Beta regression is commonly used to model variables that have values between 0 to 1, typically when the data points of Y variable represent a proportion of individuals from a subset of the total population (assuming that it follows a beta distribution). This often addresses the problem of heteroskedasticity.
Some examples of Y variables where beta regression would be appropriate
1. From GasolineYield data: Proportion of crude oil converted to gasoline after distillation and fractionation
2. Proportion of individuals infected with ‘xyz’ when exposed to various levels of artifical preservative agent 898D.
Example: Gasoline Yield
The example below shows an example implementation of beta regression using the GasolineYield data from betareg package.
library (betareg)
data("GasolineYield", package = "betareg") # initialize data
inputData <- GasolineYield # plug-in your data here
trainingIndex <- c(1:(nrow(inputData)-1)) # create row indices of training data
trainingData <- inputData[trainingIndex, ] # training data
testData <- inputData[-trainingIndex, ] # test data
betaMod <- betareg(yield ~ batch + temp, data = trainingData) # train model. Tune var names.
summary (betaMod) # model summary
predict (betaMod, testData) # predict on test data (0.19 vs actual 0.18)
# summary (betaMod)
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)
http://cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf
