fitCF: Fit a model of Clutch Frequency for marine turtles.

Description

This function fits a model of clutch frequency. This model is an enhanced version of the one published by Briane et al. (2007). Parameters are mu and sd being the parameters of a distribution used to model the clutch frequency. This distribution is used only as a guide but has not statistical meaning. The parameter p is the -logit probability that a female is seen on the beach for a particular nesting event. It includes both the probability that it is captured but also the probability that it uses that specific beach. Several categories of females can be included in the model using index after the name of the parameter, for example mu1, sd1 and mu2, sd2 indicates that two categories of females with different clutch frequencies distribution are present. Similarly p1 and p2 indicates that two categories of females with different capture probabilities are present. If more than one category is used, then it is necessary to include the parameter OTN to indicate the relative frequencies of each category. If two categories are used, one OTN parameter named ONT1 must be included. The OTN2 is forced to be 1. Then the relative frequency for category 1 is OTN1/(OTN1+1) and for category 2 is 1/(OTN1+1). Same logic must be applied for 3 and more categories with always the last one being fixed to 1. if p or a are equal to -Inf, the probability is 0 and if they are equal to +Inf, the probability is 1. The best way to indicate capture probability for 3D model (OCF, ECF, Period) is to indicate p.period common for all categories and a1, a2, etc for each category. The capture probability for category 1 will be p.period * a1, and for category 2 will be p.period * a2, etc. In this case, the parameters p.period should be indicated in fitted parameters as well as a1, but a2 must be fixed to +Inf in fixed.parameters. Then the capture probability for category 2 will be p.period and for category 1 a1 * p.period.

Usage

fitCF(x = c(mu = 4, sd = 100, p = 0), fixed.parameters = NULL,
  data = stop("Data formated with TableECFOCF() must be provided"),
  method = c("Nelder-Mead", "BFGS"), control = list(trace = 1, REPORT =
  100, maxit = 500), itnmax = c(500, 100), hessian = TRUE,
  parallel = TRUE, verbose = FALSE)

Arguments

Initial parameters to be fitted

fixed.parameters

Parameters that are fixed.

data

CMR data formated using TableECFOCF()

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

parallel

If TRUE, will use parallel computing for ECFOCF_f()

verbose

If TRUE, print the parameters at each step

Value

Return a list of class ECFOCF with the fit information. The list has the following items:

data: The observations to be fitted
par: The fitted parameters
SE: The standard error of parameters if hessian is TRUE
value: The -log likelihood of observations within the fitted model
AIC: The AIC of fitted model
mu: The vector of fitted mu values
sd: The vector of fitted sd values
prob: The vector of fitted capture probabilities
a: The vector of fitted capture probabilities multiplier
OTN: The vector of fitted relative probabilities of contribution
period_categories: A list with the different period probabilities as named vectors for each category
period: The combined period probabilities using OTN as named vector
CF_categories: A list with the different CF probabilities as named vectors for each category
CF: The combined CF probabilities using OTN as named vector
ECFOCF_categories: A list with the different probability ECFOCF tables for each category
ECFOCF: The combined table of ECFOCF using OTN probabilities tables
ECFOCF_0: The combined table of ECFOCF probabilities tables using OTN without the OCF=0
SE_df: A data.frame with SE and 95% confidence intervals for meanx and vx (mean and variance of clutch frequency for x category), OTNx (proportion for x category), and probx (capture probability for x category)

Details

fitCF fit a model of Clutch Frequency for marine turtles.

