Description Usage Arguments Details Value See Also Examples
Various parameters that control fitting of beta regression models
using betareg
.
1 2 3 |
phi |
logical indicating whether the precision parameter
phi should be treated as a full model parameter ( |
method |
characters string specifying the |
maxit |
integer specifying the |
trace |
logical or integer controlling whether tracing information on
the progress of the optimization should be produced (passed to |
hessian |
logical. Should the numerical Hessian matrix from the |
start |
an optional vector with starting values for all parameters (including phi). |
fsmaxit |
integer specifying maximal number of additional (quasi) Fisher scoring iterations. For details see below. |
fstol |
numeric tolerance for convergence in (quasi) Fisher scoring. For details see below. |
... |
arguments passed to |
All parameters in betareg
are estimated by maximum likelihood
using optim
with control options set in betareg.control
.
Most arguments are passed on directly to optim
, and start
controls
how optim
is called.
After the optim
maximization, an additional (quasi) Fisher scoring
can be perfomed to further enhance the result or to perform additional bias reduction.
If fsmaxit
is greater than zero, this additional optimization is
performed and it converges if the threshold fstol
is attained
for the cross-product of the step size.
Starting values can be supplied via start
or estimated by
lm.wfit
, using the link-transformed response.
Covariances are in general derived analytically. Only if type = "ML"
and
hessian = TRUE
, they are determined numerically using the Hessian matrix
returned by optim
. In the latter case no Fisher scoring iterations are
performed.
The main parameters of interest are the coefficients in the linear predictor of the
model and the additional precision parameter phi which can either
be treated as a full model parameter (default) or as a nuisance parameter. In the latter case
the estimation does not change, only the reported information in output from print
,
summary
, or coef
(among others) will be different. See also examples.
A list with the arguments specified.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | options(digits = 4)
data("GasolineYield", package = "betareg")
## regression with phi as full model parameter
gy1 <- betareg(yield ~ batch + temp, data = GasolineYield)
gy1
## regression with phi as nuisance parameter
gy2 <- betareg(yield ~ batch + temp, data = GasolineYield, phi = FALSE)
gy2
## compare reported output
coef(gy1)
coef(gy2)
summary(gy1)
summary(gy2)
|
Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield)
Coefficients (mean model with logit link):
(Intercept) batch1 batch2 batch3 batch4 batch5
-6.160 1.728 1.323 1.572 1.060 1.134
batch6 batch7 batch8 batch9 temp
1.040 0.544 0.496 0.386 0.011
Phi coefficients (precision model with identity link):
(phi)
440
Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield, phi = FALSE)
Coefficients (mean model with logit link):
(Intercept) batch1 batch2 batch3 batch4 batch5
-6.160 1.728 1.323 1.572 1.060 1.134
batch6 batch7 batch8 batch9 temp
1.040 0.544 0.496 0.386 0.011
(Intercept) batch1 batch2 batch3 batch4 batch5
-6.15957 1.72773 1.32260 1.57231 1.05971 1.13375
batch6 batch7 batch8 batch9 temp (phi)
1.04016 0.54369 0.49590 0.38579 0.01097 440.27839
(Intercept) batch1 batch2 batch3 batch4 batch5
-6.15957 1.72773 1.32260 1.57231 1.05971 1.13375
batch6 batch7 batch8 batch9 temp
1.04016 0.54369 0.49590 0.38579 0.01097
Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield)
Standardized weighted residuals 2:
Min 1Q Median 3Q Max
-2.875 -0.815 0.160 0.838 2.048
Coefficients (mean model with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.159571 0.182325 -33.78 < 2e-16 ***
batch1 1.727729 0.101229 17.07 < 2e-16 ***
batch2 1.322597 0.117902 11.22 < 2e-16 ***
batch3 1.572310 0.116105 13.54 < 2e-16 ***
batch4 1.059714 0.102360 10.35 < 2e-16 ***
batch5 1.133752 0.103523 10.95 < 2e-16 ***
batch6 1.040162 0.106036 9.81 < 2e-16 ***
batch7 0.543692 0.109127 4.98 6.3e-07 ***
batch8 0.495901 0.108926 4.55 5.3e-06 ***
batch9 0.385793 0.118593 3.25 0.0011 **
temp 0.010967 0.000413 26.58 < 2e-16 ***
Phi coefficients (precision model with identity link):
Estimate Std. Error z value Pr(>|z|)
(phi) 440 110 4 6.3e-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: 0.962
Number of iterations: 51 (BFGS) + 3 (Fisher scoring)
Call:
betareg(formula = yield ~ batch + temp, data = GasolineYield, phi = FALSE)
Standardized weighted residuals 2:
Min 1Q Median 3Q Max
-2.875 -0.815 0.160 0.838 2.048
Coefficients (mean model with logit link):
Estimate Std. Error z value Pr(>|z|)
(Intercept) -6.159571 0.182325 -33.78 < 2e-16 ***
batch1 1.727729 0.101229 17.07 < 2e-16 ***
batch2 1.322597 0.117902 11.22 < 2e-16 ***
batch3 1.572310 0.116105 13.54 < 2e-16 ***
batch4 1.059714 0.102360 10.35 < 2e-16 ***
batch5 1.133752 0.103523 10.95 < 2e-16 ***
batch6 1.040162 0.106036 9.81 < 2e-16 ***
batch7 0.543692 0.109127 4.98 6.3e-07 ***
batch8 0.495901 0.108926 4.55 5.3e-06 ***
batch9 0.385793 0.118593 3.25 0.0011 **
temp 0.010967 0.000413 26.58 < 2e-16 ***
---
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: 0.962
Number of iterations: 51 (BFGS) + 3 (Fisher scoring)
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