`moultmcmc.Rd`

Bayesian inference for Underhill-Zucchini moult models and expansions

```
moultmcmc(
moult_column,
date_column,
id_column = NULL,
start_formula = ~1,
duration_formula = ~1,
sigma_formula = ~1,
type = 2,
lump_non_moult = FALSE,
data,
init = "auto",
flat_prior = TRUE,
beta_sd = 0,
log_lik = FALSE,
use_phi_approx = FALSE,
active_moult_recaps_only = TRUE,
same_sigma = FALSE,
...
)
```

- moult_column
the name the column in

`data`

containing moult indices, i.e. a numeric vector of (linearized) moult scores in [0,1] (0 = old plumage, 1 = new plumage; for model types 1-5), numerical moult codes (1 = old plumage, 2 = moulting, 3 = new plumage; for model type 1), or a mixed column created by`consolidate_moult_records`

for model type 12.- date_column
the name the column in

`data`

containing sampling dates, encoded as days since an arbitrary reference date, i.e. a numeric vector- id_column
(optional) factor identifier. Usually a season-individual combination to encode within-season recaptures, defaults to NULL. When provided moultmcmc will attempt to fit the relevant recaptures model.

- start_formula
model formula for start date

- duration_formula
model formula for duration

- sigma_formula
model formula for start date sigma

- type
integer (one of 1,2,3,4,5,12) referring to type of moult data and consequently model to be fitted (see details)

- lump_non_moult
logical; should pre- and post-moult observations be treated as indistinguishable? if TRUE and type %in% c(1,2,12), the relevant lumped model will be fitted (see details).

- data
Input data frame must contain a numeric column "date" and a column "moult_cat" which is a numeric vector of categorical moult codes (1 = old plumage,2 = moulting,3 = new plumage).

- init
Specification of initial values for all or some parameters. Can be the string "auto" for an automatic guess based on the data, or any of the permitted

`rstan`

options: the digit 0, the strings "0" or "random", or a function. See the detailed documentation for the init argument in`rstan::stan`

.- flat_prior
use uniform prior on start date and duration (TRUE) or vaguely informative truncated normal prior (FALSE). Defaults to TRUE.

- beta_sd
use zero-centred normal priors for regression coefficients other than intercepts? If <= 0 the stan default of improper flat priors is used.

- log_lik
boolean retain pointwise log-likelihood in output? This enables model assessment and selection via the loo package. Defaults to FALSE, can lead to very large output arrays when sample size is large.

- use_phi_approx
logical flag whether to use stan's Phi_approx function to calculate the "old" likelihoods

- active_moult_recaps_only
logical flag whether to ignore repeated observations outside the active moult phase

- same_sigma
logical flag, currently unused

- ...
Arguments passed to

`rstan::sampling`

(e.g. iter, chains).

An object of class `stanfit`

returned by `rstan::sampling`

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.