# How to interpret the result of ppm model?

I have a dataset of Populus Alba trees distribution in Hungary. I made a ppm model and used temperature, elevation and precipitation as covariates (this is the code: ppm1_alba <- ppm(p_alba_ppp ~ temp_im_hungary + prec_im_hungary + elevation_im_hungary). I need to estimate the effect of the temperature, elevation and precipitation on the distribution of tress. I used ppm model because I'm using spatstat package.I used a "ppp" object to built the model and covariates are "im" objects. I don't exactly know how to interpret the result as there is no Pvalue. Could anyone help me?

Fitted trend coefficients:
(Intercept)      temp_im_hungary      prec_im_hungary elevation_im_hungary
-25.12321300           0.25118693           0.00582099          -0.04465693

Estimate        S.E.       CI95.lo      CI95.hi Ztest
(Intercept)          -25.12321300 3.415243260 -31.816966783 -18.42945921   ***
temp_im_hungary        0.25118693 0.325343625  -0.386474861   0.88884871
prec_im_hungary        0.00582099 0.002262749   0.001386084   0.01025590     *
elevation_im_hungary  -0.04465693 0.012035001  -0.068245104  -0.02106877   ***
Zval
(Intercept)          -7.3562002
temp_im_hungary       0.7720665
prec_im_hungary       2.5725306
elevation_im_hungary -3.7105883


Careful reading of the ppm documentation is required in cases in which the user is not already thoroughly grounded in the underlying statistical methodology. This gitbook provides an introduction or refresher. See also the package vignettes.

Fits a point process model to an observed point pattern

is the headline description of what ppm produces, which alerts the user that this is a particular type of model, different from a linear regression model or a logistic regression model for example. Accordingly, the test statistic, diagnostics and interpretation can be expected to differ, as well.

Partial additional information can be derived from the ppm.object documentation.

The paper cited in the references section provides background for one use case, the Gibbs point process, in which different points typically inhibit each other. (The other is a Poisson point process, in which different points do not interact with each other.) From a domain perspective it seems likely that temperature, elevation and precipitation do interact (if for no other reason than the adiabatic lapse rate) and thus the present model is Gibbs. (Note that the RHE in that cases represents the logarithm of the first order potential of the Gibbs point process.) Because S.E. is displayed in the OP, however, it appears that the model is treating the RHE as non-interacting.

This observation leads to the print.ppm method for displaying the results of a fitted object in which it is to be seen that only for Poisson are the standard errors printed by default and that in any event the print method is designed to return only a subset of the available information in a ppm object. Further detail can be obtained with reference to the ppm.object documentation and inspection using str().

Further to the understanding of the model information are the concepts of regular and irregular parameters:

regular parameters: A parameter φ is called regular if the log likelihood is a linear function of θ where θ = θ(ψ) is some transformation of ψ. [Then θ is called the canonical parameter.]

Irregular are all other, and must be provided as a fixed value in the call.

With this all in mind, turn to what the fitted model shows about P. alba and what weight school be given to it. If by distribution is meant the presence or absence of the species at a given spatial coordinate, the outcome is binary; if global density (\widehat{\lambda}) is meant, how should the outcome be described?

The conclusion offered here is that interpreting the output of any model run depends critically on the details of how the model is constructed in terms of formal arguments and the precise estimate desired.

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