# When should you not use logistic regression GLM with a binary response variable?

I came across a set of data that does not seem to "flip" from 0 to 1 (binary response variable) when the predictor variable increase. Thus, this is the plot I got after plotting the variables. Should this not be used as a logistic generalized linear model with binomial family?

Since my glm fitting, and subsequent curve plotting gave a non-sigmoidal curve, that looks like below:

The curve came out non-sigmoidal unlike most, so did I not pick the right variables or should I not use this model to begin with?

It's not that the curve is non-sigmoidal, it's just that the left part of the sigmoid curve is cut off in the plot and doesn't have support from the data.

Your question amounts to, "what is the right model for my data?" This is a fundamentally unanswerable question. If we knew the answer we wouldn't need statistics. You can try many different models to see which has the best fit, e.g., using a measure of fit such as AIC or BIC. It's an empirical question of whether a binomial model with a logistic link is the best for this data. It might also be that the linear predictor could be specified better using terms beyond just a linear term, such as polynomials or splines, in addition to a change in link. Generalized additive models may be an effective way to improve the fit of the model. It's important to take measures against overfitting, though, such as cross-validation.

• I see that "review" or X4 are all positive, how can there be a need to extend the horizontal axis to the negative scale? thanks! Commented Dec 10, 2020 at 12:53
• I'm not talking about the data, I'm talking about the curve, which extends from -Inf to +Inf. You just only showed the part of the curve where your data lie, and in that part the sigmoid part of the curve is absent. But the curve is an inherent feature of logistic regression, not of your data.
– Noah
Commented Dec 10, 2020 at 21:20