IPFit: Fit a model of Internesting Period for marine turtles.

Description Usage Arguments Details Value Author(s) See Also Examples

Description

This function fits a model of internesting period using maximum likelihood or using Metropolis-Hastings algorithm with Bayesian model.
The fit using maximum likelihood is not the best strategy because the objective function is based on a stochastic model (and then a single set of parameters does not produce exactly the same output each time). The use of Metropolis-Hastings algorithm (a Markov chain Monte Carlo method) should be prefered.

Usage

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IPFit(
  x = NULL,
  fixed.parameters = NULL,
  data = stop("Formated data must be provided"),
  method = c("Nelder-Mead", "BFGS"),
  control = list(trace = 1, REPORT = 100, maxit = 500),
  itnmax = c(500, 100),
  hessian = TRUE,
  verbose = TRUE,
  parallel = TRUE,
  model = c("MH", "ML"),
  parametersMH,
  n.iter = 10000,
  n.chains = 1,
  n.adapt = 100,
  thin = 30,
  trace = TRUE,
  adaptive = TRUE,
  adaptive.lag = 500,
  adaptive.fun = function(x) {     ifelse(x > 0.234, 1.3, 0.7) },
  intermediate = NULL,
  filename = "intermediate.Rdata"
)

Arguments

x

Initial parameters to be fitted

fixed.parameters

Parameters that are fixed.

data

Data as a vector

method

Method to be used by optimx()

control

List of controls for optimx()

itnmax

A vector with maximum iterations for each method.

hessian

Logical to estimate SE of parameters

verbose

If TRUE, show the parameters for each tested model

parallel

If TRUE, will use parallel computing

model

Can be ML for Maximum likelihood or MH for Metropolis Hastings

parametersMH

The priors. See MHalgoGen

n.iter

See MHalgoGen

n.chains

See MHalgoGen

n.adapt

See MHalgoGen

thin

See MHalgoGen

trace

See MHalgoGen

adaptive

See MHalgoGen

adaptive.lag

See MHalgoGen

adaptive.fun

See MHalgoGen

intermediate

See MHalgoGen

filename

See MHalgoGen

Details

IPFit fit a model of Internesting Period for marine turtles.

Value

Return a list of class IP with the fit informations and the fitted model.

Author(s)

Marc Girondot

See Also

Other Model of Internesting Period: IPModel(), IPPredict(), plot.IP(), summary.IP()

Examples

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## Not run: 
library(phenology)
# Example
data <- structure(c(`0` = 0, `1` = 47, `2` = 15, `3` = 6, `4` = 5, `5` = 4, 
                    `6` = 2, `7` = 5, `8` = 57, `9` = 203, `10` = 205, `11` = 103, 
                    `12` = 35, `13` = 24, `14` = 12, `15` = 10, `16` = 13, `17` = 49, 
                    `18` = 86, `19` = 107, `20` = 111, `21` = 73, `22` = 47, `23` = 30, 
                    `24` = 19, `25` = 17, `26` = 33, `27` = 48, `28` = 77, `29` = 83, 
                    `30` = 65, `31` = 37, `32` = 27, `33` = 23, `34` = 24, `35` = 22, 
                    `36` = 41, `37` = 42, `38` = 44, `39` = 33, `40` = 39, `41` = 24, 
                    `42` = 18, `43` = 18, `44` = 22, `45` = 22, `46` = 19, `47` = 24, 
                    `48` = 28, `49` = 17, `50` = 18, `51` = 19, `52` = 17, `53` = 4, 
                    `54` = 12, `55` = 9, `56` = 6, `57` = 11, `58` = 7, `59` = 11, 
                    `60` = 12, `61` = 5, `62` = 4, `63` = 6, `64` = 11, `65` = 5, 
                    `66` = 6, `67` = 7, `68` = 3, `69` = 2, `70` = 1, `71` = 3, `72` = 2, 
                    `73` = 1, `74` = 2, `75` = 0, `76` = 0, `77` = 3, `78` = 1, `79` = 0, 
                    `80` = 2, `81` = 0, `82` = 0, `83` = 1), Year = "1994", 
                    Species = "Dermochelys coriacea", 
                    location = "Yalimapo beach, French Guiana", 
                    totalnumber = 2526L, class = "IP")
  par(mar=c(4, 4, 1, 1)+0.4)
  plot(data, xlim=c(0,100))
  text(100, 190, labels=bquote(italic(.(attributes(data)$Species))), pos=2)
  text(100, 150, labels=attributes(data)$location, pos=2, cex=0.8)
  text(100, 110, labels=paste0(as.character(attributes(data)$totalnumber), " females"), pos=2)
  
