-
Notifications
You must be signed in to change notification settings - Fork 4
/
fitpsd.R
707 lines (581 loc) · 21.2 KB
/
fitpsd.R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
#
# This file contains code related to patch size distribution fitting. These
# functions can fit Power-law (pl), Truncated Power-law (tpl), Lognormal
# (lnorm) and Exponential (exp) distributions using maximum likelihood, as
# per Clauset et al. 's (2007) recommandations.
#
# In addition, it provides the estimation of xmin using the ks-distance for
# power-laws (same, following Clauset et al. 2007)
# Optimisation global options
ITERLIM <- 10000
GRADTOL <- 1e-10
STEPTOL <- 1e-10
STEPMAX <- 5
ifnotfinite <- function(x, otherwise = .Machine$double.xmax) {
ifelse(is.finite(x), x, sign(x) * otherwise)
}
warnbound <- function() {
getOption("spatialwarnings.debug.fit_warn_on_bound", default = FALSE)
}
warnNA <- function() {
getOption("spatialwarnings.debug.fit_warn_on_NA", default = FALSE)
}
# This is a safe version of nlm that returns a sensible result (NaNs) when
# the algorithm fails to converge. This can happen quite often when looking
# for pathological cases (e.g. fitting distribution based on few points in the
# tails, etc.).
optim_safe <- function(f, pars0,
lower = rep(-Inf, length(pars0)),
upper = rep(Inf, length(pars0)),
fit_on_logscale = FALSE, ...) {
if ( fit_on_logscale ) {
optimf <- function(pars) {
f(exp(pars))
}
pars0 <- log(pars0)
lower <- suppressWarnings(ifnotfinite(log(lower)))
upper <- suppressWarnings(ifnotfinite(log(upper)))
} else {
optimf <- f
}
optiresult <- try({
optim(pars0, optimf,
control = list(maxit = ITERLIM),
lower = lower, upper = upper,
method = "L-BFGS-B", ...)
}, silent = TRUE)
# Code results above 3 means a true problem, below 3 the
# solution is either exact or approximate.
# Sometimes L-BFGS-B gets stuck in a very flat area just because our initial
# guess was very good, and L-BFGS-B does not like that (it reports
# abnormal termination of line search). Or L-BFGS-B will try the bounds of
# the parameter space, which will return error. So here we try to use BFGS
# which should report success if our initial guess was not too bad.
if ( inherits(optiresult, "try-error") || optiresult[["convergence"]] > 3 ) {
optiresult_bfgs <- try({
optim(pars0, optimf,
control = list(maxit = ITERLIM),
method = "BFGS", ...)
}, silent = TRUE)
# If success, go with BFGS results
if ( inherits(optiresult_bfgs, "try-error") ) {
optiresult <- optiresult_bfgs
}
}
# If we could not reach a proper solution, report an error
if ( inherits(optiresult, "try-error") ) {
optiresult <- list(value = NaN,
par = rep(NaN, length(pars0)),
convergence = 128)
return(optiresult)
}
if ( optiresult[["convergence"]] > 3 ) {
warning(paste0('optim returned an error (error code:',
optiresult[["convergence"]], ").\n",
"Make sure the results are reasonable using plot_distr"))
}
# Convert the estimated pars back from log scale
if ( fit_on_logscale ) {
optiresult[["par"]] <- exp(optiresult[["par"]])
}
return(optiresult)
}
# Bounds on parameters, these should be large and no observed distribution should
# have values beyond them
# Power-laws lambdas
PLMIN <- 1 + sqrt(.Machine$double.eps)
PLMAX <- 10
# Exponential rates
EXPMIN <- sqrt(.Machine$double.eps) # A very close value to, but not, zero
EXPMAX <- 10
# Bounds for truncated power-laws
TPL_EXPOMIN <- -1 # Taken from Clauset's code
TPL_EXPOMAX <- 10
TPL_RATEMIN <- sqrt(.Machine$double.eps)
