Beta regression is commonly used when you want to model Y that are probabilities themselves.
This is evident when the value of Y is a proportion that ranges between 0 to 1. The data points of Y variable typically represent a proportion of events that form a subset of the total population (assuming that it follows a beta distribution).
Use Cases
- From GasolineYield data: Proportion of crude oil converted to gasoline after distillation and fractionation
- Proportion of individuals infected with ‘xyz’ when exposed to various levels of artificial preservative agent.
Example: Gasoline Yield
Lets predict the gasoline yield as a function of batch and temperature. 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)
#> 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)This page is based on the examples available in Beta regression vignette.