KAMP bivariate expectation

Computes the KAMP (K-function Adjusted for Marked Permutations) expectation for bivariate point patterns. This function calculates Ripley's K using both the traditional Ripley's K method (based on Kcross) and the KAMP-adjusted CSR baseline (based on Kest).

The KAMP-adjusted CSR represents a more robust baseline for K (compared to traditional CSR) that accounts for spatial clustering or inhomogeneity in a point pattern compared to the traditional CSR assumption, while avoiding the computational burden of permuting the point pattern.

Note: This function uses the spatstat package under the hood. See ?Kcross and ?Kest for more details on the K calculation methods.

See kamp_expectation_biv_mat for the matrix-based implementation of the KAMP bivariate expectation.

Usage

kamp_expectation_biv(
  ppp_obj,
  rvec = c(0, 0.05, 0.075, 0.1, 0.15, 0.2),
  correction = "trans",
  markvar1 = "immune1",
  markvar2 = "immune2",
  thin_pct = 0
)

Arguments

ppp_obj

A point pattern object from the spatstat.geom package.

rvec

Vector of radii at which to calculate the KAMP expectation. Defaults to c(0, 0.05, 0.075, 0.1, 0.15, 0.2).

correction

Type of edge correction. Defaults to translational.

markvar1

Variable used to mark the points in the point pattern object for the first type. Default is "immune1".

markvar2

Variable used to mark the points in the point pattern object for the second type. Default is "immune2".

thin_pct

Percentage that determines how much to thin the amount of points in the point pattern object. Default is 0.

Value

A dataframe with the following columns:

r

The radius at which K was calculated.

k

The observed K value

theo_csr

The theoretical K under CSR

kamp_csr

The adjusted CSR representing the KAMP permuted expectation.

kamp_fundiff

The difference between observed K and KAMP CSR

Details

Computes KAMP Expectation for Bivariate Point Patterns

Examples

if (requireNamespace("spatstat.geom", quietly = TRUE) &&
    requireNamespace("spatstat.random", quietly = TRUE)) {

  # Simulates a window
  win <- spatstat.geom::owin(c(0, 1), c(0, 1))

  # Generates 200 total points
  pp <- spatstat.random::rpoispp(lambda = 200, win = win)

  # Assigns three marks: immune1, immune2, and background
  marks <- sample(c("immune1", "immune2", "background"), pp$n, replace = TRUE, prob = c(0.3, 0.3, 0.4))

  # Creates marked point pattern
  marked_pp <- spatstat.geom::ppp(pp$x, pp$y, window = win, marks = factor(marks))

  # Computes KAMP expectation
  result <- kamp_expectation_biv(marked_pp, markvar1 = "immune1", markvar2 = "immune2")
  print(result)
}
#> # A tibble: 6 × 5
#>       r       k theo_csr kamp_csr kamp_fundiff
#>   <dbl>   <dbl>    <dbl>    <dbl>        <dbl>
#> 1 0     0        0        0            0      
#> 2 0.05  0.00588  0.00785  0.00712     -0.00124
#> 3 0.075 0.0171   0.0177   0.0181      -0.00100
#> 4 0.1   0.0287   0.0314   0.0319      -0.00317
#> 5 0.15  0.0673   0.0707   0.0700      -0.00272
#> 6 0.2   0.127    0.126    0.122        0.00498