TPL_RATEMAX <- 10
# Riemann zeta function with xmin taken into account :
# sum( 1/k^-expo ) for i=xmin to i = inf
# This is vectorized over xmins so that we do not sum things several times.
zeta_w_xmin <- function(expo, xmins) {
perm <- order(xmins)
xmins <- xmins[order(xmins)]
# Compute zeta value
zetaval <- gsl::zeta(expo)
# Initialize
output <- rep(NaN, length(xmins))
current_k <- xmins[1]
output[perm[1]] <- zetaval - sum_all_one_over_k(from = 1, to = xmins[1], expo)
# If there is only one value, we bail now
if ( length(xmins) <= 1) {
return(output)
}
for ( i in 2:length(xmins)) {
next_k <- xmins[i]
if (next_k > current_k) {
output[perm[i]] <- output[perm[i-1]] -
sum_all_one_over_k(from = current_k,
to = next_k, expo)
current_k <- next_k
} else {
output[perm[i]] <- output[perm[i-1]]
}
}
return(output)
}
# PL fitting
# ---------------------------------------
# Normalizing constant for pl with xmin
displnorm <- function(expo, xmin) {
# Adjust constant for threshold (note that this has no effect if xmin == 1,
# as expected)
const <- gsl::zeta(expo)
const - sum_all_one_over_k(from = 1, to = xmin, expo)
}
# PL: P(x=k)
dpl <- function(x, expo, xmin = 1, log = FALSE) {
const <- displnorm(expo, xmin)
# Compute values
if ( ! log ) {
ans <- (1/const) * x^(-expo)
ans[x < xmin] <- NaN
} else {
if ( const < 0 ) {
# Const can be negative as nlm finds its way: the check makes sure
# no warning is produced by the log.
ans <- NaN
} else {
ans <- -expo * log(x) - log(const)
}
}
return(ans)
}
# PL: P(x>=k)
ippl <- function(x, expo, xmin = 1) {
const <- displnorm(expo, xmin)
is_below_xmin <- x < xmin
ps <- zeta_w_xmin(expo, x[!is_below_xmin]) / const
# Values below threshold are NA'ed
ans <- NaN*x
ans[!is_below_xmin] <- ps
return(ans)
}
# PL: Log likelihood
pl_ll <- function(dat, expo, xmin) {
sum( dpl(dat, expo, xmin, log = TRUE) )
}
#' @title Distribution-fitting functions
#'
#' @description These functions fit parametric distributions to a set of
#' discrete values.
#'
#' @param dat The set of values to which the distribution are fit
#'
#' @param xmin The minimum possible value to consider when fitting the
#' distribution
#'
#' @return A list containing at list the following components:
#'
#' \describe{
#' \item{\code{type}}{The type of distribution fitted (as a character string)}
#' \item{\code{method}}{The method used for the fit - here, maximum likelihood, 'll'}
#' \item{\code{ll}}{The log likelihood at the estimated parameter values}
#' \item{\code{xmin}}{The value of xmin used for the fit}
#' \item{\code{npars}}{The number of parameters of the distribution}
#' }
#'
#' Additionally, this list may have one or more of the following elements depending on
#' the type of distribution that has been fitted:
#' \describe{
#' \item{\code{plexpo}}{The exponent of the power-law}
#' \item{\code{cutoff}}{The rate of truncation, for truncated power law and
#' exponential fits}
#' \item{\code{meanlog}}{The mean of the lognormal distribution}
#' \item{\code{sdlog}}{The s.d. of the lognormal distribution}
#' }
#'
#' @details These functions will fit distributions to a set of values using
#' maximum-likelihood estimation. In the context of the 'spatialwarnings'
#' package, they are most-often used to fit parametric distributions on patch
#' size distributions. As a result, these functions assume that the data
#' contains only integer, strictly positive values. The type of distribution
#' depends on the prefix of the function: 'pl' for power-law, 'tpl' for
#' truncated power-law, 'lnorm' for lognormal and 'exp' for an exponential
#' distribution.
