PSEUDO-R2 IN LOGISTIC REGRESSION MODEL
PSEUDO-R2 IN LOGISTIC REGRESSION MODEL
Key takeaways
Bibliography: Hu, B., Shao, J., Palta, M., 2006. PSEUDO-R2 IN LOGISTIC REGRESSION MODEL. Statistica Sinica 16, 847–860.
Authors:: Bo Hu, Jun Shao, Mari Palta
Collections:: Methods
First-page: 850
Logistic regression with binary and multinomial outcomes is commonly used, and researchers have long searched for an interpretable measure of the strength of a particular logistic model. This article describes the large sample properties of some pseudo-R2 statistics for assessing the predictive strength of the logistic regression model. We present theoretical results regarding the convergence and asymptotic normality of pseudo-R2s. Simulation results and an example are also presented. The behavior of the pseudo-R2s is investigated numerically across a range of conditions to aid in practical interpretation.
content: "@huPSEUDOR2LOGISTICREGRESSION2006" -file:@huPSEUDOR2LOGISTICREGRESSION2006
Reading notes
Imported on 2024-05-06 13:40
⭐ Important
- & Itisuseful toconsider whether the limits ofpseudo- R2 can beinterpreted muchas R2 can befor linear regression analysis. (p. 850)
- & limits tend toincrease asthe absolute value of increases with other parameters xed, whichisconsisten twith the behavior ofthe usual R2 inlinear regression models (p. 850)
- & However, wenote that the limits tend to below, even inmo dels where the parameters indicate arather strong association with the outcome. (p. 850)
- & As the pseudo-R2 measures do not correspond inmagnitude to what isfamiliar from R2 for ordinary regression (p. 851)
- & Itmaybenoted that neither R2 N nor R2 M can equal 1,except indegenerate models. This propertyisalogical consequence ofthe nature ofbinary outcomes. The denominator, 1 (L(~ ))2=n,equals the numerator when L( ^ )equals 1,whic h occurs only for adegenerate outcome that isalw ays0or1.In (p. 852)
- & anyperfectly tting model for binary data would predict probabilities that are only 0or1.This constitutes adegenerate logistic model, whichcannot be t. Incomparison t (p. 852)
- & PSEUDO-R2 INLOGISTIC REGRESSION MODEL 853 the R2 for alinear model, R2 of1implies residual variance of0.As the variance and entropyofbinomial and multinomial data depend on the mean, this again can occur only when the predicted probabilities are 0and 1.The mean-entropy dependence in uences the size ofthe pseudo-R2sand tends tokeep them away from 1evenwhen the mean probabilities are strongly dependentonthe covariate. (p. 853)