moult: Models to analyse data of moult in birds

In moult: Models for Analysing Moult in Birds

Models to analyse data of moult in birds

Description

Estimate duration and mean start date of moult from moult score data by maximum likelihood. Covariates to model duration and start of moult are possible.

Usage

moult(formula, data, start = NULL, type = 2, method = "BFGS", fixed = NULL, 
             fixed.val = NULL, prec = 0.02)
            
moult_alternative(formula, data, start = NULL, type = 2, method = "BFGS", 
                  fixed = NULL, fixed.val = NULL, prec = 0.02)

Arguments

formula	symbolic description of the model, see details.
start	starting values for parameters.
data	an optional data frame containing the variables in the model. If not found in data, the variables are taken from the environment from which moult was called.
type	integer (one of 1,2,3,4,5) referring to type of moult data and consequently model to be fitted (see details).
method	optimisation algorithm, passed to optim.
fixed	logical vector specifying which parameter values to fix during optimization.
fixed.val	numeric vector with values for the fixed parameters.
prec	numeric, measurement precision of moult index (proportion of feather mass grown), default = 0.02.

Details

formula is specified in 5 parts:

moult.index ~ days | x1 + x2 | y1 + y2 | z1 + z2

where moult.index is a numerical vector with values between 0 and 1, days is a vector with corresponding day numbers on which moult indeces were observed. The next three parts contain explanatory variables for modelling duration, mean start date and standard deviation in start date, respectively. If no explanatory variables are wanted for duration, say, this can be specified by leaving a blank between the first and second vertical lines, or equivalently, inserting a 1 between the vertical lines (which means all durations will be assumed equal). Similarly for mean start date and standard deviation. The minimum formula must contain moult.index ~ days, which will assume the same duration, mean start date and standard deviation for all individuals.

type refers to the type of moult data available (see Underhill and Zucchini (1998) and Underhill, Zucchini and Summers (1990)).

type = 1

sample is representative of entire population (not yet moulting, in moult, and birds which have completed moult). For type 1 data, any value between 0 and 1 (> 0 and < 1) can be used as the moult index for birds in active moult. The value used does not matter, only the fact that they are in moult.

type = 2

(default) sample is representative of entire population (not yet moulting, in moult, and birds which have completed moult). Moult scores are required.

type = 3

sample is representative only of birds in moult. Individuals with moult scores 0 or 1 are ignored.

type = 4

sample is representative only of birds in moult and those that have completed moult. Individuals with moult scores 0 are ignored.

type = 5

sample is representative only of birds that have not started moult or that are in moult. Individuals with moult scores 1 are ignored.

To fix parameters fixed will be a logical vector, e.g. fixed = c(F, F, T), fixed.val = 3.5 will fix the standard deviation in start date to exp(3.5) and only estimate the remaining two parameters.

moult uses the R function optim to minimise the negative log-likelihood.

Note: The standard deviation parameters are estimated on the log-scale. Thus the corresponding elements in the covariance matrix are also on the log-scale. Starting values for the standard deviation should also be supplied on the log-scale. Standard errors for the standard deviation parameters are on the scale of the standard deviation (in days), estimated using the delta method.

moult_alternative offers a different parameterization (still in testing!): the duration of moult parameter is as before, but instead of start of moult, the parameter estimated is the halfway date, i.e. the date at which 50% of individuals have completed 50% of moult. The standard deviation parameter now is for the standard deviation between indiviudals in reaching 50% of moult. Start and end of moult can be derived as halfway date - 0.5 x duration, + 0.5 x duration, respectively. This alternative parameterization attempts to reduce the problem of strong negative correlation between the previous parameters start of moult and duration, and gives a more robust estimate for timing of moult (Les Underhill, pers. comm., Jackson 2018).

Value

coefficients	parameter estimates split up into duration, mean start date and standard deviation of start date.
loglik	log-likelihood at parameter estimates.
vcov	variance covariance matrix for paramter estimates (duration, mean start date, SD(start date)).
standard.errors	vector of standard errors for parameter estimates, obtained from diagonal elements of vcov, see details (duration, mean start date, SD(start date)).
type	type of data assumed, see details.
residuals	vector of residuals: observed - fitted moult index.
fitted.values	a vector of fitted values (moult scores).
n	number of observations.
df.residual	residual degrees of freedom for fitted model.
terms	duration formula, mean formula, full formula.
X	model matrix with covariates.
y	observed response (moult index) values.
Day	observed observation days.
mean.formula	model formula for mean start date.
duration.formula	model formula for duration of moult.
formula	model formula for mean start and duration of moult.
sd.formula	grouping variable used to estimate standard deviations in mean start dates, different for each group.
optim	object returned by call to optim, which minimises negative log-likelihood.
converged	logical value indicating whether algorithm has converged or not.
convergence.value	value for convergence returned by optim, see optim for details.

Author(s)

Birgit Erni [e-mail]

References

Erni, B., Bonnevie, B. T., Oschadleus, H.-D., Altwegg, R. and Underhill, L. G. (2013) moult: An R package to analyze moult in birds. Journal of Statistical Software, 52(8), 1–23. doi: 10.18637/jss.v052.i08

Jackson, C. 2018. The moult and migration strategies of Lesser Sand Plover, Greater Sand Plover and Terek Sandpiper. PhD Thesis, University of Cape Town, South Africa.

Underhill, L. G. and Zucchini, W. (1988) A model for avian primary moult. Ibis 130, 358–372.

Underhill, L. G. and Zucchini, W. and Summers, R. W. (1990) A model for avian primary moult-data types based on migration strategies and an example using the Redshank Tringa totanus. Ibis 132, 118–123.

See Also

predict.moult, ms2pfmg

Examples

data(sanderlings)

m2 <- moult(MIndex ~ Day, data = sanderlings) 
summary(m2)

moult documentation built on Aug. 30, 2022, 9:06 a.m.