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What is the relationship between marks and covariates in point process

I am confused about marks and covariates in point process. I am trying to create a model of a marked point pattern with few covariates in R by using spatstat, but I am not sure the relationship between marks and covariates. Could anyone help me?

Thanks.

---- update I have a given point pattern about populations of settlements in given location, and few covariates such as soil fertility, annual rainfall and so on. And I would like to describe the distribution of settlements.

Solution

  • For point processes the distinction between marks and covariates are:

    • Marks are values attached to each point (settlement) and often the mark is not meaningful at other locations.

    • Covariates are conceptually meaningful/available throughout the entire survey region (observation window).

    Mark values can in principle be anything, but basically only two types are supported in spatstat at the time of writing: 1) marks with a numerical value and 2) categorical (factor-valued) marks. In spatstat there is a strong emphasis on the latter, which are referred to as 'multitype' patterns. For multitype patterns you can build models with the spatstat function ppm, but currently there are no modelling tools for patterns with numerical marks.

    To analyse your data with spatstat you probably have to either discard the population size information or use cut.ppp to divide the settlements into groups like "big", "medium", and "small" or what ever makes sense in your study, and then proceed with the analysis of this multitype pattern.

    Update based on comments: Assume we have a multitype point pattern X (of class ppp) and two covariate images im1 and im2 (of class im). Then a Poisson model with the same covariate effect for each level of the mark is:

    ppm(X ~ marks + im1 + im2)

    A model allowing for "interaction", i.e., different effects of the covariates for each level of the factor is:

    ppm(X ~ marks * im1 + marks * im2)

    For both models the interpretation of the model depend on the contrasts in force (by default treatment contrasts). It is exactly like using lm or glm.