#'
#' In the context of distribution-fitting, 'xmin' represents the minimum value
#' that a distribution can take. It is often used to represent the minimum
#' scale at which a power-law model is appropriate (Clauset et al. 2009), and
#' can be estimated on an empirical distribution using
#' \code{\link{xmin_estim}}. Again, please note that the fitting procedure
#' assumes here that xmin is equal or grater than one.
#'
#' Please note that a best effort is made to have the fit converge, but
#' it may sometimes fail when the parameters are far from their usual
#' range, and numerical issues may occur. It is good practice to make
#' sure the fits are sensible when convergence warnings are reported.
#'
#' For reference, the shape of the distributions is as follow:
#'
#' \describe{
#' \item{power-law}{\eqn{x^{-a}}{x^(-a)} where a is the power-law exponent}
#' \item{exponential}{\eqn{exp(-bx)}{exp(-bx)} where b is the truncation rate
#' of the exponential}
#' \item{truncated power-law}{\eqn{x^{-a}exp(-bx)}{x^(-a)exp(-bx)} where a
#' and b are the exponent of the power law and the rate of truncation}
#' }
#'
#' The lognormal form follows the \link[=dlnorm]{standard definition}.
#'
#' The following global options can be used to change the behavior of fitting functions
#' and/or produce more verbose output:
#' \describe{
#' \item{spatialwarnings.constants.reltol}{the relative tolerance to use to compute
#' the power-law normalizing constant
#' \deqn{sum_{k=1}^{\infty} x^{ak}e^{-bk}}{sum( x^(ak)exp(-bk)) for k in 1:Inf}.
#' Increase to increase the precision of this constant, which can be useful in some
#' cases, typically with large sample sizes. Default is 1e-8.}
#' \item{spatialwarnings.constants.maxit}{the maximum number of iterations to compute
#' the normalizing constant of a truncated power-law. Increase if you get a warning
#' that the relative tolerance level (defined above) was not reached. Default is 1e8}
#' \item{spatialwarnings.debug.fit_warn_on_bound}{logical value. Warn if the fit is
#' at the boundary of the valid range for distribution parameter}
#' \item{spatialwarnings.debug.fit_warn_on_NA}{logical value. Warn if the returned fit
#' has \code{NA}/\code{NaN} parameters}
#' }
#'
#' @seealso \code{\link{patchdistr_sews}}, \code{\link{xmin_estim}}
#'
#' @references
#'
#' Clauset, Aaron, Cosma Rohilla Shalizi, and M. E. J. Newman. 2009. “Power-Law
#' Distributions in Empirical Data.” SIAM Review 51 (4): 661–703.
#' https://doi.org/10.1137/070710111.
#'
#' @examples
#'
#' # Fit an exponential model to patch size distribution
#' exp_fit(patchsizes(forestgap[[8]]))
#'
#' # Use the estimated parameters as an indicator function
#' \donttest{
#'
#' get_truncation <- function(mat) {
#' c(exp_cutoff = exp_fit(patchsizes(mat))$cutoff)
#' }
#' trunc_indic <- compute_indicator(forestgap, get_truncation)
#' plot(trunc_indic)
#' plot(indictest(trunc_indic, nulln = 19))
#'
#' }
#'
#'@export
pl_fit <- function(dat, xmin = 1) {
# Cut data to specified range
dat <- dat[dat >= xmin]
# Start with the approximation given in Clauset's
npts <- length(dat)
expo_estim <- 1 + npts / (sum(log(dat)) - npts*log(xmin-.5))
negll <- function(expo) {
result <- - pl_ll(dat, expo, xmin)
if ( is.infinite(result) ) {
return(NaN)
} else {
return(result)
}
}
est <- optim_safe(negll, expo_estim,
lower = PLMIN, upper = PLMAX)
result <- list(type = 'pl',
method = 'll',
plexpo = est[["par"]],
ll = - est[['value']],
xmin = xmin,
npars = 1)
if ( warnNA() && is.na(result[["plexpo"]]) ) {
warning("Fitting of PL returned NA")
return(result)
}
if ( warnbound() && any(abs(result[["plexpo"]] - c(PLMIN, PLMAX)) < 1e-8) ) {
warning("Estimated PL exponent is on the boundary of the valid range")
}
return(result)
}
#' @title Estimate the minimum patch size of a power-law distribution
#'
#' @description When fitting a power-law to a discrete distribution, it might
#' be worth discarding points below a certain threshold (xmin) to improve
#' the fit. This function estimates the optimal xmin based on the
#' Kolmogorov-Smirnoff distance between the fit and the empirical
#' distribution, as suggested by Clauset et al. (2009).
