Looking here at the beta reg packge:
https://cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf
The code below is using a categorical batch variable and a continuous temp variable to predict yield which is (0,1). How does one interpret the coefficients. For example:
(1) batch1 has a coefficient of 1.72. This does NOT mean batch1 increases yield by 1.72%, relative to batch10-the reference group, because yield is between 0 and 1. Since the default betareg uses the logit link it appears the coefficient 1.72 is the log odds ratio and exp(1.72)= 5.58 is the odds ratio AND the interpretation is (using the odds ratio) that the batch 1 odds of "....." is 5.58 times higher than batch 10 the reference group.
I left "....." blank because if this was a typical logistic regression with 2 outcome categories (high yield and low yield) I would say the odds of batch 1 being in the high yield outcome category is 5.58 times higher than the odds of batch 10 the reference group. BUT with a beta regression the outcome is continuous so I cannot say "odds of batch 1 being in the high yield outcome category" because in a beta regression there is no category. SO what do you say: the batch 1 odds OF WHAT? is 5.58 times higher than the referecce group batch10.
(2) SImilarly for temp., increasing temp by 1 degree increases the odds OF WHAT? by 1.01 [exp(.01)] times?
(3) Apart from the vignette link above. Can you provide any references for intuitive explanations of the beta regression model? Can you the beta regression model have an identity link vs. logit? Intuitively what is the motivation for the logit link in the beta regression model?
Thank you.
> library(betareg)
> data("GasolineYield", package = "betareg")
> gy_logit <- betareg(yield ~ batch + temp, data = GasolineYield)
> summary(gy_logit)
Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield)
Standardized weighted residuals 2:
Min 1Q Median 3Q Max
-2.8750 -0.8149 0.1601 0.8384 2.0483
Coefficients (mean model with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.1595710 0.1823247 -33.784 < 2e-16 ***
batch1 1.7277289 0.1012294 17.067 < 2e-16 ***
batch2 1.3225969 0.1179020 11.218 < 2e-16 ***
batch3 1.5723099 0.1161045 13.542 < 2e-16 ***
batch4 1.0597141 0.1023598 10.353 < 2e-16 ***
batch5 1.1337518 0.1035232 10.952 < 2e-16 ***
batch6 1.0401618 0.1060365 9.809 < 2e-16 ***
batch7 0.5436922 0.1091275 4.982 6.29e-07 ***
batch8 0.4959007 0.1089257 4.553 5.30e-06 ***
batch9 0.3857930 0.1185933 3.253 0.00114 **
temp 0.0109669 0.0004126 26.577 < 2e-16 ***
Phi coefficients (precision model with identity link):
Estimate Std. Error z value Pr(>|z|)
(phi) 440.3 110.0 4.002 6.29e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Type of estimator: ML (maximum likelihood)
Log-likelihood: 84.8 on 12 Df
Pseudo R-squared: 0.9617
Number of iterations: 51 (BFGS) + 3 (Fisher scoring)