Examples

Run this code

# NOT RUN {
library(phenology)
# Example
data(MarineTurtles_2002)
ECFOCF_2002 <- TableECFOCF(MarineTurtles_2002)

# Paraetric model for clutch frequency
o_mu1p1_CFp <- fitCF(x = c(mu = 2.1653229641404539, 
                 sd = 1.1465246643327098, 
                 p = 0.25785366120357966), 
                 fixed.parameters=NULL, 
                 data=ECFOCF_2002, hessian = TRUE)
 
# Non parametric model for clutch frequency
o_mu1p1_CFnp <- fitCF(x = c(mu.1 = 18.246619595610383, 
                       mu.2 = 4.2702163522832892, 
                       mu.3 = 2.6289986859556458, 
                       mu.4 = 3.2496360919228611, 
                       mu.5 = 2.1602522716550943, 
                       mu.6 = 0.68617023351032846, 
                       mu.7 = 4.2623607001877026, 
                       mu.8 = 1.1805600042630455, 
                       mu.9 = 2.2786176350939731, 
                       mu.10 = 0.47676265496204945, 
                       mu.11 = 5.8988238539197062e-08, 
                       mu.12 = 1.4003187851424953e-07, 
                       mu.13 = 2.4128444894899776e-07, 
                       mu.14 = 2.4223748020049825e-07, 
                       p = 0.32094401970037578), 
                 fixed.parameters=c(mu.15 = 1E-10), 
                 data=ECFOCF_2002, hessian = TRUE)
                 
o_mu2p1 <- fitCF(x = c(mu1 = 1.2190766766978423, 
                     sd1 = 0.80646454821956925, 
                     mu2 = 7.1886819592223246, 
                     sd2 = 0.18152887523015518, 
                     p = 0.29347220802963259, 
                     OTN = 2.9137627675219533), 
                  fixed.parameters=NULL,
                  data=ECFOCF_2002, hessian = TRUE)

o_mu1p2 <- fitCF(x = c(mu = 5.3628701816871462, 
                     sd = 0.39390555498088764, 
                     p1 = 0.61159637544418755, 
                     p2 = -2.4212753004659189, 
                     OTN = 0.31898004668901009),
                 data=ECFOCF_2002, hessian = TRUE)
                 
o_mu2p2 <- fitCF(x = c(mu1 = 0.043692606004492131, 
                   sd1 = 1.9446036983033428, 
                   mu2 = 7.3007868915644751, 
                   sd2 = 0.16109296152913491, 
                   p1 = 1.6860260469536992, 
                   p2 = -0.096816113083788985, 
                   OTN = 2.2604431232973501), 
                  data=ECFOCF_2002, hessian = TRUE)

compare_AIC(mu1p1=o_mu1p1_CFp, 
            mu2p1=o_mu2p1, 
            mu1p2=o_mu1p2, 
            mu2p2=o_mu2p2)
                 
o_mu3p3 <- fitCF(x = c(mu1 = 0.24286312214288761, 
                            sd1 = 0.34542255091729313, 
                            mu2 = 5.0817174343025551, 
                            sd2 = 1.87435099405695, 
                            mu3 = 5.2009265101740683, 
                            sd3 = 1.79700447678357, 
                            p1 = 8.8961708614726156, 
                            p2 = 0.94790116453886453, 
                            p3 = -0.76572930634505421, 
                            OTN1 = 1.2936848663276974, 
                            OTN2 = 0.81164278235645926),
                 data=ECFOCF_2002, hessian = TRUE)
                 

o_mu3p1 <- fitCF(x = structure(c(0.24387978183477, 
                                   1.2639261745506, 
                                   4.94288464711349, 
                                   1.945082889758, 
                                   4.9431672350811, 
                                   1.287663104591, 
                                   0.323636536050397, 
                                   1.37072039291397, 
                                   9.28055412564559e-06), 
                                  .Names = c("mu1", "sd1", "mu2", 
                                             "sd2", "mu3", "sd3", 
                                             "p", "OTN1", "OTN2")),
                 data=ECFOCF_2002, hessian = TRUE)
                 

o_mu1p3 <- fitCF(x = structure(c(4.65792402108387, 
                                   1.58445909785, 
                                   -2.35414198317177, 
                                   0.623757854800649, 
                                   -3.62623634029326, 
                                   11.6950204755787, 
                                   4.05273728846523), 
                                   .Names = c("mu", "sd", 
                                              "p1", "p2", "p3", 
                                              "OTN1", "OTN2")),
                 data=ECFOCF_2002, hessian = TRUE)
                 
compare_AIC(mu1p1=o_mu1p1, 
            mu2p1=o_mu2p1, 
            mu1p2=o_mu1p2, 
            mu2p2=o_mu2p2, 
            mu3p3=o_mu3p3, 
            mu1p3=o_mu1p3, 
            mu3p1=o_mu3p1)
            
