Methods for betareg Objects
summary.betareg.RdMethods for extracting information from fitted beta
regression model objects of class "betareg".
Usage
# S3 method for class 'betareg'
summary(object, phi = NULL, type = "quantile", ...)
# S3 method for class 'betareg'
coef(object, model = c("full", "mean", "precision"), phi = NULL, ...)
# S3 method for class 'betareg'
vcov(object, model = c("full", "mean", "precision"), phi = NULL, ...)
# S3 method for class 'betareg'
bread(x, phi = NULL, ...)
# S3 method for class 'betareg'
estfun(x, phi = NULL, ...)Arguments
- object, x
fitted model object of class
"betareg".- phi
logical indicating whether the parameters in the precision model (for phi) should be reported as full model parameters (
TRUE) or nuisance parameters (FALSE). The default is taken fromobject$phi.- type
character specifying type of residuals to be included in the summary output, see
residuals.betareg.- model
character specifying for which component of the model coefficients/covariance should be extracted. (Only used if
phiisNULL.)- ...
currently not used.
Details
A set of standard extractor functions for fitted model objects is available for
objects of class "betareg", including methods to the generic functions
print and summary which print the estimated
coefficients along with some further information. The summary in particular
supplies partial Wald tests based on the coefficients and the covariance matrix.
As usual, the summary method returns an object of class "summary.betareg"
containing the relevant summary statistics which can subsequently be printed
using the associated print method.
A logLik method is provided, hence AIC
can be called to compute information criteria.
References
Cribari-Neto F, Zeileis A (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. doi:10.18637/jss.v034.i02
Ferrari SLP, Cribari-Neto F (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815.
Simas AB, Barreto-Souza W, Rocha AV (2010). Improved Estimators for a General Class of Beta Regression Models. Computational Statistics & Data Analysis, 54(2), 348–366.
Examples
options(digits = 4)
data("GasolineYield", package = "betareg")
gy2 <- betareg(yield ~ batch + temp | temp, data = GasolineYield)
summary(gy2)
#>
#> Call:
#> betareg(formula = yield ~ batch + temp | temp, data = GasolineYield)
#>
#> Quantile residuals:
#> Min 1Q Median 3Q Max
#> -2.104 -0.585 -0.143 0.690 2.520
#>
#> Coefficients (mean model with logit link):
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -5.923236 0.183526 -32.27 < 2e-16 ***
#> batch1 1.601988 0.063856 25.09 < 2e-16 ***
#> batch2 1.297266 0.099100 13.09 < 2e-16 ***
#> batch3 1.565338 0.099739 15.69 < 2e-16 ***
#> batch4 1.030072 0.063288 16.28 < 2e-16 ***
#> batch5 1.154163 0.065643 17.58 < 2e-16 ***
#> batch6 1.019445 0.066351 15.36 < 2e-16 ***
#> batch7 0.622259 0.065632 9.48 < 2e-16 ***
#> batch8 0.564583 0.060185 9.38 < 2e-16 ***
#> batch9 0.359439 0.067141 5.35 8.6e-08 ***
#> temp 0.010359 0.000436 23.75 < 2e-16 ***
#>
#> Phi coefficients (precision model with log link):
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.36409 1.22578 1.11 0.27
#> temp 0.01457 0.00362 4.03 5.7e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Type of estimator: ML (maximum likelihood)
#> Log-likelihood: 87 on 13 Df
#> Pseudo R-squared: 0.952
#> Number of iterations: 33 (BFGS) + 28 (Fisher scoring)
coef(gy2)
#> (Intercept) batch1 batch2 batch3
#> -5.92324 1.60199 1.29727 1.56534
#> batch4 batch5 batch6 batch7
#> 1.03007 1.15416 1.01944 0.62226
#> batch8 batch9 temp (phi)_(Intercept)
#> 0.56458 0.35944 0.01036 1.36409
#> (phi)_temp
#> 0.01457
