R: Table 1 of Huggins (1989)

Huggins89.t1 {VGAM} | R Documentation

## 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 The latter used variables beginning with `z`, not `t`, and may be withdrawn very soon.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 = t01,
                                 T02 = t02, T03 = t03, T04 = t04, T05 = t05, T06 = t06,
                                 T07 = t07, T08 = t08, T09 = t09, T10 = t10)
    small.table1 <- subset(Huggins89table1,
                           y01 + y02 + y03 + y04 + y05 + y06 + y07 + y08 + y09 + y10 > 0)
    # fit.tbh is the bottom equation on p.133.
    # It is a M_tbh model.
    fit.tbh <-
      vglm(cbind(y01, y02, y03, y04, y05, y06, y07, y08, y09, y10) ~  x2 + x3.tij,
           xij = list(x3.tij ~ t01 + t02 + t03 + t04 + t05 + t06 + t07 + t08 + t09 + t10 +
                                     T02 + T03 + T04 + T05 + T06 + T07 + T08 + T09 + T10 - 1),
           posbernoulli.tb(parallel.t = TRUE ~ x2 + x3.tij),
           data = small.table1, trace = TRUE,
           form2 = ~  x2 + x3.tij +
                      t01 + t02 + t03 + t04 + t05 + t06 + t07 + t08 + t09 + t10 +
                            T02 + T03 + T04 + T05 + T06 + T07 + T08 + T09 + 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(y01, y02, y03, y04, y05, y06, y07, y08, y09, 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(y01, y02, y03, y04, y05, y06, y07, y08, y09, 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(y01, y02, y03, y04, y05, y06, y07, y08, y09, 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(y01, y02, y03, y04, y05, y06, y07, y08, y09, 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

[Package VGAM version 1.1-3 Index]