######### Fit using Maximum-Likelihood

par <- c(meanIP = 9.8229005713237623, 
         sdIP = 0.079176011861863474, 
         minIP = 6.8128364577569309, 
         pAbort = 1.5441529841959203, 
         meanAbort = 2.7958742380756121, 
         sdAbort = 0.99370406770777175, 
         pCapture = -0.80294884905867658, 
         meanECF = 4.5253772889275758, 
         sdECF = 0.20334743335612529)

fML <- IPFit(x=par, 
             fixed.parameters=c(N=20000),
             data=data, 
             verbose=FALSE, 
             model="ML")

# Plot the fitted ECF
plot(fML, result="ECF")

# Plot the Internesting Period distribution
plot(fML, result="IP")

# Plot the distribution of days between tentatives
plot(fML, result="Abort", xlim=c(0, 15))
#' 
######### Fit using ML and non parametric ECF

par <- c(ECF.2 = 0.044151921569961131, 
         ECF.3 = 2.0020778325280748, 
         ECF.4 = 2.6128345101617083, 
         ECF.5 = 2.6450582416622375, 
         ECF.6 = 2.715198206774927, 
         ECF.7 = 2.0288031327239904, 
         ECF.8 = 1.0028041546528881, 
         ECF.9 = 0.70977432157689235, 
         ECF.10 = 0.086052204035003091, 
         ECF.11 = 0.011400419961702518, 
         ECF.12 = 0.001825219438794076, 
         ECF.13 = 0.00029398731859899116, 
         ECF.14 = 0.002784886479846703, 
         meanIP = 9.9887100433529721, 
         sdIP = 0.10580250625108811, 
         minIP = 6.5159124624132048, 
         pAbort = 2.5702251748938956, 
         meanAbort = 2.2721679285648841, 
         sdAbort = 0.52006431730489933, 
         pCapture = 0.079471782729506113)
         
fML_NP <- IPFit(x=par, 
             fixed.parameters=c(N=20000),
             data=data, 
             verbose=FALSE, 
             model="ML")
             
par <- fML_NP$ML$par

fML_NP <- IPFit(x=par, 
             fixed.parameters=c(N=1000000),
             data=data, 
             verbose=FALSE, 
             model="ML")
             
par <- c(ECF.2 = 0.016195025683080871, 
         ECF.3 = 2.0858089267994315, 
         ECF.4 = 3.1307578727979348, 
         ECF.5 = 2.7495760827322622, 
         ECF.6 = 2.8770821670450939, 
         ECF.7 = 2.1592708144943145, 
         ECF.8 = 1.0016227335391867, 
         ECF.9 = 0.80990178270345259, 
         ECF.10 = 0.081051214954249967, 
         ECF.11 = 0.039757901443389344, 
         ECF.12 = 6.3324056808464527e-05, 
         ECF.13 = 0.00037500864146146936, 
         ECF.14 = 0.0010383506745475582, 
         meanIP = 10.004121090603523, 
         sdIP = 0.10229422354470977, 
         minIP = 6.5051758088487883, 
         pAbort = 2.5335985958484839, 
         meanAbort = 2.3145895392189173, 
         sdAbort = 0.51192514362374153, 
         pCapture = 0.055440514236842105, 
         DeltameanIP = -0.046478049165483697)

fML_NP_Delta <- IPFit(x=par, 
             fixed.parameters=c(N=20000),
             data=data, 
             verbose=FALSE, 
             model="ML")
             
par <- fML_NP_Delta$ML$par
             
fML_NP_Delta <- IPFit(x=par, 
             fixed.parameters=c(N=1000000),
             data=data, 
             verbose=FALSE, 
             model="ML")
             
# Test for stability of -Ln L value according to N
grandL.mean <- NULL
grandL.sd <- NULL
N <- c(10000, 20000, 30000, 40000, 50000,
            60000, 70000, 80000, 90000,  
            100000, 200000, 300000, 400000, 500000, 
            600000, 700000, 800000, 900000,  
            1000000)
for (Ni in N) {
    print(Ni)
    smallL <- NULL
    for (replicate in 1:100) {
         smallL <- c(smallL, 
         getFromNamespace(".IPlnL", ns="phenology")
                 (x=par, fixed.parameters=c(N=Ni), data=data))
    }
    grandL.mean <- c(grandL.mean, mean(smallL))
    grandL.sd <- c(grandL.sd, sd(smallL))
}

grandL.mean <- c(242.619750064524, 239.596145944548, 238.640010536147, 237.965573853263, 
237.727506424543, 237.240740566494, 237.527948232993, 237.297225856515, 
237.17073080938, 237.103397800143, 236.855939567838, 
236.704861853456, 236.82264801458, 236.606065021519, 236.685930841831, 
236.697562908131, 236.568003663293, 236.58097471402, 236.594282543024
)
grandL.sd <- c(6.54334049298099, 3.04916614991682, 2.57932397492509, 2.15990307710982, 
1.59826856034413, 1.54505295915354, 1.59734964880484, 1.41845032728396, 
1.43096821211286, 1.20048923027244, 0.912467350448495, 
0.75814052890774, 0.668841336554019, 0.539505594152166, 0.554662419326559, 
0.501551009304687, 0.415199780254872, 0.472274287714195, 0.386237047201706
)

plot_errbar(x=N, y=grandL.mean, errbar.y = 2*grandL.sd, 
            xlab="N", ylab="-Ln L (2 SD)", bty="n", las=1)
             
