression in SPSS, but that tests the relationship between the value of the predictor and falling into 0 or 1 categories of the outcome. But I want to test the relationship only between smaller values of the predictor and falling into [0,1]. I don't want the cases of high predictors that fall into 0 to worsen my results. Also, deleting those cases is not an option because I need them for other hypotheses.

  • $\begingroup$ It sounds as if you should be looking at average outcome as a smoothed function of your predictor. Logit of outcome versus e.g. restricted cubic splines for your predictor is one of many possibilities. Note that nothing stops you omitting values from an analysis if you think that they are irrelevant to your purpose. $\endgroup$
    – Nick Cox
    Jun 16, 2013 at 13:32

1 Answer 1


This cannot be done. When you say "smaller numbers are more likely...." they have to be more likely than something, and that something is higher numbers.

You didn't say what the variables are, so I'll make up some: Let's say the DV is "Owns a home" and the IV is "income".

Now, you can ask "What proportion of people with income under $20,000 own a home?" and you can ask "Are people with lower incomes less likely to own homes (than people with higher incomes)?" and there are other questions you can ask too. But the question you ask has no possible answer, it is "Are people with low incomes less likely to own homes (than no one at all)?"

  • $\begingroup$ I thought it could be looked at as - Are lower values more likely to fall into 0 than to fall into 1. Would that make sense? $\endgroup$
    – IvLi
    Jun 16, 2013 at 13:39
  • $\begingroup$ Indeed, you can do that, as long as you define "lower values" with a cutoff. $\endgroup$
    – Peter Flom
    Jun 16, 2013 at 13:49

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