#'
#' @param dat A vector of integer values
#'
#' @param bounds A vector of two values representing the bounds in which
#' the best xmin is searched
#'
#' @return The estimated xmin as an integer value
#'
#' @details The function returns NA if \code{dat} has only three unique values
#' or if the power-law fit failed.
#'
#' @seealso \code{\link{patchdistr_sews}}
#'
#' @references
#'
#' Clauset, A., Shalizi, C. R., & Newman, M. E. (2009).
#' Power-law distributions in empirical data. SIAM review, 51(4), 661-703.
#'
#' @examples
#'
#' \donttest{
#' psd <- patchsizes(forestgap[[5]])
#' xmin_estim(psd)
#' }
#'@export
xmin_estim <- function(dat, bounds = range(dat)) {
# Create a vector of possible values for xmin
xmins <- sort(unique(dat))
# We need at least 3 values for a pl fit, so the last value of xmin
# needs to have three points after it
if ( length(xmins) <= 3 ) {
return(NaN)
}
# We build a vector of possible xmins. The last three values are stripped
# away as they won't allow enough data for a fit
xmins <- head(xmins, length(xmins)-3)
xmins <- xmins[xmins >= min(bounds) & xmins <= max(bounds)]
# Compute all ks-distances
kss <- adply(xmins, 1, get_ks_dist, dat = dat)[ ,2]
if ( all(is.nan(kss)) ) {
return(NaN)
}
# Note that sometimes the fit fails, especially when xmin is around the
# distribution tail -> we need to remove some NAs here
xmin <- xmins[!is.na(kss) & kss == min(kss, na.rm = TRUE)]
# Note that xmin can be NaN
return(xmin)
}
get_ks_dist <- function(xmin, dat) {
# Crop dat to values above xmin and compute cdf
dat <- dat[dat >= xmin]
# Compute empirical (inverse) cdf values
udat <- unique(dat)
cdf_empirical <- rep(NA, length(dat))
for ( val in udat ) {
cdf_empirical[dat == val] <- mean(dat >= val)
}
# Fit and retrieve cdf. Note: here we suppress the warnings because finding
# xmin requires removing patches below a threshold, which often leads to fit
# being done on pathological cases like few unique patch sizes
fit <- suppressWarnings({
pl_fit(dat, xmin = xmin)
})
