In reference to the aforementioned example, the 6 variable model (McFadden’s pseudo $R^2$ = 0.192) fits the data better than the 5 variable model (McFadden’s pseudo $R^2$ = 0.131), which I formally tested using a log-likelihood ratio test, which indicates there is a significant difference ( p < 0.001) between the two models, and thus the 6 variable model is preferred for the given data set.Let's start our investigation of the coefficient of determination, r 2, by looking at two different examples - one example in which the relationship between the response y and the predictor x is very weak and a second example in which the relationship between the response y and the predictor x is fairly strong. It is also important to note that McFadden's pseudo $R^2$ is best used to compare different specifications of the same model (i.e. As such, the model mentioned above with a McFadden's pseudo $R^2$ of 0.192 is likely not a terrible model, at least by this metric, but it isn't particularly strong either.
I did some more focused research on this topic, and I found that interpretations of McFadden's pseudo $R^2$ (also known as likelihood-ratio index) are not clear however, it can range from 0 to 1, but will never reach or exceed 1 as a result of its calculation.Ī rule of thumb that I found to be quite helpful is that a McFadden's pseudo $R^2$ ranging from 0.2 to 0.4 indicates very good model fit. Last year I wrote a blog post about McFadden's $R^2$ in logistic regression, which has some further simulation illustrations. what constitutes a large correlation?), is that can never be a definitive answer. McFadden's $R^2$ is defined as $1 - LL_$ is close to zero, and McFadden's pseudo- $R^2$ squared is close to 1, indicating very good predictive ability.Īs to what can be considered a good value, my personal view is that like that similar questions in statistics (e.g. And values from 0.2-0.4 indicate (in McFadden's words) excellent model fit. So basically, $\rho^2$ can be interpreted like $R^2$, but don't expect it to be as big. Those unfamiliar with $\rho^2$ should be forewarned that its values tend to be considerably lower than those of the $R^2$ index.For example, values of 0.2 to 0.4 for $\rho^2$ represent EXCELLENT fit." McFadden states "while the $R^2$ index is a more familiar concept to planner who are experienced in OLS, it is not as well behaved as the $\rho^2$ measure, for ML estimation. Discussion of model evaluation (in the context of multinomial logit models) begins on page 306 where he introduces $\rho^2$ (McFadden's pseudo $R^2$). 15 "Quantitative Methods for Analyzing Travel Behaviour on Individuals: Some Recent Developments". Edited by David Hensher and Peter Stopher. The interpretation of McFadden's pseudo $R^2$ between 0.2-0.4 comes from a book chapter he contributed to: Bahvioural Travel Modelling. My interpretation is that larger values of $\rho^2$ (McFadden's pseudo $R^2$) are better than smaller ones. įigure 5.5 shows the relationship between $\rho^2$ and traditional $R^2$ measures from OLS. Zarembka (ed.), Frontiers in Econometrics. (1974) “Conditional logit analysis of qualitative choice behavior.” Pp. The seminal reference that I can see for McFadden's pseudo $R^2$ is: McFadden, D. So I figured I'd sum up what I've learned about McFadden's pseudo $R^2$ as a proper answer. Any insight and/or references are greatly appreciated! Before answering this question, I am aware that this isn't the best measure to describe a logistic regression model, but I would like to have a greater understanding of this statistic regardless! I have done a great deal of research on this topic, and I have yet to find the answer that I am looking for in terms of being able to interpret a McFadden's pseudo R-squared of 0.192. a given model that has a McFadden's pseudo R-squared of 0.192 is better than any existing model with a McFadden's pseudo R-squared of 0.180 (for even non-nested models)? These are just possible ways to look at McFadden’s pseudo R-squared however, I assume these two views are way off, thus the reason why I am asking this question here. Would we would want to keep that 6th variable in the model?) or is it an absolute quantity (e.g. a 6 variable model has a McFadden's pseudo R-squared of 0.192, whereas a 5 variable model (after removing one variable from the aforementioned 6 variable model), this 5 variable model has a pseudo R-squared of 0.131. Is it a relative comparison for nested models (e.g. What is the interpretation of this pseudo R-squared?
I have a binary logistic regression model with a McFadden's pseudo R-squared of 0.192 with a dependent variable called payment (1 = payment and 0 = no payment).
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