I am currently working on an application of logistic regression for lanslide susceptibility assessment. In order to extract predictors' values form raster layers, I generated equally spaced grid points in landslide area and landslide - free area. It is generally recognized that the point samples should be about the same size (number of 1 - landslide points = number of 0 - non-landslide points). If this is the case, then the density of points will be significantly higher inside the landslide area than outside the landslide area, because the landslide area is generally much smaller than the landslide free area. Some say this difference in density is a critical issue. How does it affect the quality and reliability of the computed regression model? Are there any sampling alternatives?
This is a technical aspect of the data collection and the accuracy of the sampling collection device. If the equipment to be used such as a GPS has a large error problem, then the result might be affected based on a number of factors. 1. The number of samples collected. 2. the typology of the sampling methodology used, i.e. either random smapling, stratified sampling technique or any other sampling procedure. 3. The observation of envrionmental conditions can also affect the quality of the outcome of the study. Please read through these literature materials they will help greatly.
1. http://www.nat-hazards-earth-syst-sci.net/10/1851/2010/nhess-10-1851-2010.pdf
2. http://eusoils.jrc.ec.europa.eu/library/themes/landslides/Documents/VDEeckhaut_et_al_Florence_2010.pdf
Thank you Raji. The two articles are interesting and helpful in some extent.
Dear Cristian,
your question is a very central one in landslide susceptibility assessment and it has no definite answer so far.
Depending on several factors, the choice of keeping 0 and 1 sample points even might be good or bad. For example, when dealing with an area where environmental factors (such as slope, geology, rainfall etc) have a relatively low spatial variability (so, high autocorrelation) your approach may be ok.
Conversely, when dealing with a heterogeneous study area, there may be problems of under-representation of some of the existing covariates combinations if you have a sample point density outside landslides which is lower than inside.
The regression (or classification) method itself conditions the impact of sample size on the result. Artificial neural networks, for example, tend to consider the most represented parameter combinations as more likely (sort of weighting the relative number of learning vectors) so that it will be more advisable to keep the proportion between landslide and non-landslide sample points as similar to the ratio between landslide and non-landslide area as possible.
I have a paper in the NHESS Discussion online library right now which treats some of this problems. You can find it here: http://www.nat-hazards-earth-syst-sci-discuss.net/1/583/2013/nhessd-1-583-2013.pdf
I hope this can be of help!
Thank you very much Filippo. You NHESS article is very interesting and helpful. I haven't tested yet the artificial neural networks yet. So far we explored the logistic regression approach. We have also a paper in the NHESS Discussion. If you wish to see it, please follow the link: http://www.nat-hazards-earth-syst-sci-discuss.net/1/1749/2013/nhessd-1-1749-2013.pdf
I agree completely with the comment from Filippo! From my opinion, it is not necessary to take the number of landslide points and non-landslide points equally, as it is not the case in nature. It is good in some cases but not in others. What really matter is the ratio of landslides over whole area, e.x. if the landslides affected only 10% of your study area, then the appropriate landslide points should be somewhere at, saying, 10-20% of your dataset.
In the case of my landslide points are limited (scarce), after some trials and I see that my regression model depends heavily on the balance of landslide and non-landslide data, I will try other methods (like decision tree, neural network or simple index overlay, Bayes…)
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