I have found a way to approach the question that I posed, that is
having deriv and deriv3 deal with an indexed term in the formula.
Unless, there is a more direct approach (and my minimal investigation
of the code involved suggested that it would not be simple to implement,
for me at least), this should be tractable as long as the number of
elements indexed is not too large. In short, I reparameterize the problem
so that each of the indices corresponds to a separate column in the
data.frame. Then, I can apply both deriv and deriv3, the only
post-editing of the functions being to deal with the derivative at 0,
because a log appears.
For anyone interested, here is the example:
gg <- model.matrix(~-1 + Gun/GL, ddsub)[1:51, c(4:6)]
ddsub$Rgun <- gg[, 1]
ddsub$Ggun <- gg[, 2]
ddsub$Bgun <- gg[, 3]
dd.der3 <- deriv3(f, c("Blev", "Br", "Bg", "Bb", "gamm"),
function(Blev, Br, Bg, Bb, gamm, Rgun, Ggun, Bgun) {})
###edit to deal with log(0) case
dd.der3 <- function (Blev, Br, Bg, Bb, gamm, Rgun, Ggun, Bgun)
{
.expr1 <- Rgun^gamm
.expr4 <- Ggun^gamm
.expr7 <- Bgun^gamm
.expr10 <- ifelse(Rgun == 0, 0, log(Rgun))
.expr11 <- .expr1 * .expr10
.expr12 <- ifelse(Ggun == 0, 0, log(Ggun))
.expr13 <- .expr4 * .expr12
.expr14 <- ifelse(Bgun == 0, 0, log(Bgun))
.expr15 <- .expr7 * .expr14
.value <- Blev + Br * .expr1 + Bg * .expr4 + Bb * .expr7
.grad <- array(0, c(length(.value), 5), list(NULL, c("Blev",
"Br", "Bg", "Bb", "gamm")))
.hessian <- array(0, c(length(.value), 5, 5), list(NULL,
c("Blev", "Br", "Bg", "Bb", "gamm"), c("Blev", "Br",
"Bg", "Bb", "gamm")))
.grad[, "Blev"] <- 1
.grad[, "Br"] <- .expr1
.hessian[, "Br", "Br"] <- 0
.hessian[, "Br", "Bg"] <- .hessian[, "Bg", "Br"] <- 0
.hessian[, "Br", "Bb"] <- .hessian[, "Bb", "Br"] <- 0
.hessian[, "Br", "gamm"] <- .hessian[, "gamm", "Br"] <- .expr11
.grad[, "Bg"] <- .expr4
.hessian[, "Bg", "Bg"] <- 0
.hessian[, "Bg", "Bb"] <- .hessian[, "Bb", "Bg"] <- 0
.hessian[, "Bg", "gamm"] <- .hessian[, "gamm", "Bg"] <- .expr13
.grad[, "Bb"] <- .expr7
.hessian[, "Bb", "Bb"] <- 0
.hessian[, "Bb", "gamm"] <- .hessian[, "gamm", "Bb"] <- .expr15
.grad[, "gamm"] <- Br * .expr11 + Bg * .expr13 + Bb * .expr15
.hessian[, "gamm", "gamm"] <- Br * (.expr11 * .expr10) +
Bg * (.expr13 * .expr12) + Bb * (.expr15 * .expr14)
attr(.value, "gradient") <- .grad
attr(.value, "hessian") <- .hessian
.value
}
dd.nls.d4 <- nls(Lum ~ dd.der3(Blev, Br, Bg, Bb, gamm,
Rgun, Ggun, Bgun),
data = ddsub,
start = list(Blev = B[2], Br = B[3], Bg = B[4] , Bb = B[5],
gamm = B[1])
)
summary(dd.nls.d4)
Formula: Lum ~ dd.der3(Blev, Br, Bg, Bb, gamm, Rgun, Ggun, Bgun)
Parameters:
Estimate Std. Error t value Pr(>|t|)
Blev -0.06552 0.04766 -1.375 0.176
Br 16.74186 0.13245 126.402 <2e-16 ***
Bg 50.51605 0.14802 341.281 <2e-16 ***
Bb 8.12063 0.13452 60.368 <2e-16 ***
gamm 2.51187 0.01561 160.916 <2e-16 ***
confint(dd.nls.d4)
Waiting for profiling to be done...
