I have fitted a logistic regression model (with 6 variables) and obtained a McFadden pseudo R-squared of 0.15. I am now seeking guidance on interpreting odds ratios in light of this value. My understanding is that an excellent fit falls within the range of 0.2 to 0.4 for the McFadden pseudo R-squared. Given the lower McFadden pseudo R-squared value, I am uncertain about the reliability and meaningfulness of interpreting odds ratios from this model. I would appreciate guidance on whether odds ratios can still provide meaningful insights in the context of a suboptimal fit?
(edit) The primary goal of my research is to determine whether a specific variable among the six predictors is a meaningful addition in explaining the dependent variable. I am interested in assessing its individual contribution and determining if it significantly enhances the model's explanatory power.
My initial thoughts about the conclusion were as follows: The obtained McFadden pseudo R-squared value of 0.15 indicates a suboptimal fit for the current model. Given this lower value, it is challenging to draw strong conclusions about the significance of any single variable in explaining the dependent variable. However, upon examining the odds ratios, it appears likely that the specific variable of interest has a notable influence on the dependent variable, even within the limitations of the current model. Based on this observation, it is plausible that including additional variables to improve the model fit could further strengthen the evidence of the variable's impact.
It is mainly this last section I am unsure of whether a conclusion like this is correct?