Compute 95% confidence intervals for derived estimates from the U submatrix of a matrix population model

This function computes the 95% confidence interval for measures derived from the U submatrix of a matrix population model using parametric bootstrapping. In this approach a sampling distribution of the U submatrix is generated by taking a large number of random independent draws using the sampling distribution of each underlying transition rate. The approach rests on our assumption that survival-related processes are binomial (see the function add_mpm_error() for details).

Usage

compute_ci_U(mat_U, sample_size, FUN, ..., n_sim = 1000, dist.out = FALSE)

Arguments

mat_U

A matrix that describes the growth and survival process.

sample_size

either (1) a single matrix of sample sizes for each element of the U matrix, (2) a single value applied to the whole matrix

FUN

A function to apply to each simulated matrix population model. This function must take, as input, a single U submatrix of a matrix population model (i.e., the U matrix). For functions that require the A matrix, use compute_ci.

...

Additional arguments to be passed to FUN.

n_sim

An integer indicating the number of simulations to run. Default is 1000.

dist.out

Logical. If TRUE, returns a list with both the quantiles and the simulated estimates. Default is FALSE.

Value

If dist.out is FALSE, a numeric vector of the 2.5th and 97.5th quantiles of the estimated measures. If dist.out = TRUE, a list with two elements: quantiles and estimates. quantiles is a numeric vector of the 2.5th and 97.5th quantiles of the estimated measures, and estimates is a numeric vector of the estimated measures.

Details

The main inputs is the U matrix, which describes the survival-related processes. The underlying assumption is that the U matrix is the average of a binomial process. The confidence interval will depend largely on the sample size used.

References

Chapter 12 in Caswell, H. (2001). Matrix Population Models. Sinauer Associates Incorporated.

See also

Other errors: add_mpm_error(), calculate_errors(), compute_ci()

Author

Owen Jones jones@biology.sdu.dk

Examples

set.seed(42) # set seed for repeatability

# Data for use in example
matU <- matrix(c(
  0.1, 0.0,
  0.2, 0.4
), byrow = TRUE, nrow = 2)


# Example of use to calculate 95% CI of life expectancy
compute_ci_U(
  mat_U = matU, sample_size = 10, FUN =
    Rage::life_expect_mean
)
#>     2.5%    97.5% 
#> 1.000000 2.334524 

# Example of use to calculate 95% CI of generation time and show the
# distribution of those bootstrapped estimates
xx <- compute_ci_U(
  mat_U = matU, sample_size = 100, FUN =
    Rage::life_expect_mean, dist.out = TRUE
)

summary(xx$quantiles)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   1.314   1.405   1.495   1.495   1.586   1.676 
hist(xx$estimates)