2.5% 97.5%
Blev -0.1612492 0.02988387
Br 16.4752317 17.00843251
Bg 50.2193167 50.81325840
Bb 7.8496610 8.39135292
gamm 2.4811018 2.54296647
ms.curv(dd.nls.d4)
Parameter effects: c^theta x sqrt(F) = 0.0123
Intrinsic: c^iota x sqrt(F) = 0.0068
Here is the data.frame after the new columns have been added,
Lum GL Gun Rgun Ggun Bgun
0.15 0 rouge 0 0 0
0.07 0.0588 rouge 0.0588 0 0
0.1 0.1216 rouge 0.1216 0 0
0.19 0.1843 rouge 0.1843 0 0
0.4 0.2471 rouge 0.2471 0 0
0.73 0.3098 rouge 0.3098 0 0
1.2 0.3725 rouge 0.3725 0 0
1.85 0.4353 rouge 0.4353 0 0
2.91 0.498 rouge 0.498 0 0
3.74 0.5608 rouge 0.5608 0 0
5.08 0.6235 rouge 0.6235 0 0
6.43 0.6863 rouge 0.6863 0 0
8.06 0.749 rouge 0.749 0 0
9.84 0.8118 rouge 0.8118 0 0
12 0.8745 rouge 0.8745 0 0
14.2 0.9373 rouge 0.9373 0 0
16.6 1 rouge 1 0 0
0.1 0 vert 0 0 0
0.1 0.0588 vert 0 0.0588 0
0.17 0.1216 vert 0 0.1216 0
0.46 0.1843 vert 0 0.1843 0
1.08 0.2471 vert 0 0.2471 0
2.22 0.3098 vert 0 0.3098 0
3.74 0.3725 vert 0 0.3725 0
5.79 0.4353 vert 0 0.4353 0
8.36 0.498 vert 0 0.498 0
11.6 0.5608 vert 0 0.5608 0
15.4 0.6235 vert 0 0.6235 0
19.9 0.6863 vert 0 0.6863 0
24.6 0.749 vert 0 0.749 0
30.4 0.8118 vert 0 0.8118 0
36.1 0.8745 vert 0 0.8745 0
43 0.9373 vert 0 0.9373 0
49.9 1 vert 0 1 0
0.06 0 bleu 0 0 0
0.06 0.0588 bleu 0 0 0.0588
0.08 0.1216 bleu 0 0 0.1216
0.13 0.1843 bleu 0 0 0.1843
0.25 0.2471 bleu 0 0 0.2471
0.43 0.3098 bleu 0 0 0.3098
0.66 0.3725 bleu 0 0 0.3725
1.02 0.4353 bleu 0 0 0.4353
1.46 0.498 bleu 0 0 0.498
1.93 0.5608 bleu 0 0 0.5608
2.49 0.6235 bleu 0 0 0.6235
3.2 0.6863 bleu 0 0 0.6863
3.96 0.749 bleu 0 0 0.749
4.9 0.8118 bleu 0 0 0.8118
5.68 0.8745 bleu 0 0 0.8745
6.71 0.9373 bleu 0 0 0.9373
7.93 1 bleu 0 0 1
I still do not know why confint does not work for me on this problem
without the derivatives and it does for Gabor. I'm on a Mac Pro and
he may not be. If anyone else on a Mac has this problem, it would
be useful to know.
Thanks.
ken
Gabor Grothendieck wrote:
> I mixed up examples. Here it is again. As with the last one
> confint(dd.plin) gives an error (which I assume is a problem with
> confint that needs to be fixed) but other than that it works without
> issuing errors and I assume you don't need the confint(dd.plin)
> in any case since dd.plin is just being used to get starting values.
>
>> gg <- model.matrix(~ Gun/GL - Gun, dd)
>> dd.plin <- nls(Lum ~ gg^gamm, dd, start = list(gamm = 2.4),
> + alg = "plinear"
> + )
>> confint(dd.plin)
> Waiting for profiling to be done...
> Error in eval(expr, envir, enclos) : (subscript) logical subscript too
> long
>>
>>
>> B <- as.vector(coef(dd.plin))
>> st <-list(Blev = B[2], beta = B[3:5], gamm = B[1])
>>
>>
>>
>> dd.nls <- nls(Lum ~ Blev + beta[Gun] * GL^gamm,
> + data = dd, start = st
> + )
>>
>> confint(dd.nls)
> Waiting for profiling to be done...
