# Two-Way ANOVA-Like Method to Analyze Replicated Point Patterns

### Description

Test for effects of both individual factors and their interaction on replicated spatial patterns in a two factorial design.

### Usage

1 2 3 4 5 6 7 8 | ```
K2w(pplist = NULL, dataKijk = NULL, nijk = NULL, r, r0 = NULL, rmax = NULL,
tratA, tratB = NULL, wt = NULL, nsim = 999, correction = "trans", ...)
## S3 method for class 'k2w'
print(x,...)
## S3 method for class 'k2w'
plot(x, trat=NULL, ..., lty = NULL, col = NULL,
lwd = NULL, xlim = NULL, ylim = NULL, xlab = NULL, ylab = NULL,
legend = TRUE, legendpos = "topleft", fun="L", main=NULL)
``` |

### Arguments

`pplist` |
A list of point patterns with the ppp format of spatstat. This argument os alternative to |

`dataKijk` |
A |

`nijk` |
A vector with the number of points in each of the replicated point patterns. |

`r` |
Vector of values for the argument r at which the K functions have been or should be evaluated. If the K functions are to be computed (i.e., if |

`r0` |
Minimum r value for which K(r) estimates will be employed to compute BTSS. |

`rmax` |
Maximum r value for which K(r) estimates will be employed to compute BTSS. |

`tratA` |
A |

`tratB` |
A |

`wt` |
A weighting function employed to compute the BTSS. It can be either an R expression, a vector (with |

`nsim` |
Number of resamples to estimate the sampling distribution of the BTSS statistic. |

`correction` |
Any selection of the options "border", "bord.modif", "isotropic", "Ripley", "translate", "translation", "none" or "best". It specifies the edge correction to be applied if K functions should be computed. |

`...` |
Additional arguments for Kest function of spatstat (only applies if K functions should be computed) or additional graphical arguments for the matplot function. |

`x` |
an object of class |

`trat` |
(optional) Factor employed to compute the averaged K functions that will be ploted. By default, |

`lty` |
(optional) numeric vector of values of the graphical parameter |

`col` |
(optional) numeric vector of values of the graphical parameter |

`lwd` |
(optional) numeric vector of values of the graphical parameter |

`xlim` |
(optional) range of x axis. |

`ylim` |
(optional) range of y axis. |

`xlab` |
(optional) label for x axis. |

`ylab` |
(optional) label for y axis. |

`legend` |
Logical flag or |

`legendpos` |
The position of the legend. Either a character string keyword (see legend for keyword options) or a pair of coordinates in the format |

`fun` |
One of |

`main` |
text to display as the title of the plot. By default, the name of the |

### Details

This function implements a extension of the non-parametric one-way ANOVA-like method of Diggle et al. (1991) to the two-way case, and particularly to test the effects of the interaction of two factors on the spatial structure of replicated point patterns. From a set of K functions, it generates weighted averaged K functions for each level and combinations of levels of the factors and computes a statistic analogous to a *between-treatment sum of squares* (BTSS) in clasical ANOVA. More details are available in Ramon et al. (in revision).

### Value

`K2w`

returns an object of class `k2w`

. Basically, a list with components:

` btss.i ` |
Between treatment sum of squares (BTSS) for factor A. |

` btss.j ` |
BTSS for factor B. |

` btss.ij ` |
BTSS for the interaction of factors A and B. |

` btss.i.res ` |
Resampled distribution of the BTSS statistic for factor A. |

` btss.j.res ` |
Resampled distribution of BTSS for factor B. |

` btss.ij.res ` |
Resampled distribution of BTSS for the interaction of factors A and B. |

` KrepA ` |
Weighted average of the replicated K functions for each level of factor A. |

` KrepB ` |
Weighted average of the replicated K functions for each level of factor B. |

` KrepAB ` |
Weighted average of the replicated K functions for each combination of levels of factors A and B. |

` K0i ` |
Global weighted average (i.e., all K fucntions averaged together). |

` K0j ` |
Global weighted average (i.e., all K fucntions averaged together). |

` K0ij ` |
Global weighted average (i.e., all K fucntions averaged together). |

` Rik ` |
Data.frame with the residual functions for factor A. |

` Rjk ` |
Data.frame with the residual functions for factor B. |

` Rijk ` |
Data.frame with the residual functions for the interaction of factors A and B. |

` nsumA ` |
Total number of points among the replicates in each level of factor A. |

` nsumB ` |
Total number of points among the replicates in each level of factor B. |

` nsumAB ` |
Total number of points among the replicates in each combinatipon of levels of factors A and B. |

` wt ` |
Weighting function employed to compute the BTSS. |

` tratA ` |
Factor A. |

`tratB ` |
Factor B. |

` tratAB ` |
Factor with the combination of levels of A and B. |

` dataKijk ` |
Data.frame with the empirical, replicated, K-functions. |

` nijk ` |
Vector with the number of points in each replicate. |

` r ` |
Vector of r distances at which K functions are estimated. |

` r0 ` |
Minimum r value for which K values have been employed to compute BTSS. |

` KA.res ` |
Data.frame with the weighted average of replicated K functions for each level of factor A, for each of the nsim resamples. |

` KB.res ` |
Data.frame with the weighted average of replicated K functions for each level of factor B, for each of the nsim resamples. |

` KAB.res ` |
Data.frame with the weighted average of replicated K functions for each combination of levels of factors A and B, for each of the nsim resamples. |

` nameA ` |
name of the R object with factor A. |

` nameB ` |
name of the R object with factor B. |

### Author(s)

Marcelino de la Cruz

### References

Diggle, P.J., Nicholas, L. & Benes, F.M. (1991) Analysis of Variance for Replicated Spatial Point Patterns in Clinical Neuroanatomy. *Journal of the American Statistical Association*, 86, 618-625.

Ramon, P., De la Cruz, M., Chacon-Labella, J. & Escudero, A. (in revision). A new two-way ANOVA-like method for analyzing replicated point patterns in ecology.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 |

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