This function estimates parameters of Francis (1988)'s growth model using tagging data. The data are fitted using a constrained maximum likelihood optimization performed by optim using the "L-BFGS-B" method.
grotag(L1 = NULL, L2 = NULL, T1 = NULL, T2 = NULL, alpha = NULL, beta = NULL,
design = list(nu = 0, m = 0, p = 0, sea = 0),
stvalue = list(sigma = 0.9, nu = 0.4, m = -1, p = 0.1, u = 0.4, w = 0.4),
upper = list(sigma = 5, nu = 1, m = 2, p = 1, u = 1, w = 1),
lower = list(sigma = 0, nu = 0, m = -2, p = 0, u = 0, w = 0), gestimate = TRUE,
st.ga = NULL, st.gb = NULL, st.galow = NULL, st.gaup = NULL, st.gblow = NULL,
st.gbup = NULL, control = list(maxit = 10000))
list element containing the model output similar to Table 3 of Francis (1988). The Akaike's Information Criterion (AIC) is also added to the output.
list element containing the conventional paramaters of the von Bertalanffy model (Linf and K).
list element containing the parameter correlation matrix.
list element containing the predicted values from the model.
list element containing the residuals of the model fit.
Vector of length at release of tagged fish
Vector of length at recovery of tagged fish
Vector of julian time at release of tagged fish
Vector of julian time at recovery of tagged fish
Numeric value giving an arbitrary length alpha
Numeric value giving an arbitrary length beta (beta > alpha)
List specifying the design of the model to estimate. Use 1 to designate whether a parameter(s) should be estimated. Type of parameters are: nu=growth variability (1 parameter), m=bias parameter of measurement error (1 parameter), p=outlier probability (1 parameter), and sea=seasonal variation (2 parameters: u and w). Model 1 of Francis is the default settings of 0 for nu, m, p and sea.
Starting values of sigma (s) and depending on the design argument, nu, m, p, u, and w used as input in the nonlinear estimation (function optim) routine.
Upper limit of the model parameters' (nu, m, p, u, and w) region to be investigated.
Lower limit of the model parameters' (nu, m, p, u, and w) region to be investigated.
Logical specifying whether starting values of ga and gb (growth increments of alpha and beta) should be estimated automatically. Default = TRUE.
If gestimate=FALSE, user-specified starting value for ga.
If gestimate=FALSE, user-specified starting value for gb.
If gestimate=FALSE, user-specified lower limit for st.ga used in optimization.
If gestimate=FALSE, user-specified upper limit for st.ga used in optimization.
If gestimate=FALSE, user-specified lower limit for st.gb used in optimization.
If gestimate=FALSE, user-specified upper limit for st.gb used in optimization.
Additional controls passed to the optimization function optim.
Marco Kienzle Marco.Kienzle@gmail.com
Gary A. Nelson, Massachusetts Division of Marine Fisheries gary.nelson@mass.gov
The methods of Francis (1988) are used on tagging data to the estimate of growth and growth variability. The estimation of all models discussed is allowed. The growth variability defined by equation 5 in the reference is used throughout.
Francis, R.I.C.C., 1988. Maximum likelihood estimation of growth and growth variability from tagging data. New Zealand Journal of Marine and Freshwater Research, 22, p.42-51.
grotagplus
data(bonito)
#Model 4 of Francis (1988)
with(bonito,
grotag(L1=L1, L2=L2, T1=T1, T2=T2,alpha=35,beta=55,
design=list(nu=1,m=1,p=1,sea=1),
stvalue=list(sigma=0.9,nu=0.4,m=-1,p=0.2,u=0.4,w=0.4),
upper=list(sigma=5,nu=1,m=2,p=0.5,u=1,w=1),
lower=list(sigma=0,nu=0,m=-2,p=0.0,u=0,w=0),control=list(maxit=1e4)))
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