> 2.5% 97.5%
> Blev -1.612492e-01 2.988387e-02
> beta1 6.108282e-06 8.762679e-06
> beta2 1.269000e-05 1.792914e-05
> beta3 3.844042e-05 5.388546e-05
> gamm 2.481102e+00 2.542966e+00
>>
>> dd.deriv2 <- function (Blev, beta, gamm, GL)
> + {
> + .expr1 <- GL^gamm
> + .value <- Blev + rep(beta, each = 17) * .expr1
> + .grad <- array(0, c(length(.value), 5), list(NULL, c("Blev",
> + "beta.rouge", "beta.vert", "beta.bleu", "gamm")))
> + .grad[, "Blev"] <- 1
> + .grad[1:17, "beta.rouge"] <- .expr1[1:17]
> + .grad[18:34, "beta.vert"] <- .expr1[1:17]
> + .grad[35:51, "beta.bleu"] <- .expr1[1:17]
> + .grad[, "gamm"] <- ifelse(GL == 0, 0, rep(beta, each = 17) * (.expr1
> *
> + log(GL)))
> + attr(.value, "gradient") <- .grad
> + .value
> + }
>>
>>
>> dd.nls.d2 <- nls(Lum ~ dd.deriv2(Blev, beta, gamm, GL), data = dd,
> + start = list(Blev = B[2], beta = B[3:5], gamm =
> B[1]))
>>
>> confint(dd.nls.d2)
> Waiting for profiling to be done...
> 2.5% 97.5%
> Blev -1.612492e-01 2.988391e-02
> beta1 1.269000e-05 1.792914e-05
> beta2 3.844041e-05 5.388546e-05
> beta3 6.108281e-06 8.762678e-06
> gamm 2.481102e+00 2.542966e+00
>>
>> R.version.string # XP
> [1] "R version 2.4.0 Patched (2006-10-24 r39722)"
>>
>
>
> On 11/18/06, Gabor Grothendieck <[EMAIL PROTECTED]> wrote:
>> This works for me in terms of giving results without error messages
>> except for the confint(dd.plin) which I assume you don't really need
>> anyways.
>>
>> > gg <- model.matrix(~ Gun/GL - Gun, dd)
>> > dd.plin <- nls(Lum ~ gg^gamm, dd, start = list(gamm = 2.4),
>> + alg = "plinear"
>> + )
>> > confint(dd.plin)
>> Waiting for profiling to be done...
>> Error in eval(expr, envir, enclos) : (subscript) logical subscript too
>> long
>> >
>> >
>> > B <- as.vector(coef(dd.nls0))
>> > st <-list(Blev = B[2], beta = B[3:5], gamm = B[1])
>> >
>> >
>> >
>> > dd.nls <- nls(Lum ~ Blev + beta[Gun] * GL^gamm,
>> + data = dd, start = st
>> + )
>> >
>> > confint(dd.nls)
>> Waiting for profiling to be done...
>> 2.5% 97.5%
>> Blev -1.612492e-01 2.988386e-02
>> beta1 6.108282e-06 8.762679e-06
>> beta2 1.269000e-05 1.792914e-05
>> beta3 3.844042e-05 5.388546e-05
>> gamm 2.481102e+00 2.542966e+00
>> >
>> > dd.deriv2 <- function (Blev, beta, gamm, GL)
>> + {
>> + .expr1 <- GL^gamm
>> + .value <- Blev + rep(beta, each = 17) * .expr1
>> + .grad <- array(0, c(length(.value), 5), list(NULL, c("Blev",
>> + "beta.rouge", "beta.vert", "beta.bleu", "gamm")))
>> + .grad[, "Blev"] <- 1
>> + .grad[1:17, "beta.rouge"] <- .expr1[1:17]
>> + .grad[18:34, "beta.vert"] <- .expr1[1:17]
>> + .grad[35:51, "beta.bleu"] <- .expr1[1:17]
>> + .grad[, "gamm"] <- ifelse(GL == 0, 0, rep(beta, each = 17) *
>> (.expr1 *
>> + log(GL)))
>> + attr(.value, "gradient") <- .grad
>> + .value
>> + }
>> >
>> >
>> > dd.nls.d2 <- nls(Lum ~ dd.deriv2(Blev, beta, gamm, GL), data = dd,
>> + start = list(Blev = B[2], beta = B[3:5], gamm =
>> B[1]))
>> >
>> > confint(dd.nls.d2)
>> Waiting for profiling to be done...
