Calculate the log likelihood of the binomial function (and its derivatives)
Source:R/llik.R
llikBeta.RdCalculate the log likelihood of the binomial function (and its derivatives)
Arguments
- x
Observation
- shape1, shape2
non-negative parameters of the Beta distribution.
- full
Add the data frame showing x, mean, sd as well as the fx and derivatives
Value
data frame with fx for the log pdf value of with
dShape1 and dShape2 that has the derivatives with respect to the parameters at
the observation time-point
Details
In an rxode2() model, you can use llikBeta() but you have to
use all arguments. You can also get the derivative of shape1 and shape2 with
llikBetaDshape1() and llikBetaDshape2().
Examples
# \donttest{
x <- seq(1e-4, 1 - 1e-4, length.out = 21)
llikBeta(x, 0.5, 0.5)
#> fx dShape1 dShape2
#> 1 3.46049030 -7.82404601 1.38619436
#> 2 0.37793108 -1.60763953 1.33490633
#> 3 0.05888752 -0.91549105 1.28084495
#> 4 -0.11510253 -0.51035907 1.22369308
#> 5 -0.22855163 -0.22284360 1.16307581
#> 6 -0.30780832 0.00019998 1.09854562
#> 7 -0.36444410 0.18245488 1.02956227
#> 8 -0.40444714 0.33655795 0.95546529
#> 9 -0.43118004 0.47005363 0.87543540
#> 10 -0.44655956 0.58780889 0.78843918
#> 11 -0.45158271 0.69314718 0.69314718
#> 12 -0.44655956 0.78843918 0.58780889
#> 13 -0.43118004 0.87543540 0.47005363
#> 14 -0.40444714 0.95546529 0.33655795
#> 15 -0.36444410 1.02956227 0.18245488
#> 16 -0.30780832 1.09854562 0.00019998
#> 17 -0.22855163 1.16307581 -0.22284360
#> 18 -0.11510253 1.22369308 -0.51035907
#> 19 0.05888752 1.28084495 -0.91549105
#> 20 0.37793108 1.33490633 -1.60763953
#> 21 3.46049030 1.38619436 -7.82404601
llikBeta(x, 1, 3, TRUE)
#> x shape1 shape2 fx dShape1 dShape2
#> 1 0.00010 1 3 1.09841228 -7.37700704 0.33323333
#> 2 0.05009 1 3 0.99583622 -1.16060056 0.28194530
#> 3 0.10008 1 3 0.88771347 -0.46845208 0.22788392
#> 4 0.15007 1 3 0.77340972 -0.06332009 0.17073205
#> 5 0.20006 1 3 0.65217518 0.22419538 0.11011478
#> 6 0.25005 1 3 0.52311481 0.44723895 0.04558459
#> 7 0.30004 1 3 0.38514811 0.62949385 -0.02339876
#> 8 0.35003 1 3 0.23695415 0.78359692 -0.09749574
#> 9 0.40002 1 3 0.07689437 0.91709260 -0.17752562
#> 10 0.45001 1 3 -0.09709808 1.03484786 -0.26452185
#> 11 0.50000 1 3 -0.28768207 1.14018615 -0.35981385
#> 12 0.54999 1 3 -0.49835866 1.23547815 -0.46515214
#> 13 0.59998 1 3 -0.73386918 1.32247438 -0.58290740
#> 14 0.64997 1 3 -1.00086054 1.40250426 -0.71640308
#> 15 0.69996 1 3 -1.30906667 1.47660124 -0.87050615
#> 16 0.74995 1 3 -1.67357647 1.54558459 -1.05276105
#> 17 0.79994 1 3 -2.11966363 1.61011478 -1.27580462
#> 18 0.84993 1 3 -2.69469457 1.67073205 -1.56332009
#> 19 0.89992 1 3 -3.50495854 1.72788392 -1.96845208
#> 20 0.94991 1 3 -4.88925549 1.78194530 -2.66060056
#> 21 0.99990 1 3 -17.32206846 1.83323333 -8.87700704
et <- et(seq(1e-4, 1-1e-4, length.out=21))
et$shape1 <- 0.5
et$shape2 <- 1.5
model <- function() {
model({
fx <- llikBeta(time, shape1, shape2)
dShape1 <- llikBetaDshape1(time, shape1, shape2)
dShape2 <- llikBetaDshape2(time, shape1, shape2)
})
}
rxSolve(model, et)
#>
#>
#>
#>
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#> # A tibble: 1 × 0
#> ── Initial Conditions ($inits): ──
#> named numeric(0)
#> ── First part of data (object): ──
#> # A tibble: 21 × 6
#> time fx dShape1 dShape2 shape1 shape2
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.0001 4.15 -6.82 0.386 0.5 1.5
#> 2 0.0501 1.02 -0.608 0.335 0.5 1.5
#> 3 0.100 0.647 0.0845 0.281 0.5 1.5
#> 4 0.150 0.415 0.490 0.224 0.5 1.5
#> 5 0.200 0.241 0.777 0.163 0.5 1.5
#> 6 0.250 0.0976 1.00 0.0985 0.5 1.5
#> # ℹ 15 more rows
# }