Description Usage Arguments Details Value Note References See Also Examples
Estimate the effective sample size for catchatage or catchatlength data, based on the multinomial distribution.
1 2 3 4 
model 
fitted 
what 
name of model element: 
series 
vector of strings indicating which gears or surveys to analyze (all by default). 
init 
initial sample size, determining the relative pattern of the effective sample size between years. 
FUN 
function to standardize the effective sample size. 
ceiling 
largest possible sample size in one year. 
digits 
number of decimal places to use when rounding, or

P 
observed catchatage or catchatlength matrix. 
Phat 
fitted catchatage or catchatlength matrix. 
The init
sample sizes set a fixed pattern for the relative
sample sizes between years. For example, if there are two years of
catchatage data and the initial sample sizes are 100 in year 1 and
200 in year 2, the effective sample size will be two times greater in
year 2 than in year 1, although both will be scaled up or down
depending on how closely the model fits the catchatage data. The
value of init
can be one of the following:
NULL
means read the initial sample sizes from the
existing SS
column (default).
means read the initial sample sizes from the SS
column in that model (object of class scape
).
means those are the initial sample sizes (same length as the number of years).
FALSE
means ignore the initial sample sizes and use the empirical multinomial sample size (nhat) in each year.
1
means calculate one effective sample size to use across all years, e.g. the mean or median of nhat.
The idea behind FUN=mean
is to guarantee that regardless of the
value of init
, the mean effective sample size will always be
the same. Other functions can be used to a similar effect, such as
FUN=median
.
The estN
function is implemented for basic singlesex datasets.
If the data are sexspecific, estN
pools (averages) the sexes
before estimating effective sample sizes. The general function
estN.int
, on the other hand, is suitable for analyzing any
datasets in matrix
format. The int in estN.int
stands for internal (not integer), analogous to rep.int
,
seq.int
, sort.int
, and similar functions.
Numeric vector of effective sample sizes (one value if init=1
),
or a list of such vectors when analyzing multiple series.
This function uses the empirical multinomial sample size to estimate an effective sample size, which may be appropriate as likelihood weights for catchatage and catchatlength data. The better the model fits the data, the larger the effective sample size. See McAllister and Ianelli (1997), Gavaris and Ianelli (2002), and Magnusson et al. (2013).
estN
can be used iteratively, along with
estSigmaI
and estSigmaR
to assign
likelihood weights that are indicated by the model fit to the data.
Sigmas and sample sizes are then adjusted between model runs, until
they converge. The iterate
function facilitates this procedure.
If P[t,a] is the observed proportion of fish at age (or length bin) a in year t, and Phat[t,a] is the fitted proportion, then the estimated sample size in that year is:
nhat[t] = sum_a(Phat[t,a]*(1Phat[t,a])) / sum_a((P[t,a]Phat[t,a])^2)
Due to the nonrandom and nonindependent nature of sampling fish, the effective sample size, for statistical purposes, is much less than the number of fish sampled. Common starting points include using the number of tows as the sample size in each year, or using the empirical multinomial sample sizes. Those “initial” sample sizes can then be scaled up or down. Sample sizes between 20 and 200 are common in the stock assessment literature.
Gavaris, S. and Ianelli, J. N. (2002) Statistical issues in fisheries' stock assessments. Scandinavian Journal of Statistics 29, 245–271.
Magnusson, A., Punt, A. E., and Hilborn, R. (2013) Measuring uncertainty in fisheries stock assessment: the delta method, bootstrap, and MCMC. Fish and Fisheries 14, 325–342.
McAllister, M. K. and Ianelli, J. N. (1997) Bayesian stock assessment using catchage data and the samplingimportance resampling algorithm. Canadian Journal of Fisheries and Aquaticic Sciences 54, 284–300.
getN
, getSigmaI
, getSigmaR
,
estN
, estSigmaI
, and estSigmaR
extract and estimate sample sizes and sigmas.
iterate
combines all the get*
and est*
functions in one call.
plotCA
and plotCL
show what is behind the
samplesize estimation.
scapepackage
gives an overview of the package.
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  ## Exploring candidate sample sizes:
getN(x.sbw) # sample sizes used in assessment: number of tows
estN(x.sbw) # effective sample size, given data (tows) and model fit
estN(x.sbw, ceiling=200) # could use this
estN(x.sbw, init=FALSE) # from model fit, disregarding tows
plotCA(x.sbw) # years with good fit => large sample size
estN(x.sbw, init=1) # one sample size across all years
estN(x.sbw, init=c(rep(1,14),rep(2,9))) # two sampling periods
## Same mean, regardless of init:
mean(estN(x.sbw, digits=NULL))
mean(estN(x.sbw, digits=NULL, init=FALSE))
mean(estN(x.sbw, digits=NULL, init=1))
mean(estN(x.sbw, digits=NULL, init=c(rep(1,14),rep(2,9))))
## Same median, regardless of init:
median(estN(x.sbw, FUN=median, digits=NULL))
median(estN(x.sbw, FUN=median, digits=NULL, init=FALSE))
median(estN(x.sbw, FUN=median, digits=NULL, init=1))
median(estN(x.sbw, FUN=median, digits=NULL, init=c(rep(1,14),rep(2,9))))
## Multiple series:
getN(x.ling, "CLc") # sample size used in assessment
getN(x.ling, "CLc", digits=0) # rounded
estN(x.ling, "CLc") # model fit implies larger sample sizes
getN(x.ling, "CLc", series="1", digits=0) # get one series
estN(x.ling, "CLc", series="1") # estimate one series

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