>> 2.5% 97.5%
>> Blev -1.612492e-01 2.988391e-02
>> beta1 1.269000e-05 1.792914e-05
>> beta2 3.844041e-05 5.388546e-05
>> beta3 6.108281e-06 8.762678e-06
>> gamm 2.481102e+00 2.542966e+00
>> >
>> > R.version.string # XP
>> [1] "R version 2.4.0 Patched (2006-10-24 r39722)"
>> >
>>
>>
>> On 11/18/06, Ken Knoblauch <[EMAIL PROTECTED]> wrote:
>> > Thank you for your rapid response.
>> >
>> > This is reproducible on my system. Here it is again, with, I hope,
>> > sufficient detail to properly document what does not work and what
>> > does on my system,
>> >
>> > But my original question, properly motivated or not, concerns whether
>> > there is a way to use or adapt deriv() to work if a term is indexed,
>> > as here my term beta is indexed by Gun?
>> >
>> > In any case, it is puzzling that the error is not reproducible and so
>> > I would be curious to track that down, if it is specific to my system.
>> >
>> > Thank you. Before retrying, I upgraded to the latest patched version
>> > (details at the end).
>> >
>> > ####The data, again
>> > dd
>> > Lum GL Gun mBl
>> > 0.15 0 rouge 0.09
>> > 0.07 15 rouge 0.01
>> > 0.1 31 rouge 0.04
>> > 0.19 47 rouge 0.13
>> > 0.4 63 rouge 0.34
>> > 0.73 79 rouge 0.67
>> > 1.2 95 rouge 1.14
>> > 1.85 111 rouge 1.79
>> > 2.91 127 rouge 2.85
>> > 3.74 143 rouge 3.68
>> > 5.08 159 rouge 5.02
>> > 6.43 175 rouge 6.37
>> > 8.06 191 rouge 8
>> > 9.84 207 rouge 9.78
>> > 12 223 rouge 11.94
>> > 14.2 239 rouge 14.14
>> > 16.6 255 rouge 16.54
>> > 0.1 0 vert 0.04
>> > 0.1 15 vert 0.04
>> > 0.17 31 vert 0.11
>> > 0.46 47 vert 0.4
>> > 1.08 63 vert 1.02
>> > 2.22 79 vert 2.16
>> > 3.74 95 vert 3.68
>> > 5.79 111 vert 5.73
>> > 8.36 127 vert 8.3
>> > 11.6 143 vert 11.54
>> > 15.4 159 vert 15.34
>> > 19.9 175 vert 19.84
>> > 24.6 191 vert 24.54
>> > 30.4 207 vert 30.34
>> > 36.1 223 vert 36.04
>> > 43 239 vert 42.94
>> > 49.9 255 vert 49.84
>> > 0.06 0 bleu 0
>> > 0.06 15 bleu 0
>> > 0.08 31 bleu 0.02
>> > 0.13 47 bleu 0.07
>> > 0.25 63 bleu 0.19
>> > 0.43 79 bleu 0.37
>> > 0.66 95 bleu 0.6
>> > 1.02 111 bleu 0.96
>> > 1.46 127 bleu 1.4
>> > 1.93 143 bleu 1.87
>> > 2.49 159 bleu 2.43
>> > 3.2 175 bleu 3.14
>> > 3.96 191 bleu 3.9
>> > 4.9 207 bleu 4.84
>> > 5.68 223 bleu 5.62
>> > 6.71 239 bleu 6.65
>> > 7.93 255 bleu 7.87
>> >
>> > ###For initial values - this time using plinear algorithm insted of
>> optim
>> > gg <- model.matrix(~-1 + Gun/GL, dd)[ , c(4:6)]
>> > dd.plin <- nls(Lum ~ cbind(rep(1, 51), gg^gamm), data = dd,
>> > start = list(gamm = 2.4),
>> > alg = "plinear"
>> > )
>> > B <- as.vector(coef(dd.plin))
>> > st <-list(Blev = B[2], beta = B[3:5], gamm = B[1])
>> >
>> >
>> > dd.nls <- nls(Lum ~ Blev + beta[Gun] * GL^gamm,
>> > data = dd, start = st
>> > )
>> > confint(dd.plin)
>> >
>> > Waiting for profiling to be done...