vcov(gy2)
#> (Intercept) batch1 batch2 batch3 batch4
#> (Intercept) 3.368e-02 -4.124e-03 -8.216e-03 -8.839e-03 -3.672e-03
#> batch1 -4.124e-03 4.078e-03 2.483e-03 2.524e-03 2.189e-03
#> batch2 -8.216e-03 2.483e-03 9.821e-03 3.401e-03 2.395e-03
#> batch3 -8.839e-03 2.524e-03 3.401e-03 9.948e-03 2.427e-03
#> batch4 -3.672e-03 2.189e-03 2.395e-03 2.427e-03 4.005e-03
#> batch5 -4.461e-03 2.240e-03 2.548e-03 2.594e-03 2.206e-03
#> batch6 -3.902e-03 2.204e-03 2.439e-03 2.475e-03 2.178e-03
#> batch7 -3.007e-03 2.146e-03 2.267e-03 2.285e-03 2.133e-03
#> batch8 -6.259e-04 1.993e-03 1.804e-03 1.775e-03 2.013e-03
#> batch9 -1.801e-03 2.068e-03 2.031e-03 2.026e-03 2.072e-03
#> temp -7.753e-05 4.999e-06 1.504e-05 1.657e-05 3.891e-06
#> (phi)_(Intercept) -1.860e-02 1.682e-04 9.769e-04 1.420e-03 1.409e-04
#> (phi)_temp 4.618e-05 2.069e-07 -1.937e-06 -2.948e-06 6.530e-08
#> batch5 batch6 batch7 batch8 batch9
#> (Intercept) -4.461e-03 -3.902e-03 -3.007e-03 -6.259e-04 -1.801e-03
#> batch1 2.240e-03 2.204e-03 2.146e-03 1.993e-03 2.068e-03
#> batch2 2.548e-03 2.439e-03 2.267e-03 1.804e-03 2.031e-03
#> batch3 2.594e-03 2.475e-03 2.285e-03 1.775e-03 2.026e-03
#> batch4 2.206e-03 2.178e-03 2.133e-03 2.013e-03 2.072e-03
#> batch5 4.309e-03 2.223e-03 2.156e-03 1.977e-03 2.065e-03
#> batch6 2.223e-03 4.402e-03 2.140e-03 2.003e-03 2.070e-03
#> batch7 2.156e-03 2.140e-03 4.308e-03 2.044e-03 2.078e-03
#> batch8 1.977e-03 2.003e-03 2.044e-03 3.622e-03 2.100e-03
#> batch9 2.065e-03 2.070e-03 2.078e-03 2.100e-03 4.508e-03
#> temp 5.827e-06 4.454e-06 2.259e-06 -3.585e-06 -7.000e-07
#> (phi)_(Intercept) 1.011e-03 5.045e-04 -4.523e-04 -1.307e-03 -3.533e-04
#> (phi)_temp -2.185e-06 -8.969e-07 1.470e-06 3.675e-06 1.119e-06
#> temp (phi)_(Intercept) (phi)_temp
#> (Intercept) -7.753e-05 -1.860e-02 4.618e-05
#> batch1 4.999e-06 1.682e-04 2.069e-07
#> batch2 1.504e-05 9.769e-04 -1.937e-06
#> batch3 1.657e-05 1.420e-03 -2.948e-06
#> batch4 3.891e-06 1.409e-04 6.530e-08
#> batch5 5.827e-06 1.011e-03 -2.185e-06
#> batch6 4.454e-06 5.045e-04 -8.969e-07
#> batch7 2.259e-06 -4.523e-04 1.470e-06
#> batch8 -3.585e-06 -1.307e-03 3.675e-06
#> batch9 -7.000e-07 -3.533e-04 1.119e-06
#> temp 1.902e-07 4.666e-05 -1.175e-07
#> (phi)_(Intercept) 4.666e-05 1.503e+00 -4.342e-03
#> (phi)_temp -1.175e-07 -4.342e-03 1.309e-05
logLik(gy2)
#> 'log Lik.' 86.98 (df=13)
AIC(gy2)
#> [1] -148
coef(gy2, model = "mean")
#> (Intercept) batch1 batch2 batch3 batch4 batch5
#> -5.92324 1.60199 1.29727 1.56534 1.03007 1.15416
#> batch6 batch7 batch8 batch9 temp
#> 1.01944 0.62226 0.56458 0.35944 0.01036
coef(gy2, model = "precision")
#> (Intercept) temp
#> 1.36409 0.01457
summary(gy2, phi = FALSE)
#>
#> Call:
#> betareg(formula = yield ~ batch + temp | temp, data = GasolineYield)
#>
#> Quantile residuals:
#> Min 1Q Median 3Q Max
#> -2.104 -0.585 -0.143 0.690 2.520
#>
#> Coefficients (mean model with logit link):
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -5.923236 0.183526 -32.27 < 2e-16 ***
#> batch1 1.601988 0.063856 25.09 < 2e-16 ***
#> batch2 1.297266 0.099100 13.09 < 2e-16 ***
#> batch3 1.565338 0.099739 15.69 < 2e-16 ***
#> batch4 1.030072 0.063288 16.28 < 2e-16 ***
#> batch5 1.154163 0.065643 17.58 < 2e-16 ***
#> batch6 1.019445 0.066351 15.36 < 2e-16 ***
#> batch7 0.622259 0.065632 9.48 < 2e-16 ***
#> batch8 0.564583 0.060185 9.38 < 2e-16 ***
#> batch9 0.359439 0.067141 5.35 8.6e-08 ***
#> temp 0.010359 0.000436 23.75 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Type of estimator: ML (maximum likelihood)
#> Log-likelihood: 87 on 13 Df
#> Pseudo R-squared: 0.952
#> Number of iterations: 33 (BFGS) + 28 (Fisher scoring)