I am not sure whether the percent increase/decrease in odd ratios of binary logistic regression can be used as a measure of effect size in ordinal logistic regression too. I would greatly appreciate some pointers towards the estimation of effect size in ordinal logistic regression.
Thanks Fei. Yes, Pesudo-R2 and classification accuracy are some measures of how fit is the overall model. I am specifically talking about the relative importance of predictors in practical sense. Even though the predictors are statistically significant they might not substantial effect size to be of any importance in real life. In logistic regression, one such measure is the percentage change in odd ratios. I am not sure whether the same applies for ordinal logistic regression.
Hi Nabin,
A Stata program I authored - domin - (see: http://ideas.repec.org/c/boc/bocode/s457629.html) allows one to dominance analyze ordinal logistic regression using whatever model fit statistics you would like (though McFadden's pseudo r2 is aguably best). Dominance statistics can be interpreted in terms of relative importance (see Budescu, 1993; see also Budescu & Azen, 2004; Groemping, 2007).
I also have a paper about this topic that I can send along if you are interested.
- joe
Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. Psychological Bulletin, 114(3), 542.
Budescu, D. V., & Azen, R. (2004). Beyond global measures of relative importance: some insights from dominance analysis. Organizational Research Methods, 7(3), 341-350.
Grömping, U. (2007). Estimators of relative importance in linear regression based on variance decomposition. The American Statistician, 61(2)
Thank you Josehp for your response and references. I think our library should have these papers, if not I will write to you.
In my understanding McFadden's pseudo r2 is measure of overall fit of the model. I am also interested in measuring relative contributions of predictors in the model. I am not sure whether your approach address this issue too.
Nabin
Hi Nabin,
Dominance analysis provides 3 different fit statistics that all provide information about relative contribution to prediction using an r2.
The most general are called general dominance weights and are conceptually identical to Shapley values (http://en.wikipedia.org/wiki/Shapley_value) in that they are an exact additive decomposition of the r2 (decomposes into components that sum back to the overall r2). General dominance weights almost always allow rank ordering of predictors.
The second is conditional dominance weights - these are averaged r2's within a # of predictors in the model (i.e., there is a conditional dominance weight for every predictor and # of predictors - so for predictor X there is a conditional weight for 1 predictor in the model [by itself], 2 predictors in the model [X and another predictor] averaged across other predictors, 3 predictors in the model [X and 2 other predictors] averaged across predictors], etc.). If a predictor always obtains a higher conditional dominance weight than another predictor across all possible # of predictors, it "conditionally dominates" that other predictor.
The final and strongest criterion is "complete dominance" in which a predictor's contribution to r2 is compared to another predictor's contribution to r2 across all possible combinations of other predictors. If a predictor X _always_ obtains a higher r2 contribution than predictor Y across all combinations of predictors, then predictor X completely dominates predictor Y.
All this is in the help file for - domin -, and all these statistics are computed should you choose to use the program.
Hope this helps,
- joe
Thank you Malte. Yes, I am estimating an ordered logit model. I will check those books out.
Nabin
Thank you Alvin. I am wondering whether we can interpret Nagelkerke R2 or Pseudo R2 of the logistic regression as that of R2 of the OLS.
Nabin
Joseph Nicholas Luchman got this paper: Luchman, J. N. (2015). Determining subgroup difference importance with complex survey designs: An application of weighted dominance analysis. Survey Practice, 8(4). Retrieved from http://www.isr.umich.edu/src/smp/asda/Luchman%202015%20.pdf which is mentioned in this summary https://rmc.ehe.osu.edu/files/2018/08/DominanceAnalysisFeb2018.pdf
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