
posbernoulli.b(link = "logit", parallel.b = FALSE, apply.parint = TRUE,
icap.prob = NULL, irecap.prob = NULL)
CommonVGAMffArguments
for information about
these arguments.
With an intercept-only model
setting parallel.b = TRUE
results in the $M_0$ model;
it just deletes the 2nd"vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.posbernoulli.tb
.posbernoulli.t
for details.
Each sampling occasion has the same probability and this is modelled here.
But once an animal is captured, it is marked so that its future
capture history can be recorded. The effect of the recapture
probability is modelled through a second linear/additive predictor,
and this usually differs from the first linear/additive predictor
by just a different intercept (because parallel.b = TRUE
but the parallelism does not apply to the intercept).
It is well-known that some species of animals are affected by capture,
e.g., trap-shy or trap-happy. This
See posbernoulli.t
for other information,
e.g., common assumptions.
The number of linear/additive predictors is $M = 2$,
and the default links
are $(logit \,p_c, logit \,p_r)^T$
where $p_c$ is the probability of capture and
$p_r$ is the probability of recapture.
The fitted value returned is of the same dimension as
the response matrix, and depends on the capture history:
prior to being first captured, it is cap.prob
.
Afterwards, it is recap.prob
.
By default, the constraint matrix for the intercept term is set up so that $p_r$ differs from $p_c$ by a simple binary effect. This allows an estimate of the trap-happy/trap-shy effect.
posbernoulli.t
.posbernoulli.t
(including estimating $N$),
posbernoulli.tb
,
Perom
,
dposbern
,
rposbern
,
posbinomial
.# Perom data ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
# Fit a M_b model
M_b <- vglm(cbind(y1, y2, y3, y4, y5, y6) ~ 1,
data = Perom, posbernoulli.b, trace = TRUE)
coef(M_b, matrix = TRUE)
constraints(M_b, matrix = TRUE)
summary(M_b)
# Fit a M_bh model
M_bh <- vglm(cbind(y1, y2, y3, y4, y5, y6) ~ sex + weight,
posbernoulli.b, trace = TRUE, data = Perom)
coef(M_bh, matrix = TRUE)
constraints(M_bh) # (2,2) element of "(Intercept)" is the behavioural effect
summary(M_bh) # Estimate of behavioural effect is positive (trap-happy)
# Fit a M_h model
M_h <- vglm(cbind(y1, y2, y3, y4, y5, y6) ~ sex + weight,
data = Perom,
posbernoulli.t(parallel.t = TRUE), trace = TRUE)
coef(M_h, matrix = TRUE)
constraints(M_h, matrix = TRUE)
summary(M_h)
# Fit a M_0 model
M_0 <- vglm(cbind( y1 + y2 + y3 + y4 + y5 + y6,
6 - y1 - y2 - y3 - y4 - y5 - y6) ~ 1,
data = Perom, posbinomial, trace = TRUE)
coef(M_0, matrix = TRUE)
constraints(M_0, matrix = TRUE)
summary(M_0)
# Simulated data set ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
set.seed(123); nTimePts <- 5; N <- 1000
hdata <- rposbern(n = N, nTimePts = nTimePts, pvars = 2,
is.popn = TRUE) # N is the popn size
nrow(hdata) # Less than N
# The truth: xcoeffs are c(-2, 1, 2) and cap.effect = -1
model1 <- vglm(cbind(y1, y2, y3, y4, y5) ~ x2,
posbernoulli.b, data = hdata, trace = TRUE)
coef(model1)
coef(model1, matrix = TRUE)
constraints(model1, matrix = TRUE)
summary(model1)
head(depvar(model1)) # Capture history response matrix
head(model1@extra$cap.hist1) # Info on its capture history
head(model1@extra$cap1) # When it was first captured
head(fitted(model1)) # Depends on capture history
(trap.effect <- coef(model1)["(Intercept):2"]) # Should be -1
head(model.matrix(model1, type = "vlm"), 21)
head(hdata)
summary(hdata)
dim(depvar(model1))
vcov(model1)
model1@extra$N.hat # Estimate of the population size; should be about N
model1@extra$SE.N.hat # SE of the estimate of the population size
# An approximate 95 percent confidence interval:
round(model1@extra$N.hat + c(-1, 1) * 1.96 * model1@extra$SE.N.hat, 1)
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