I created a binary logistic regression model with some results of goodness-to -fit tests as follow:
-Omnibus Test of Model Coefficient (Chi-sq.=22.471, p0.5)
- Classification table; overall correct percentage of prediction: 64%
-Cox & Snell R square: 0.079
-Nagelkerke R square: 0.106
Besides, I have some significant Odds ratio of parameters in the model.
My questions are:
1). Does the model's goodness of fit tests result matter with the significance of the B or Exp(B) ?
2) When interpreting the result, should the model's goodness of fit is not ideal, is it meaningful to conclude the significant predictors in the model?
Dear Danny,
There is no exact equivalent to R squared in binary logistic regression. The two R square alternatives you have mentioned are similar but they cannot be interpreted in terms of percentage of variance explained. Another useful measure is to compare the correct prediction % against the original constant model (with no variables). As in linear regression, this should be used in the context of parsimony, i.e. the best model is the one with the greatest explanatory power for the least complexity.
Dear Danny,
There is no exact equivalent to R squared in binary logistic regression. The two R square alternatives you have mentioned are similar but they cannot be interpreted in terms of percentage of variance explained. Another useful measure is to compare the correct prediction % against the original constant model (with no variables). As in linear regression, this should be used in the context of parsimony, i.e. the best model is the one with the greatest explanatory power for the least complexity.
There is no relation between percentage of explanation of variance and coefficient in a binary logistic regression model. The model coefficient for some independent variable depends on the scale of that independent variable, because what the model coefficient literally means is "a 1-unit increase in this variable is associated with a B increase in the log odds of the outcome". 1 unit of the independent variable could mean a lot of different things, depending on the distribution of that variable.
what is your c-index value? it looks like most important question to ask for binary logistic regression model.
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