# Plot the fitted ECF
plot(fML_NP_Delta, result="ECF")

# Plot the Internesting Period distribution
plot(fML_NP_Delta, result="IP")

# Plot the distribution of days between tentatives
plot(fML_NP_Delta, result="Abort", xlim=c(0, 15))

print(paste("Probability of capture", invlogit(-fML_NP_Delta$ML$par["pCapture"])))
# Confidence interval at 95%
print(paste(invlogit(-fML_NP_Delta$ML$par["pCapture"]-1.96*fML_NP_Delta$ML$SE["pCapture"]), "-", 
invlogit(-fML_NP_Delta$ML$par["pCapture"]+1.96*fML_NP_Delta$ML$SE["pCapture"])))

print(paste("Probability of abort", invlogit(-fML_NP_Delta$ML$par["pAbort"])))
# Confidence interval at 95%
print(paste(invlogit(-fML_NP_Delta$ML$par["pAbort"]-1.96*fML_NP_Delta$ML$SE["pAbort"]), "-", 
invlogit(-fML_NP_Delta$ML$par["pAbort"]+1.96*fML_NP_Delta$ML$SE["pAbort"])))
             
compare_AIC(parametric=fML$ML, 
            nonparameteric=fML_NP$ML, 
            nonparametricDelta=fML_NP_Delta$ML)

######### Fit using Metropolis-Hastings algorithm
# ECF.1 = 1 is fixed
par <- c(ECF.2 = 0.044151921569961131, 
         ECF.3 = 2.0020778325280748, 
         ECF.4 = 2.6128345101617083, 
         ECF.5 = 2.6450582416622375, 
         ECF.6 = 2.715198206774927, 
         ECF.7 = 2.0288031327239904, 
         ECF.8 = 1.0028041546528881, 
         ECF.9 = 0.70977432157689235, 
         ECF.10 = 0.086052204035003091, 
         ECF.11 = 0.011400419961702518, 
         ECF.12 = 0.001825219438794076, 
         ECF.13 = 0.00029398731859899116, 
         ECF.14 = 0.002784886479846703, 
         meanIP = 9.9887100433529721, 
         sdIP = 0.10580250625108811, 
         minIP = 6.5159124624132048, 
         pAbort = 2.5702251748938956, 
         meanAbort = 2.2721679285648841, 
         sdAbort = 0.52006431730489933, 
         pCapture = 0.079471782729506113)

df <- data.frame(Density=rep("dunif", length(par)), 
Prior1=c(rep(0, 13), 8, 0.001, 0, -8, 0, 0.001, -8), 
Prior2=c(rep(10, 13), 12, 1, 10, 8, 2, 1, 8), 
SDProp=unname(c(ECF.2 = 6.366805760909012e-05, 
                ECF.3 = 6.366805760909012e-05, 
                ECF.4 = 6.366805760909012e-05, 
                ECF.5 = 6.366805760909012e-05, 
                ECF.6 = 6.366805760909012e-05, 
                ECF.7 = 6.366805760909012e-05, 
                ECF.8 = 6.366805760909012e-05, 
                ECF.9 = 6.366805760909012e-05, 
                ECF.10 = 6.366805760909012e-05, 
                ECF.11 = 6.366805760909012e-05, 
                ECF.12 = 6.366805760909012e-05, 
                ECF.13 = 6.366805760909012e-05, 
                ECF.14 = 6.366805760909012e-05, 
                meanIP = 6.366805760909012e-05, 
                sdIP = 6.366805760909012e-05, 
                minIP = 6.366805760909012e-05, 
                pAbort = 6.366805760909012e-05, 
                meanAbort = 6.366805760909012e-05, 
                sdAbort = 6.366805760909012e-05, 
                pCapture = 6.366805760909012e-05)),               
Min=c(rep(0, 13), 8, 0.001, 0, -8, 0, 0.001, -8), 
Max=c(rep(10, 13), 12, 1, 10, 8, 2, 1, 8),
Init=par, stringsAsFactors = FALSE)
rownames(df)<- names(par)

fMH <- IPFit(parametersMH=df, 
fixed.parameters=c(N=10000),
data=data, 
verbose=FALSE, 
n.iter = 10000,
n.chains = 1, n.adapt = 100, thin = 1, trace = TRUE,
adaptive = TRUE, 
model="MH")

# Plot the fitted ECF
plot(fMH, result="ECF")


## End(Not run)

phenology documentation built on Oct. 23, 2020, 7:22 p.m.