>> > Error in eval(expr, envir, enclos) : (subscript) logical subscript too
>> long
>> > ### Here is the error that I observe
>> > confint(dd.nls)
>> > Waiting for profiling to be done...
>> > Error in prof$getProfile() : step factor 0.000488281 reduced below
>> > 'minFactor' of 0.000976562
>> >
>> > dd.deriv2 <- function (Blev, beta, gamm, GL)
>> > {
>> > .expr1 <- GL^gamm
>> > .value <- Blev + rep(beta, each = 17) * .expr1
>> > .grad <- array(0, c(length(.value), 5), list(NULL, c("Blev",
>> > "beta.rouge", "beta.vert", "beta.bleu", "gamm")))
>> > .grad[, "Blev"] <- 1
>> > .grad[1:17, "beta.rouge"] <- .expr1[1:17]
>> > .grad[18:34, "beta.vert"] <- .expr1[1:17]
>> > .grad[35:51, "beta.bleu"] <- .expr1[1:17]
>> > .grad[, "gamm"] <- ifelse(GL == 0, 0, rep(beta, each = 17) *
>> (.expr1 *
>> > log(GL)))
>> > attr(.value, "gradient") <- .grad
>> > .value
>> > }
>> >
>> > dd.nls.d2 <- nls(Lum ~ dd.deriv2(Blev, beta, gamm, GL), subset(dd, Gun
>> !=
>> > "gris"),
>> > start = list(Blev = B[2], beta = B[3:5], gamm =
>> B[1]))
>> >
>> >
>> > #####But not here
>> > confint(dd.nls.d2)
>> > Waiting for profiling to be done...
>> > 2.5% 97.5%
>> > Blev -1.612492e-01 2.988387e-02
>> > beta1 1.269000e-05 1.792914e-05
>> > beta2 3.844042e-05 5.388546e-05
>> > beta3 6.108282e-06 8.762679e-06
>> > gamm 2.481102e+00 2.542966e+00
>> >
>> > R version 2.4.0 Patched (2006-11-16 r39921)
>> > i386-apple-darwin8.8.1
>> >
>> > locale:
>> > C
>> >
>> > attached base packages:
>> > [1] "stats" "graphics" "grDevices" "utils" "datasets"
>> > [6] "methods" "base"
>> >
>> > other attached packages:
>> > MASS lattice
>> > "7.2-29" "0.14-13"
>> >
>> > best,
>> >
>> > ken
>> >
>> >
>> > Gabor Grothendieck wrote:
>> > > Please provide reproducible code which shows the error.
>> > >
>> > >>
>> > >> st <- list(Blev = -0.06551802, beta = c(1.509686e-05, 4.55525e-05,
>> > > + 7.32272e-06), gamm = 2.51187)
>> > >>
>> > >> dd.nls <- nls(Lum ~ Blev + beta[Gun] * GL^gamm,
>> > > + data = dd, start = st)
>> > >>
>> > >> confint(dd.nls)
>> > > Waiting for profiling to be done...
>> > > 2.5% 97.5%
>> > > Blev -1.612492e-01 2.988388e-02
>> > > beta1 6.108282e-06 8.762679e-06
>> > > beta2 1.269000e-05 1.792914e-05
>> > > beta3 3.844042e-05 5.388546e-05
>> > > gamm 2.481102e+00 2.542966e+00
>> > >> R.version.string
>> > > [1] "R version 2.4.0 Patched (2006-10-24 r39722)"
>> > >
>> > >
>> > >
>> > >
>> > > On 11/17/06, Ken Knoblauch <[EMAIL PROTECTED]> wrote:
>> > >> Hi,
>> > >>
>> > >> I'm fitting a standard nonlinear model to the luminances measured
>> > >> from the red, green and blue guns of a TV display, using nls.