if ( is.na(fit[['plexpo']]) ) {
# Note: a warning was already produced in this case as it means that the
# fit failed to converge: we do not produce one here again.
return(NaN)
}
cdf_fitted <- ippl(dat, fit[["plexpo"]], fit[["xmin"]])
# # debug
# plot(data.frame(dat, rbinom(length(dat), 1, .5)), type = 'n')
# plot(log10(data.frame(dat, cdf_empirical)))
# points(log10(data.frame(dat, cdf_fitted)), col = 'red')
# browser()
# zeta.fit(dat, xmin)$exponent
# fit$expo
# We return the ks distance
maxks <- max(abs(cdf_empirical - cdf_fitted))
# cat(xmin, ",", max(dat), "->", maxks, "\n" )
return( maxks )
}
# EXP fitting
# ---------------------------------------
# pexp/dexp is already implemented in R
# EXP: P(x = k)
ddisexp <- function(dat, rate, xmin = 1, log = FALSE) {
# sum(P = k) for k = 1 to inf
if ( log ) {
const <- log(1 - exp(-rate)) + rate * xmin
return( ifelse(dat < xmin, NaN, const - rate * dat) )
} else {
const <- (1 - exp(-rate)) * exp(rate*xmin)
return( ifelse(dat < xmin, NaN, const * exp(-rate * dat)) )
}
}
# EXP: P(x>=k)
# Imported and cleaned up from powerRlaw (def_disexp.R)
ipdisexp <- function(x, rate, xmin) {
# p >= k
p <- pexp(x + .5, rate, lower.tail = FALSE)
# p >= 1
const <- 1 - pexp(xmin + .5, rate)
return(p/const)
}
exp_ll <- function(dat, rate, xmin) {
sum( ddisexp(dat, rate, xmin, log = TRUE))
}
#'@rdname pl_fit
#'@export
exp_fit <- function(dat, xmin = 1) {
dat <- dat[dat>=xmin]
rate0 <- 1 / mean(dat)
negll <- function(rate) {
- exp_ll(dat, rate, xmin)
}
est <- optim_safe(negll, rate0,
fit_on_logscale = TRUE,
lower = EXPMIN,
upper = EXPMAX)
result <- list(type = 'exp',
method = 'll',
cutoff = est[['par']],
ll = - est[["value"]],
npars = 1)
if ( warnbound() && any(abs(result[["cutoff"]] - c(EXPMIN, EXPMAX)) < 1e-8) ) {
warning("Estimated EXP exponent is on the boundary of the valid range")
}
return(result)
}
# LNORM fitting
# ---------------------------------------
# LNORM: P(X=k)
ddislnorm <- function(x, meanlog, sdlog, xmin, log = FALSE) {
p_over_thresh <- plnorm(xmin - .5, meanlog, sdlog, lower.tail = FALSE)
p_equals_k <- plnorm(x-.5, meanlog, sdlog, lower.tail = FALSE) -
plnorm(x+.5, meanlog, sdlog, lower.tail = FALSE)
if ( !log ) {
return( ifelse(x<xmin, NaN, p_equals_k / p_over_thresh) )
} else {
return( ifelse(x<xmin, NaN, log(p_equals_k) - log(p_over_thresh)) )
}
}
# LNORM: P(X>=k)
ipdislnorm <- function(x, meanlog, sdlog, xmin) {
px_supto_k <- plnorm(x - .5, meanlog, sdlog, lower.tail = FALSE)
px_supto_xmin <- plnorm(xmin - .5, meanlog, sdlog, lower.tail = FALSE)
ifelse(x<xmin, NaN, px_supto_k / px_supto_xmin)
}
# LNORM: LL
lnorm_ll <- function(x, meanlog, sdlog, xmin) {
x <- x[x>=xmin]
sum( ddislnorm(x, meanlog, sdlog, xmin, log = TRUE) )
}
# LNORM: fit
#'@rdname pl_fit
#'@export
lnorm_fit <- function(dat, xmin = 1) {
# Pars[1] holds mean of log-transformed data
# Pars[2] holds sd
pars0 <- c( mean(log(dat)), sd(log(dat)) )
negll <- function(pars) {
ll <- - lnorm_ll(dat, pars[1], pars[2], xmin)
if ( is.finite(ll) ) ll else 1e10
}
est <- optim_safe(negll, pars0)
result <- list(type = 'lnorm',
method = 'll',
meanlog = est[['par']][1],
sdlog = est[['par']][2],
ll = - est[["value"]],
npars = 2)
