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I'm doing logistic regression with binary target and one categorical variable as input, but struggling to interpret how the test values and significance are so different (red on the picture below).

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Does it make sense to conclude there is an effect for a categorical variable but when looking at the parameter estimate, nothing is significant?

How do I interpret the results in this scenario?

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One possibility is that the reference category (Category D?) contains a very small number of observations. The three dummy variables compare the odds of success in "their" category with the odds of success in the reference category. So if we are very uncertain about the odds in the reference category, then that uncertainty will filter through to all the dummy variables, leading to large standard errors and non-significant results. To see if this is the case, you first look at the distribution of the categorical variable. If the reference category is indeed sparse, then you can change the reference category to the largest category.

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  • $\begingroup$ Thanks Maarten - you're right Category D is very sparse but when I switched the reference point I get similar results However, when I excluded Category D altogether, only then it's showing the significance. Can Category D still affect the results even not as a reference point? $\endgroup$ – woiya Apr 9 at 1:50
  • $\begingroup$ When you exclude Category D it does not magically disappear, instead it is merged with your new reference category. Say your reference category is Category A, then your reference category after also excluding Category D is actually Category A or Category D. So you have to make sure that that makes substantive sense. Sometimes it does, and there is no problem. However, sometimes it is clear nonsense, in which case your results will obviously also be clear nonsense. $\endgroup$ – Maarten Buis Apr 9 at 6:46
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The $\chi^2$ statistic tells you that the overall model explains something, i.~e. your model as a whole is not discarded. The parameter estimates tell you that you are not able to identify the influence of each single one parameter. Multicollinearity might be one of the reasons here. To dig into this further, I'd suggest running the regression while kicking out one the variables. You could also compare logit to a simple OLS specification (Linear Probability Model), as those coefficients are easier to interpret.

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  • $\begingroup$ The OP stated that this is a single categorical variable, so what we see as 3 variables are actually dummy/indicator variables that make up a single categorical variable. This means you cannot drop one of these without seriously changing the meaning of the remaining variables. So running multiple models kicking out one dummy variable each is in this case not a viable suggestion. $\endgroup$ – Maarten Buis Apr 8 at 13:50

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