wsValidate: Methods to assess length-bias in a proposed standard weight...

In droglenc/FSAWs: Construct and Validate Standard Weight (Ws) Equations for Fish

Methods to assess length-bias in a proposed standard weight equation.

Description

The Willis and empirical quantiles (EmpQ) methods to assess length-bias in a proposed standard weight equation.

Usage

wsValidate(
  object,
  df,
  pops,
  len,
  wt,
  min,
  max,
  w = 10,
  type = c("EmpQ", "Willis"),
  n.cutoff = 3,
  cutoff.tail = TRUE,
  qtype = 8,
  probs = 0.75,
  use.means = FALSE,
  quadratic = TRUE,
  weighted = FALSE,
  alpha = 0.05
)

## S3 method for class 'willis'
print(x, ...)

## S3 method for class 'willis'
summary(object, ...)

## S3 method for class 'empq'
coef(object, ...)

## S3 method for class 'empq'
summary(object, ...)

## S3 method for class 'empq'
anova(object, ...)

## S3 method for class 'empq'
predict(object, ...)

## S3 method for class 'empq'
fitPlot(
  object,
  pch = 16,
  col.pt = "black",
  col.mdl = "red",
  lwd.mdl = 3,
  lty.mdl = 1,
  xlab = "Midpoint Length Category",
  ylab = paste("Standardized", 100 * object$probs, "Percentile Mean Weight"),
  main = "EmpQ Method",
  ...
)

Arguments

object	An object of class RLP or EMP returned from calling rlp or emp in the main function and an object of class class empq or willis (saved from the wsValidate) in the generic functions.
df	A data frame that contains the length-weight data for each population.
pops	A string or numeric that indicates which column in df contains the variable that identifies the different populations.
len	A string or numeric that indicates which column in df contains the variable with the length data.
wt	A string or numeric that indicates which column in df contains the variable with the weight data.
min	A number that indicates the midpoint value of the smallest X-mm length category.
max	A number that indicates the midpoint value of the largest X-mm length category.
w	A number that indicates the widths for which to create length categories.
type	A string that indicates which type of bias detection method should be used.
n.cutoff	A numeric that indicates the minimum sample size in a length category that should be included in the EmpQ regression. Ignored if type="Willis".
cutoff.tail	A logical that indicates if all length categories larger than the lowest length category with a number of populations below n.cutoff should be excluded =TRUE or just those length categories with sample sizes lower than n.cutoff. Ignored if type="Willis".
qtype	Type of quantile method to use. See description of types of quantile calculation methods in quantile. Ignored if use.means=TRUE.
probs	A number that indicates the probability of the quantile. Must be between 0 and 1. Ignored if use.means=TRUE.
use.means	A logical that indicates whether mean mean weight rather than a quantile mean weight should be used in the EmpQ method.
quadratic	A logical that indicates whether a quadratic regression should be fit in the EmpQ method. Ignored if type="Willis".
weighted	A logical that indicates whether the regression in the EmpQ method should be weighted by the number of populations present in each length category. Ignored if type="Willis".
alpha	A numeric that indicates the rejection criterion to be used in the Willis method. Ignored if type="EmpQ".
x	An object saved from the wsValidate call (i.e., of class empq or willis).
...	Additional arguments for methods.
pch	A single numeric that indicates what plotting character codes should be used for the points in plot or fitPlot.
col.pt	A string used to indicate the color of the plotted points.
col.mdl	A string that indicates the type of color to use for the standard length-weight regression line.
lwd.mdl	A numeric that indicates the width of the line to use for the standard length-weight regression line.
lty.mdl	A numeric that indicates the type of line to use for the standard length-weight regression line.
xlab	A label for the x-axis of plot or fitPlot.
ylab	A label for the y-axis of plot or fitPlot.
main	A label for the main title of fitPlot.

Details

The main function can be used to assess length-bias in a proposed standard weight equation using either the method of Willis et al. (1991) (i.e., type="Willis") or the empirical quantiles (EmpQ) method of Gerow et al. (2004) (i.e., type="EmpQ"). The Willis method begins by regressing the relative weight computed from the candidate standard weight equation (supplied in object) for each individual in a population in the df data frame against length. This is repeated for each population in df. The number of positive and negative slopes from this regression that are statistically significant are counted and an exact binomial test is used to determine if there is a statistically equal number of each. If there is a statistically equal number of positive and negative significant slopes then the standard weight equation is said not to exhibit a length bias.

printing the Willis results will show the results for the individual regressions and a table that shows the number of significant negative and positive regression slopes. summary for the Willis results also shows the number of significant negative and positive regression slopes and the results from the exact binomial tests (using binom.test for whether the number of negative and positive slopes is the same or not.

The EmpQ method is performed by (1) computing the mean actual weight per w-mm length category for each population, (2) computing the quantile given in probs (default is 75th) of mean actual weight per length category across all populations, (3) standardizing the quantile mean weights by dividing each by the standard weight for the midpoint of the length categories using the proposed standard weight equation, and (4) regressing the standardized quantile mean weights against the length category midpoints. The regression can either be quadratic (i.e., quadratic=TRUE) as proposed by Gerow et al. (2004) or n-weighted (i.e., weighted=TRUE). In addition, length categories with fewer than ncutoff populations are eliminated (see cutoff.tail description above). A slope of zero for the relationship between standardized quantile mean weights and length category midpoints indicates that no length-based biases exist with the proposed standard weight equation.

For the EmpQ method, coef, summary, anova, and predict returns the typical results for the linear regression model used in the method. fitPlot shows the standardized quantile mean weights versus midpoint length category with the EmpQ method regression line overlaid.

Value

If type="Willis" then a list is returned with the following items.

• res.ind is a data.frame with the results of the individual regressions.

• res.tbl is a table summarizing the number of positive and negative significant slopes.

• res.test contains the results for the exact binomial test.

If type="EmpQ" then a list is returned with the following items:

• n.by.pop is a table of the number of populations represented in each length category.

• lm.v is the EmpQ regression model results.

• regdata is a data.frame used for the EmpQ regression.

• quadratic is a logical that indicates whether the quadratic regression was used.

• weighted is a logical that indicates whether a weighted regression was used.

• probs the numeric given in probs.

Author(s)

Derek H. Ogle, [e-mail]

References

Gerow, K.G., W.A. Hubert, R.C. Anderson-Sprecher. 2004. An alternative approach to detection of length-related biases in standard weight equations. North American Journal of Fisheries Management 24:903-910.

Willis, D.W., C.S. Guy, and B.R. Murphy. 1991. Development and evaluation of the standard weight (Ws) equation for yellow perch. North American Journal of Fisheries Management, 11:374-380.

See Also

rlp and emp.

Examples

## See examples in rlp(), emp(), and FroeseWs()

droglenc/FSAWs documentation built on Feb. 3, 2023, 8:48 a.m.