I have a simulated data set showing distribution of a certain habitat type as a point pattern.
Then I have a empirical data set but there the format is raster.
The two datasets are covering the same area.
How can I compare these two data sets?
I want to know if the simulated data is a good representation of the empirical one.
I use R for the analyses.
What exactly are you wanting to compare? A point pattern is a representation of an explicit spatial process that is significant from a spatial random assumption. A raster does not meet the same criteria of a point process. You can test the similarity of values but, this does not at all demonstrate the equivalency of an underlying spatial process.
Think of what is happening here, you are trying to compare a set of points that explicitly represent a discrete spatial process (event) to a systematic array of points with arbitrary spacing that can represent any number of spatial domains.
I would point out (pardon the pun) that ecological phenomena, such as vegetation cover or habitat type, do not meet the assumption of a point process. A point pattern (process) represents a set of "events" that exhibit random or spatial characteristics that can be quantified statistically. The idea that a simulated point process is a sampled representation of a empirical process occurring across discrete areas is an erroneous assertion. Discrete areas do not represent a point process and point pattern analysis statistics are quite inappropriate!
I would imagine that you would benefit researching "neutral theory" and its extensions into landscape pattern. Bob Gardner published several papers on neutral models for testing null hypotheses of landscape process (eg., Pearson & Gardner 1997) and developed the RULES software. This would seem much more appropriate than a simulated point pattern approach.
Based on additional information from the OP citing Lindström et al., (2010), I will expand my answer. The difficulty here is that simulated neutral point pattern landscapes (NPPL) are a function of the Kernel that defines the autocorrelation characteristics of the expected patch dynamics. This makes it very difficult to perform any type of direct comparison of the empirical landscape and the simulated NPPL. One would have to incorporate characteristics of the Kernel function into the habitat raster before comparing to the point pattern. You are still stuck with attempting to compare area characteristics to a point. Perhaps, if the Kernel function used to simulate the NPPL is uniform and not adaptive, you could use a focal operator, that shares the Kernel definition, to smooth the habitat raster and then perform some type of direct comparison between the two data. Because it will accept virtually any matrix definition as the Kernel (window), this should not be too difficult to specify in R using "focal" in the raster package. The ArcGIS focal function will also accept an ASCII file that defines the Kernel (see; NbrWeight inKernelFile arguments in FocalStatistic).
