VGAM (version 0.9-3)

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(Huggins89table1)
data(Huggins89.t1)

format

The format is a data frame.

Details

Table 1 of Huggins (1989) gives this toy data set. Note that variables t1,...,t10 are occasion-specific variables. They correspond to the response variables y1,...,y10 which have values 1 for capture and 0 for not captured.

Both Huggins89table1 and Huggins89.t1 are identical. The latter used variables beginning with z, not t, and may be withdrawn very soon.

References

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

Examples

Huggins89table1 <- transform(Huggins89table1, x3.tij = t1,
                             T2 = t2, T3 = t3, T4 = t4,  T5 =  t5, T6 = t6,
                             T7 = t7, T8 = t8, T9 = t9, T10 = t10)
small.table1 <- subset(Huggins89table1,
                       y1 + y2 + y3 + y4 + y5 + y6 + y7 + y8 + y9 + y10 > 0)
# fit.tbh is the bottom equation on p.133.
# It is a M_tbh model.
fit.tbh <-
  vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~  x2 + x3.tij,
       xij = list(x3.tij ~ t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 +
                           T2 + T3 + T4 + T5 + T6 + T7 + T8 + T9 + T10 - 1),
       posbernoulli.tb(parallel.t = TRUE ~ x2 + x3.tij),
       data = small.table1, trace = TRUE,
       form2 = ~  x2 + x3.tij +
                  t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 +
                       T2 + T3 + T4 + T5 + T6 + T7 + T8 + T9 + T10)

# These results differ a bit from Huggins (1989), probably because
# two animals had to be removed here (they were never caught):
coef(fit.tbh)  # First element is the behavioural effect
sqrt(diag(vcov(fit.tbh)))  # SEs
constraints(fit.tbh, matrix = TRUE)
summary(fit.tbh, presid = FALSE)
fit.tbh@extra$N.hat     # Estimate of the population site N; cf. 20.86
fit.tbh@extra$SE.N.hat  # Its standard error; cf. 1.87 or 4.51

fit.th <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
               posbernoulli.t, data = small.table1, trace = TRUE)
coef(fit.th)
constraints(fit.th)
coef(fit.th, matrix = TRUE)  # M_th model
summary(fit.th, presid = FALSE)
fit.th@extra$N.hat     # Estimate of the population size N
fit.th@extra$SE.N.hat  # Its standard error

fit.bh <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
               posbernoulli.b(I2 = FALSE), data = small.table1, trace = TRUE)
coef(fit.bh)
constraints(fit.bh)
coef(fit.bh, matrix = TRUE)  # M_bh model
summary(fit.bh, presid = FALSE)
fit.bh@extra$N.hat
fit.bh@extra$SE.N.hat

fit.h <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
             posbernoulli.b, data = small.table1, trace = TRUE)
coef(fit.h, matrix = TRUE)  # M_h model (version 1)
coef(fit.h)
summary(fit.h, presid = FALSE)
fit.h@extra$N.hat
fit.h@extra$SE.N.hat

Fit.h <- vglm(cbind(y1, y2, y3, y4, y5, y6, y7, y8, y9, y10) ~ x2,
              posbernoulli.t(parallel.t = TRUE ~ x2),
              data = small.table1, trace = TRUE)
coef(Fit.h)
coef(Fit.h, matrix = TRUE)  # M_h model (version 2)
summary(Fit.h, presid = FALSE)
Fit.h@extra$N.hat
Fit.h@extra$SE.N.hat