fishmethods (version 1.9-0)

vblrt: Likelihood Ratio Tests for Comparing Two von Bertalanffy Growth Curves

Description

Likelihood ratio tests for comparison of two von Bertalanffy growth curves following Kimura (1980).

Usage

vblrt(len = NULL, age = NULL, group = NULL, error = 1, select = 1, Linf = NULL, K = NULL, t0 = NULL,plottype=0,
control=list(maxiter=10000,minFactor=1/1024,tol=1e-5))

Arguments

len

the vector of lengths of individual fish.

age

the vector of ages associated with the length vector.

group

the vector of character or numeric codes specifying group association.

error

the error variance assumption. 1= constant variance for all lijs; 2= constant variance for all mean lengths at age; 3=var of lij varies with age. See methods a-c in Kimura (1980: pp. 766). The required statistics for each type of error are calculated from the individual length-age observations.

select

the selection of starting values of L-infinity, K, and t0. 1=automatic selection, 2=user-specified. If select=1, initial starting values of L-infinity, K, and t0 are calculated from Walford lines (Everhart et al. 1975), and ages represented as decimal values are truncated to the integer before linear regression is applied. If select=2, the user must specify the values of L-infinity, K, and t0.

Linf

if select=2, the starting value for L-infinity of the von Bertalanffy equation.

K

if select=2, the starting value for K of the von Bertalanffy equation.

t0

if select=2, the starting value for t0 of the von Bertalanffy equation.

plottype

the type of plot for each model. 1= observed versus predicted, 2= residuals. Default= 0 (no plot).

control

see function nls.

Value

results

list element with the likelihood ratio tests comparing von Bertalanffy models.

model Ho

list element with the nls fit for the general model.

model H1

list element with the nls for model H1 (Linf1=Linf2).

model H2

list element with the nls fit for model H2 (K1=K2).

model H3

list element with the nls fit for model H3 (t01=t02).

model H4

list element with the nls fit for model H4 (Linf1=Linf2, K1=K2, t01=t02).

rss

list element with the residual sum-of-squares from each model.

residuals

list element with the residuals from each model.

Details

Following Kimura (1980), the general model (6 parameters; one L-infinity, K, and t0 for each group) and four sub models are fitted to the length and age data using function nls (nonlinear least squares). For each general model-sub model comparison, likelihood ratios are calculated by using the residual sum-of-squares and are tested against chi-square statistics with the appropriate degrees of freedom. Individual observations of lengths-at-age are required. If error variance assumptions 2 or 3, mean lengths and required statistics are calculated. A dummy vector called cat, containing 0s for the first group with lower alpha-numeric order and 1s for the second group, is used in the estimation of group parameters. To extract the VB parameters for each group from the Ho model: # Group 1 Linf1<-x$'model Ho'$coefficients[1] K1<-x$'model Ho'$coefficients[3] t01<-x$'model Ho'$coefficients[5]

# Group 2 Linf2<-Linf1+x$'model Ho'$coefficients[2] K2<-K1+x$'model Ho'$coefficients[4] t02<-t01+x$'model Ho'$coefficients[6] where x is the output object. For models H1, H2, H3 and H4, the shared VB parameter for the second group will be the same as the first group.

References

Everhart, W. H., A. W. Eipper, and W. D. Youngs. 1975. Principles of Fishery Science. Cornell University Press.

Kimura, D. K. 1980. Likelihood methods for the von Bertalanffy growth curve. U. S. Fish. Bull. 77(4): 765-776.

Examples

## Normally, the length and age data will represent data for individuals.  
## Kimura's data are mean lengths-at-age but are usable because error=2 
## will calculate mean lengths-at-age from individual data. Since only  
## one value is present for each age,the mean length will be calculated
## as the same value.
data(Kimura)
vblrt(len=Kimura$length,age=Kimura$age,group=Kimura$sex,error=2,select=1,
plottype=2)