Step 2: Fit growth models
The calc.growth() function is the primary function in
‘MRgrowth’. It fits one or more growth models to the formatted data,
returns the fitted values of asymptotic size (A) and growth rate (k),
calculates bootstrapped confidence intervals, and optionally produces a
plot of growth curves.
Key arguments
size0 — the body size at birth or
hatching. This does not affect the estimates of A or k, but it does
affect the predicted sizes at each age in age.vect. Use a
species-typical birth or hatchling size. If you do not provide a value,
the function will use half the smallest observed size, which may be
unrealistic.
age.vect — a vector of ages for which
predicted sizes and confidence intervals will be calculated. Choose a
range that covers the full lifespan of your species. If not provided,
the function defaults to ages 1 through 4 times the largest observed
time interval, which may not cover the full age range. The number of
values in this vector has very little impact on run time, so it is best
to use fine-scale intervals (e.g., every year) to produce smooth
curves.
models — a vector of models to run and
evaluate (any combination of “vb”,“logistic”,“gompertz”). The default is
to run and compare all three.
runs — 95% confidence intervals are
calculated by bootstrapping, and the runs argument determines the number
of bootstrap replicates (higher values = better estimates but longer run
times). The default of 5000 is generally appropriate for publication.
Lower values (e.g., 100) can be used during exploratory analysis to
reduce run time. This argument only affects the confidence intervals,
not the the actual estimates of A, k, or model diagnostics (e.g., (AIC).
Therefore, for large data sets, you may want to do an initial run with
bootstrapping essentially turned off by setting it to 1. Use that run to
determine which model is the best fit, then run a second analysis using
a high number of runs (e.g., 5000) and only the best fit model. Note
that the seed argument is passed internally to set.seed(),
so results are repeatable.
type — by default, ‘MRgrowth’ uses
maximum likelihood (“ML”) estimation, but it can be changed to least
squares (“OLS”). Usually, ML and OLS will produce identical results;
however, OLS will not return AIC values. Occasionally, ML may result in
convergence issues which are not present in OLS. Therefore, if an ML
model does not converge, you may want to try it with OLS.
fixed.A — in a limited number of cases,
you may want to evaluate only the k parameter and supply a fixed
asymptotic value (A) based on existing knowledge (e.g., a different
study of a different population). As a general rule, this is not
advisable, but can be used in some cases such as small sample sizes.
Interpreting comparisons of models with and without a fixed A value is
complex. AICs are inherently penalized by the number of parameters
involved; thus, models with fixed.A have fewer parameters, which will
result in lower AICs unless the fit is substantially worse. As a result,
if you run models with and without a fixed A, and the fixed values are
close to the values that would have been estimated, you will get lower
AICs even if the other parameters (k) do not actually fit as well. This
is simply because you had one fewer parameter penalizing the AIC score.
Further, for those AICs to be valid, the value of A must have been
derived entirely independently (e.g., a different population). If it was
based on a previous run or some aspect of the population being studied
(e.g., max observed body size) then it is not independent and the AIC
score has not been accurately penalized for the number of parameters. To
help with this, two sets of AIC scores are returned when a value is
supplied for fixed.A. The “fixed” scores were calculated based on two
parameters being estimated (k and sigma). These are the “correct” AICs
for models with a fixed A, but they come with the caveats described
above. The “AIC” and “AICc” columns contain the AICs based on three
parameters being estimated (A, k, and sigma), and may be more
appropriate if the selection of A was in anyway biased. Other model
diagnostics like convergence issues and NLL should also be
consulted.
other arguments — The other inputs are
set to reasonable defaults and, in most cases, they do not need to be
altered. Indeed, in most cases, only the data set, size0, and age.vect
need to be supplied for a useful run (assuming your data is the output
of format.data()).
Adjusting initial.A and initial.k can result in slight improvements
in run time, but they are generally not noticeable. In concept,
initial.A and initial.k values could affect convergence in the ML
models, but to avoid this calc.growth() internally uses the
initial values in an OLS model to produce suitable inputs for an ML
model, and the final results are based on the ML model. So, in practice,
initial values have no effect on the final result.
Basic usage
Let’s run a simple comparison of all three models, looking at the expected size at ages 1-50 (years), with a hatchling size of 50 mm. For this example, we will keep runs low (100) to reduce run time, but for actual analyses, you want several thousand runs. Most values will be left on their default settings.
# Using low runs for vignette build speed
results <- calc.growth(
x = formatted.data,
size0 = 50,
age.vect = 1:50,
models = c("vb", "gompertz", "logistic"),
type = "ML",
runs = 100,
return.plot = TRUE
)
