Prediction Method for betareg Objects — predict.betareg • betareg

Extract various types of predictions from beta regression models: First, GLM-style predictions on the scale of responses in (0, 1) or the scale of the linear predictor are provided. Second, various quantities based on the predicted beta distributions are available, e.g., moments, quantiles, probabilities, densities, etc.

Usage

# S3 method for class 'betareg'
predict(object, newdata = NULL,
  type = c("response", "link", "precision", "variance", "parameters",
    "distribution", "density", "probability", "quantile"),
  na.action = na.pass, at = 0.5, elementwise = NULL, ...)

Arguments

object: fitted model object of class "betareg".
newdata: optionally, a data frame in which to look for variables with which to predict. If omitted, the original observations are used.
type: character indicating type of predictions: fitted means of the response (default, "response" or equivalently "mean"), corresponding linear predictor ("link"), fitted precision parameter phi ("precision"), fitted variances of the response ("variance"), all "parameters" of the response distribution, or the corresponding "distribution" object (using the infrastructure from distributions3). Finally, standard functions for the distribution can be evaluated (at argument at, see below), namely the "density" (or equivalently "pdf"), the "quantile" function, or the cumulative "probability" (or equivalently "cdf").
na.action: function determining what should be done with missing values in newdata. The default is to predict NA.
at: numeric vector at which the predictions should be evaluated if type specifies a function that takes an additional argument.
elementwise: logical. Should each element of the distribution only be evaluated at the corresponding element of at (elementwise = TRUE) or at all elements in at (elementwise = FALSE). Elementwise evaluation is only possible if the number of observations is the same as the length of at and in that case a vector of the same length is returned. Otherwise a matrix is returned. The default is to use elementwise = TRUE if possible, and otherwise elementwise = FALSE.
...: further arguments when type specifies a function, e.g., type = "density" with log = TRUE computes log-densities (or log-likelihoods).

Details

Each prediction for a betareg model internally first computes the parameters for all observations in newdata (or the original data if newdata is missing). These parameters correspond to a predicted beta distribution (or extended-support beta distribution) for each observation. Then the actual predictions can also be moments of the distributions or standard quantities such as densities, cumulative probabilities, or quantiles. The latter are computed with the d/p/q functions such as dbetar (or dxbetax or dxbeta).

Value

Either a vector or matrix of predictions with the same number of observations as rows in newdata.

Examples

options(digits = 4)

data("GasolineYield", package = "betareg")

gy2 <- betareg(yield ~ batch + temp | temp, data = GasolineYield)

