VGAM (version 0.9-1)

Huggins89.t1: Table 1 of Huggins (1989)

Description

Simulated capture data set for the linear logistic model depending on an occasion covariate and an individual covariate for 10 trapping occasions and 20 individuals.

Usage

data(Huggins89.t1)

format

The format is a data frame.

Details

Table 1 of Huggins (1989) gives this toy data set. Note that variables z1,...,z10 are occasion-specific variables. They correspond to the response variables y1,...,y10 which have values 1 for capture and 0 for not captured.

References

Huggins, R. M. (1989) On the statistical analysis of capture experiments. Biometrika, 76, 133--140.

Examples

small.Huggins89.t1 <- transform(Huggins89.t1, Zedd = z1, Z2 = z2, Z3 = z3)
small.Huggins89.t1 <- subset(small.Huggins89.t1, y1 + y2 + y3 > 0)
# fit1 is the bottom equation on p.133, but this is only for the 1st 3 responses.
# Currently posbernoulli.tb() cannot handle more than 3 Bernoulli variates.
# The fit is not very good.
fit1 <-
  vglm(cbind(y1, y2, y3) ~  x2 + Zedd,
       xij = list(Zedd ~ z1 + z2 + z3 + Z2 + Z3 - 1),
       posbernoulli.tb(parallel.t = TRUE), maxit = 155,
       data = small.Huggins89.t1, trace = TRUE,
       form2 = ~ x2 + Zedd + z1 + z2 + z3 + Z2 + Z3)
coef(fit1)
coef(fit1, matrix = TRUE)  # M_t model
constraints(fit1)
summary(fit1)
fit1@extra$N.hat     # Estimate of the population size N
fit1@extra$SE.N.hat  # Its standard error


fit.t <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
              posbernoulli.t, data = Huggins89.t1, trace = TRUE)
coef(fit.t)
coef(fit.t, matrix = TRUE)  # M_t model
summary(fit.t)
fit.t@extra$N.hat     # Estimate of the population size N
fit.t@extra$SE.N.hat  # Its standard error


fit.b <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
              posbernoulli.b, data = Huggins89.t1, trace = TRUE)
coef(fit.b)
coef(fit.b, matrix = TRUE)  # M_b model
summary(fit.b)
fit.b@extra$N.hat
fit.b@extra$SE.N.hat


fit.0 <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
             posbernoulli.b(parallel.b = TRUE), data = Huggins89.t1,
             trace = TRUE)
coef(fit.0, matrix = TRUE)  # M_0 model (version 1)
coef(fit.0)
summary(fit.0)
fit.0@extra$N.hat
fit.0@extra$SE.N.hat


Fit.0 <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
              posbernoulli.t(parallel.t = TRUE), data = Huggins89.t1,
              trace = TRUE)
coef(Fit.0)
coef(Fit.0, matrix = TRUE)  # M_0 model (version 2)
summary(Fit.0)
Fit.0@extra$N.hat
Fit.0@extra$SE.N.hat