>> > >>
>> > >> The call is:
>> > >>
>> > >> dd.nls <- nls(Lum ~ Blev + beta[Gun] * GL^gamm,
>> > >> data = dd, start = st)
>> > >> where st was initally estimated using optim()
>> > >>
>> > >> st
>> > >> $Blev
>> > >> [1] -0.06551802
>> > >>
>> > >> $beta
>> > >> [1] 1.509686e-05 4.555250e-05 7.322720e-06
>> > >>
>> > >> $gamm
>> > >> [1] 2.511870
>> > >>
>> > >> This works fine but I received an error message when I tried to
>> > >> use confint(). I thought that getting derivatives with deriv might
>> > >> help but found that deriv does not automatically handle the
>> > >> indexing of the beta parameter. I modified the output of deriv
>> > >> from the case when the term beta is not indexed to give:
>> > >>
>> > >> dd.deriv2 <- function (Blev, beta, gamm, GL)
>> > >> {
>> > >> .expr1 <- GL^gamm
>> > >> .value <- Blev + rep(beta, each = 17) * .expr1
>> > >> .grad <- array(0, c(length(.value), 5), list(NULL, c("Blev",
>> > >> "beta.rouge", "beta.vert", "beta.bleu", "gamm" )))
>> > >> .grad[, "Blev"] <- 1
>> > >> .grad[1:17, "beta.rouge"] <- .expr1[1:17]
>> > >> .grad[18:34, "beta.vert"] <- .expr1[1:17]
>> > >> .grad[35:51, "beta.bleu"] <- .expr1[1:17]
>> > >> .grad[, "gamm"] <- ifelse(GL == 0, 0, rep(beta, each = 17) *
>> (.expr1
>> > >> *
>> > >> log(GL)))
>> > >> attr(.value, "gradient") <- .grad
>> > >> .value
>> > >> }
>> > >>
>> > >> which is not general but
>> > >> now I can get a result from confint. My question: Can deriv()
>> > >> be made to handle an indexed term more automatically (elegantly)?
>> > >> I think that this would become more urgent (or require more work
>> > >> on my part) if I were to want the Hessian, too, for example, in
>> > >> anticipation of using rms.curv as described in the on-line
>> > >> complements for MASS.
>> > >>
>> > >> The plinear algorithm can be used for this model (it is similar in
>> some
>> > >> respects to the example given on p 218 of MASS, but the intercept
>> > >> terms are indexed instead, there).
>> > >>
>> > >> Thanks for any suggestions.
>> > >>
>> > >> best,
>> > >>
>> > >> Ken
>> > >>
>> > >>
>> > >> --
>> > >> Ken Knoblauch
>> > >> Inserm U371
>> > >> Institut Cellule Souche et Cerveau
>> > >> Département Neurosciences Intégratives
>> > >> 18 avenue du Doyen Lépine
>> > >> 69500 Bron
>> > >> France
>> > >> tel: +33 (0)4 72 91 34 77
>> > >> fax: +33 (0)4 72 91 34 61
>> > >> portable: +33 (0)6 84 10 64 10
>> > >> http://www.lyon.inserm.fr/371/
>> > >>
>> > >> ______________________________________________
>> > >> [email protected] mailing list
>> > >> https://stat.ethz.ch/mailman/listinfo/r-help
>> > >> PLEASE do read the posting guide
>> > >> http://www.R-project.org/posting-guide.html
>> > >> and provide commented, minimal, self-contained, reproducible code.
>> > >>
>> > >
>> >
>> >
>> > --
>> > Ken Knoblauch
>> > Inserm U371
>> > Institut Cellule Souche et Cerveau
>> > Département Neurosciences Intégratives
>> > 18 avenue du Doyen Lépine
>> > 69500 Bron
>> > France
>> > tel: +33 (0)4 72 91 34 77
>> > fax: +33 (0)4 72 91 34 61
>> > portable: +33 (0)6 84 10 64 10
>> > http://www.lyon.inserm.fr/371/
>> >
>> >
>>
>
--
Ken Knoblauch
Inserm U371
Institut Cellule Souche et Cerveau
Département Neurosciences Intégratives
18 avenue du Doyen Lépine
69500 Bron
France
tel: +33 (0)4 72 91 34 77
fax: +33 (0)4 72 91 34 61
portable: +33 (0)6 84 10 64 10
http://www.lyon.inserm.fr/371/
______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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