cbind(
  predict(gy2, type = "response"),
  predict(gy2, type = "link"),
  predict(gy2, type = "precision"),
  predict(gy2, type = "variance"),
  predict(gy2, type = "quantile", at = c(0.25, 0.5, 0.75))
)
#>                                       q_0.25   q_0.5  q_0.75
#> 1  0.09997 -2.1976   77.56 1.145e-03 0.07549 0.09653 0.12074
#> 2  0.18658 -1.4724  215.06 7.024e-04 0.16816 0.18561 0.20394
#> 3  0.32143 -0.7472  596.36 3.651e-04 0.30842 0.32123 0.33422
#> 4  0.47379 -0.1049 1471.75 1.693e-04 0.46500 0.47378 0.48256
#> 5  0.08568 -2.3676   93.73 8.269e-04 0.06490 0.08273 0.10328
#> 6  0.14212 -1.7978  208.89 5.809e-04 0.12525 0.14097 0.15774
#> 7  0.26285 -1.0312  614.00 3.151e-04 0.25073 0.26259 0.27469
#> 8  0.10324 -2.1617   85.88 1.066e-03 0.07972 0.10017 0.12344
#> 9  0.17652 -1.5401  205.86 7.027e-04 0.15806 0.17547 0.19384
#> 10 0.30245 -0.8357  554.46 3.798e-04 0.28916 0.30221 0.31547
#> 11 0.07881 -2.4587  120.07 5.996e-04 0.06119 0.07647 0.09390
#> 12 0.14365 -1.7853  309.57 3.961e-04 0.12981 0.14288 0.15665
#> 13 0.24751 -1.1120  798.12 2.331e-04 0.23709 0.24730 0.25769
#> 14 0.34394 -0.6458 1537.51 1.467e-04 0.33573 0.34387 0.35208
#> 15 0.16957 -1.5887  342.81 4.096e-04 0.15556 0.16892 0.18287
#> 16 0.27545 -0.9671  821.72 2.426e-04 0.26484 0.27527 0.28586
#> 17 0.33691 -0.6771 1235.66 1.806e-04 0.32780 0.33683 0.34594
#> 18 0.10548 -2.1378  191.40 4.904e-04 0.08984 0.10410 0.11962
#> 19 0.23606 -1.1744  742.04 2.427e-04 0.22542 0.23583 0.24645
#> 20 0.32316 -0.7393 1368.34 1.597e-04 0.31459 0.32308 0.33164
#> 21 0.05383 -2.8665  120.07 4.207e-04 0.03893 0.05137 0.06608
#> 22 0.07928 -2.4521  215.06 3.379e-04 0.06624 0.07798 0.09091
#> 23 0.16906 -1.5923  720.73 1.946e-04 0.15949 0.16876 0.17831
#> 24 0.27063 -0.9914 1677.97 1.176e-04 0.26326 0.27054 0.27789
#> 25 0.08270 -2.4062  248.80 3.037e-04 0.07039 0.08158 0.09380
#> 26 0.17116 -1.5774  798.12 1.775e-04 0.16202 0.17088 0.18000
#> 27 0.31885 -0.7590 2523.27 8.604e-05 0.31257 0.31881 0.32509
#> 28 0.12701 -1.9276  650.84 1.701e-04 0.11801 0.12663 0.13560
#> 29 0.23661 -1.1714 1885.42 9.575e-05 0.22995 0.23651 0.24316
#> 30 0.10508 -2.1420  798.12 1.177e-04 0.09759 0.10475 0.11221
#> 31 0.11952 -1.9970  978.71 1.074e-04 0.11239 0.11926 0.12637
#> 32 0.18402 -1.4894 1998.57 7.509e-05 0.17811 0.18391 0.18980

## evaluate cumulative _p_robabilities for (small) new data set
gyd <- GasolineYield[c(1, 5, 10), ]

## CDF at 0.1 for each observation
predict(gy2, newdata = gyd, type = "probability", at = 0.1)
#> Warning: contrasts dropped from factor batch
#>         1         5        10 
#> 5.407e-01 7.165e-01 6.053e-40 

## CDF at each combination of 0.1/0.2 and observations
predict(gy2, newdata = gyd, type = "probability", at = c(0.1, 0.2))
#> Warning: contrasts dropped from factor batch
#>        p_0.1     p_0.2
#> 1  5.407e-01 9.933e-01
#> 5  7.165e-01 9.991e-01
#> 10 6.053e-40 5.828e-09

## CDF at elementwise combinations of 0.1/0.2/0.3 and observations
predict(gy2, newdata = gyd, type = "probability", at = c(0.1, 0.2, 0.3))
#> Warning: contrasts dropped from factor batch
#>      1      5     10 
#> 0.5407 0.9991 0.4549 
predict(gy2, newdata = gyd, type = "probability", at = c(0.1, 0.2, 0.3), elementwise = TRUE)
#> Warning: contrasts dropped from factor batch
#>      1      5     10 
#> 0.5407 0.9991 0.4549 

## CDF at all combinations of 0.1/0.2/0.3 and observations
predict(gy2, newdata = gyd, type = "probability", at = c(0.1, 0.2, 0.3), elementwise = FALSE)
#> Warning: contrasts dropped from factor batch
#>        p_0.1     p_0.2  p_0.3
#> 1  5.407e-01 9.933e-01 1.0000
#> 5  7.165e-01 9.991e-01 1.0000
#> 10 6.053e-40 5.828e-09 0.4549