return(result)
}
# TPL fitting
# ---------------------------------------
tplnorm <- function(expo, rate, xmin) {
maxit <- getOption("spatialwarnings.constants.maxit", default = 1e8L)
reltol <- getOption("spatialwarnings.constants.reltol", default = 1e-8)
a <- tplinfsum(expo, rate, xmin, maxit, reltol)
a
}
# P(x=k)
dtpl <- function(x, expo, rate, xmin, log = FALSE) {
const <- tplnorm(expo, rate, xmin)
if ( ! log ) {
ps <- x^(-expo) * exp(- x * rate) / const
} else {
ps <- - expo * log(x) - rate * x - log(const)
}
return( ifelse(x < xmin, NaN, ps) )
}
# P(x>=k)
iptpl <- function(x, expo, rate, xmin) {
const <- tplnorm(expo, rate, xmin)
# tplsum is vectorized over x
p_inf_to_k <- tplsum(expo, rate, x, xmin) / const
return( 1 - p_inf_to_k )
}
tpl_ll <- function(x, expo, rate, xmin, approximate = FALSE) {
x <- x[x>=xmin]
ll <- sum( dtpl(x, expo, rate, xmin, log = TRUE) )
if ( !is.finite(ll) ) {
ll <- sign(ll) * .Machine$double.xmax
}
return( ll )
}
#'@rdname pl_fit
#'@export
tpl_fit <- function(dat, xmin = 1) {
negll <- function(pars) {
- tpl_ll(dat, pars[1], pars[2], xmin)
}
# Initialize and find minimum
expo0 <- pl_fit(dat, xmin)[['plexpo']]
# Do a line search over the cutoff to find a minimum, starting from zero
# up to 100
is <- seq(0, 100, length = 128)
is <- 10^seq(-7, 2, l = 128)
lls <- unlist(lapply(is, function(i) {
negll(c(expo0, i))
}))
llmin <- min(lls[abs(lls) != .Machine$double.xmax & is.finite(lls)])
expmrate0 <- is[which(lls == llmin)]
# If multiple cutoffs produce the same ll, then use the lowest one
if ( length(expmrate0) > 1 ) {
expmrate0 <- expmrate0[1]
}
# Debug thing lls
# plot( log(spatialwarnings:::cumpsd(dat)) )
# vals <- ippl(dat, expo0, xmin = xmin)
# points(log(dat), log(vals), col = "red")
# vals <- iptpl(dat, expo0, rate = 0, xmin = xmin)
# points(log(dat), log(vals), col = "darkgreen")
# vals <- iptpl(dat, expo0, rate = expmrate0, xmin = xmin)
# points(log(dat), log(vals), col = "blue")
pars0 <- c(expo0, expmrate0)
est <- optim_safe(negll, pars0,
lower = c(TPL_EXPOMIN, TPL_RATEMIN),
upper = c(TPL_EXPOMAX, TPL_RATEMAX),
fit_on_logscale = FALSE)
# For very small cutoffs, we may want to fit on log scale to get a descent estimate,
# as otherwise there is too little variation in the cutoff for BFGS
if ( any(is.na(est[["par"]])) ) {
est <- optim_safe(negll, pars0,
lower = c(TPL_EXPOMIN, TPL_RATEMIN),
upper = c(TPL_EXPOMAX, TPL_RATEMAX),
fit_on_logscale = TRUE)
}
result <- list(type = 'tpl',
method = 'll',
plexpo = est[['par']][1],
cutoff = est[['par']][2],
ll = - est[["value"]],
npars = 2)
if ( warnNA() && is.na(result[["plexpo"]]) ) {
warning("Fitting of TPL returned NA/NaN")
}
if ( is.na(result[["plexpo"]]) ) {
return(result)
}
if ( warnbound() &&
any(abs(result[["plexpo"]] - c(TPL_EXPOMIN, TPL_EXPOMAX)) < 1e-8) ) {
warning("Estimated TPL exponent is on the boundary of the valid range")
}
# We do not warn for reaching minimum exponent because this is quite common when
# fitting truncated power laws to have a very small exponent
if ( warnbound() &&
any(abs(result[["cutoff"]] - c(TPL_RATEMIN, TPL_RATEMAX)) < 1e-8) ) {
warning("Estimated TPL cutoff is on the boundary of the valid range")
}
return(result)
}