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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?

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It is routine to interpret linear models despite low $R^2$ values of $0.1$ or lower. There is a sense in which your McFadden $R^2$ of $0.15$ is better than a usual $R^2=0.15$ for a linear model, so I see no issue. I say this because $0.4$ is considered an excellent McFadden $R^2$, while such a value for the usual $R^2$ could be quite good but probably not excellent (though this is so hard to evaluate this without a context).

More concerning than the $R^2$ would be the model calibration and if the predicted probabilities are telling the truth, that is, if a predicted probability of $p$ really corresponds to the event happening with probability $p$. In other words, if you keep predicting events to happen with probabilities like $0.8$ and $0.9$ yet the events only happen $60\%$ of the time, those predicted probabilities are not honest. A model as simple as yours probably does not have major concerns about a lack of calibration, however.

Calibration is often examined graphically, such as through the rms::calibrate function in R discussed here or in Python through sklearn, discussed here.

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  • $\begingroup$ Thank you for your answer. I'm relatively new to this topic. While I've come across numerous sources mentioning that pseudo R-squared values in the range of 0.2 to 0.4 are considered "good," your response suggests that it is routine to interpret linear models with values of 0.1 or lower. I find interesting and would appreciate it if you could maybe provide me to any relevant sources that discuss the interpretation of low pseudo R-squared values? I understand that the interpretation of pseudo R-squared can be subjective and context-dependent, but any information would be appreciated. $\endgroup$
    – LeterPeko
    Jun 22, 2023 at 20:17
  • $\begingroup$ What do you mean by interpreting the pseudo $R^2$ values? $\endgroup$
    – Dave
    Jun 22, 2023 at 20:24
  • $\begingroup$ I have edited the question. I hope it gives you a better context of what I want to do. $\endgroup$
    – LeterPeko
    Jun 23, 2023 at 13:07
  • $\begingroup$ @LeterPeko It is routine to interpret models with pedestrian predictive power. $\endgroup$
    – Dave
    Jun 23, 2023 at 13:43

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