 # 3D model for (ECF, OCF, period)           
            
ECFOCF_2002 <- TableECFOCF(MarineTurtles_2002, 
                           date0=as.Date("2002-01-01"))

fp <- rep(0, dim(ECFOCF_2002)[3])
names(fp) <- paste0("p.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(mu = 2.6404831115214353, 
        sd = 0.69362774786433479, 
        mu_season = 12.6404831115214353, 
        sd_season = 1.69362774786433479)
par <- c(par, fp[attributes(ECFOCF_2002)$table["begin"]:
                 attributes(ECFOCF_2002)$table["end"]])
# The value of p (logit -capture probability) out of the period 
# of monitoring is set to +Inf (capture probability=1)
# to indicate that no turtle is nesting in the period out of 
# monitoring time
# p is set to -Inf (capture probability=0) to indicate that no
# monitoring has been done but some turtles could have been present.
fixed.parameters <- c(p=+Inf)
# The fitted values are:
par <- c(mu = 2.4911638591178051, 
         sd = 0.96855483039640977, 
         mu_season = 13.836059118657793, 
         sd_season = 0.17440085345943984, 
         p.10 = 1.3348233607728222, 
         p.11 = 1.1960387774393837, 
         p.12 = 0.63025680979544774, 
         p.13 = 0.38648155002707452, 
         p.14 = 0.31547864054366048, 
         p.15 = 0.19720001827017075, 
         p.16 = 0.083199496372073328, 
         p.17 = 0.32969130595897905, 
         p.18 = 0.36582777525265819, 
         p.19 = 0.30301248314170637, 
         p.20 = 0.69993987591518514, 
         p.21 = 0.13642423871641118, 
         p.22 = -1.3949268190534629)

o_mu1p1season1 <- fitCF(x=par, data=ECFOCF_2002, 
                        fixed.parameters=fixed.parameters)

# Same model but with two different models of capture probabilities
                        
fp <- rep(0, dim(ECFOCF_2002)[3])
names(fp) <- paste0("p1.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(mu = 2.6404831115214353, 
        sd = 0.69362774786433479, 
        mu_season = 12.6404831115214353, 
        sd_season = 1.69362774786433479)
par <- c(par, fp[attributes(ECFOCF_2002)$table["begin"]:
                 attributes(ECFOCF_2002)$table["end"]])
names(fp) <- paste0("p2.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(par, fp[attributes(ECFOCF_2002)$table["begin"]:
                 attributes(ECFOCF_2002)$table["end"]])
fixed.parameters <- c(p1=+Inf, p2=+Inf)

o_mu1p2season1 <- fitCF(x=par, data=ECFOCF_2002, 
                        fixed.parameters=fixed.parameters)

# Here the two different capture probabilities are different 
# by a constant:
# p1=invlogit(-p)     [Note that invlogit(-a1) = 1]
# p2=invlogit(-p)*invlogit(-a2)

fp <- rep(0, dim(ECFOCF_2002)[3])
names(fp) <- paste0("p.", formatC(1:(dim(ECFOCF_2002)[3]), width=2, flag="0"))
par <- c(mu = 2.6404831115214353, 
        sd = 0.69362774786433479, 
        mu_season = 12.6404831115214353, 
        sd_season = 1.69362774786433479, 
        a2=0)
par <- c(par, fp[attributes(ECFOCF_2002)$table["begin"]:
                 attributes(ECFOCF_2002)$table["end"]])
fixed.parameters <- c(a1=+Inf, p=+Inf)

o_mu1p1aseason1 <- fitCF(x=par, data=ECFOCF_2002, 
                        fixed.parameters=fixed.parameters)
                        data=ECFOCF_2002)
 
# }

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