Methods for betareg Objects

Description

Methods 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 from object$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 phi is NULL.)
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.

See Also

betareg

Examples

library("betareg")

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)