posbernoulli.tb {VGAM} | R Documentation |
Fits a GLM/GAM-like model to multiple Bernoulli responses where each row in the capture history matrix response has at least one success (capture). Sampling occasion effects and behavioural effects are accommodated.
posbernoulli.tb(link = "logitlink", parallel.t = FALSE ~ 1, parallel.b = FALSE ~ 0, drop.b = FALSE ~ 1, type.fitted = c("likelihood.cond", "mean.uncond"), imethod = 1, iprob = NULL, p.small = 1e-4, no.warning = FALSE, ridge.constant = 0.0001, ridge.power = -4)
link, imethod, iprob |
See |
parallel.t, parallel.b, drop.b |
A logical, or formula with a logical as the response.
See Suppose the model is intercept-only.
Setting The default model has a different intercept for each sampling occasion, a time-parallelism assumption for all other covariates, and a dummy variable representing a single behavioural effect (also in the intercept). The most flexible model is to set
|
type.fitted |
Character, one of the choices for the type of fitted value
returned.
The default is the first one.
Partial matching is okay.
For |
ridge.constant, ridge.power |
Determines the ridge parameters at each IRLS iteration.
They are the constant and power (exponent) for the ridge
adjustment for the working weight matrices (the capture
probability block matrix, hence the first τ diagonal
values).
At iteration a of the IRLS algorithm
a positive value is added to the first tau
diagonal elements of the working weight matrices to make
them positive-definite. This adjustment is the
mean of the diagonal elements of |
p.small, no.warning |
See |
This model
(commonly known as M_{tb}/M_{tbh}
in the capture–recapture literature)
operates on a response matrix of 0s and 1s
(n x tau).
See posbernoulli.t
for information that is in common.
It allows time and behavioural effects to be modelled.
Evidently,
the expected information matrix (EIM) seems not
of full rank (especially in early iterations), so
ridge.constant
and ridge.power
are used to
try fix up the problem.
The default link functions are
(logit p_{c1},…,logit p_{c,tau},
logit p_{r2},…,logit p_{r,tau})^T
where the subscript c denotes capture,
the subscript r denotes recapture,
and it is not possible to recapture the animal at sampling
occasion 1.
Thus M=2*tau-1.
The parameters are currently prefixed by pcapture
and precapture
for the capture and recapture probabilities.
This VGAM family function may be further modified in
the future.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions
such as vglm
,
and vgam
.
It is a good idea to apply the parallelism assumption to each
sampling occasion except possibly with respect to the intercepts.
Also, a simple behavioural effect such as being modelled
using the intercept is recommended; if the behavioural effect
is not parallel and/or allowed to apply to other covariates
then there will probably be too many parameters, and hence,
numerical problems. See M_tbh.1
below.
It is a good idea to monitor convergence.
Simpler models such as the M_0/M_h models
are best fitted with posbernoulli.t
or
posbernoulli.b
or
posbinomial
.
Thomas W. Yee.
See posbernoulli.t
.
posbernoulli.b
(including N.hat
),
posbernoulli.t
,
posbinomial
,
Select
,
fill1
,
Huggins89table1
,
Huggins89.t1
,
deermice
,
prinia
.
## Not run: # Example 1: simulated data nTimePts <- 5 # (aka tau == # of sampling occasions) nnn <- 1000 # Number of animals pdata <- rposbern(n = nnn, nTimePts = nTimePts, pvars = 2) dim(pdata); head(pdata) M_tbh.1 <- vglm(cbind(y1, y2, y3, y4, y5) ~ x2, posbernoulli.tb, data = pdata, trace = TRUE) coef(M_tbh.1) # First element is the behavioural effect coef(M_tbh.1, matrix = TRUE) constraints(M_tbh.1, matrix = TRUE) summary(M_tbh.1, presid = FALSE) # Std errors are approximate head(fitted(M_tbh.1)) head(model.matrix(M_tbh.1, type = "vlm"), 21) dim(depvar(M_tbh.1)) M_tbh.2 <- vglm(cbind(y1, y2, y3, y4, y5) ~ x2, posbernoulli.tb(parallel.t = FALSE ~ 0), data = pdata, trace = TRUE) coef(M_tbh.2) # First element is the behavioural effect coef(M_tbh.2, matrix = TRUE) constraints(M_tbh.2, matrix = TRUE) summary(M_tbh.2, presid = FALSE) # Std errors are approximate head(fitted(M_tbh.2)) head(model.matrix(M_tbh.2, type = "vlm"), 21) dim(depvar(M_tbh.2)) # Example 2: deermice subset data fit1 <- vglm(cbind(y1, y2, y3, y4, y5, y6) ~ sex + weight, posbernoulli.t, data = deermice, trace = TRUE) coef(fit1) coef(fit1, matrix = TRUE) constraints(fit1, matrix = TRUE) summary(fit1, presid = FALSE) # Standard errors are approximate # fit1 is the same as Fit1 (a M_{th} model): Fit1 <- vglm(cbind(y1, y2, y3, y4, y5, y6) ~ sex + weight, posbernoulli.tb(drop.b = TRUE ~ sex + weight, parallel.t = TRUE), # But not for the intercept data = deermice, trace = TRUE) constraints(Fit1) ## End(Not run)