2D, 3D graphs

[MarioVictor]

After conducting an NPMR, I have selected my best models and want to graph the predictors and response values in 2D and 3D. I noticed that the response values, density in this case, does not go up to the range observed in the data. For example if the highest values are 20/unity area, the axis on the graphs are only up to 1.5. I have a lot of zero data (range of 5-25% NON-zero data) and taking the means, this seems to be more in the ballpark of what I'm getting on the graphs. Can some explain to me a little more on how the model is working for finding these quantitative relationships in 2D and 3D? Does this suggest I used inappropriate model settings when running the NPMR? Are the quantitative relationships limited to these ranges? Also, plotting the response points seems to encompass more of the range of the observed response values as expected. 

Thanks!

[Bruce McCune]

Sounds like you are doing this right. Remember you are modeling the local mean response, so your high values will be offset by zeros that are sprinkled throughout. With individual response points you will see the high values, but not with graphs of the local mean.
Bruce

On Oct 27, 2015 8:41 AM, "MarioVictor" <marine...@gmail.com> wrote:

After conducting an NPMR, I have selected my best models and want to graph the predictors and response values in 2D and 3D. I noticed that the response values, density in this case, does not go up to the range observed in the data. For example if the highest values are 20/unity area, the axis on the graphs are only up to 1.5. I have a lot of zero data (range of 5-25% NON-zero data) and taking the means, this seems to be more in the ballpark of what I'm getting on the graphs. Can some explain to me a little more on how the model is working for finding these quantitative relationships in 2D and 3D? Does this suggest I used inappropriate model settings when running the NPMR? Are the quantitative relationships limited to these ranges? Also, plotting the response points seems to encompass more of the range of the observed response values as expected. 

Thanks!

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[MarioVictor]

Thank you, Bruce.

I've also been having a lot of difficulty with my 3D graphs. I've played with the Minimum Neighborhood Size for Estimate, but am still getting very disjointed, incomplete graphs. That is, the graphs have a lot of missing data and little spots with some data here and there. Comparing the 2D graphs to the 3D for two predictors, the 3D graphs are definitely not putting the relationships together. 

I've even re-run the NPMR and changed the max allowable missing est. (%) from 10-5 (and smaller) and made the min avg. neighborhood size smaller, thinking this might help form a broader, more continuous relationship. 

Other info: The xR2 values I'm getting for these models is in the 0.8-0.9 range. This seems high to me. This organism is very patchy however and found at very high densities where it occurs (and is absent or very low density elsewhere.) 

Any suggestions or insight? 

[Bruce McCune]

The high xR2 and patchy response surface suggest that the sampling of the predictor space is strongly clustered, and that the response is very similar among observations within clusters. This might be a form of pseudoreplication, if the observations within clusters aren't independent. To some extent you can work around this by insisting in the model fitting phase on a minimum average neighborhood size that is larger than the number of observations within clusters (choose "Conservative" overfitting control, or if that isn't enough, choose a manual setting for the "minimum average neighborhood size for an acceptable model"). This will give a flatter, more continuous response surface and probably a lower xR2, since the model will need to deal with more than one cluster at a time. If my guess about the observations being clustered in the predictor space is wrong, then another explanation or remedy may be needed.

Bruce

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[MarioVictor]

That makes sense for these particular results. The organisms themselves are clustered in space (though still sampled randomly based on certain strata). One may presume that their clustered patches then are more likely to be very similar in predictor features. I would argue that this is not spatial pseudoreplication, but rather the sample design didn't adequately capture all of the population and suite of environments they inhabit. I tried more conservative settings, and the lowest xR2 was about 0.57 and weirdly patchy response surfaces. I'll try changing the minimum neighborhood size some more. What do you mean "larger than #observed in clusters." How do I identify this? Do you mean from my "raw" response data or by looking at response points after the NPMR?

On Tuesday, October 27, 2015 at 8:40:59 AM UTC-7, MarioVictor wrote:

[Bruce McCune]

By larger than the size of the clusters I mean the following. Say you have sampled in 5 clusters of 20 sample units each, 100 total. To get the local mean to represent more than each individual cluster you'd might set the minimum average neighborhood size to 30 or 40 (considerably larger than an individual cluster).

On the other hand, if those 100 sample units were randomly distributed in the predictor space, the medium overfitting control would probably be fine (which would be only 5 SUs or 5% of 100 total).

-Bruce McCune

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[MarioVictor]

Thanks Bruce. Let me rephrase my question. Where in the output do I find how the data are clustered in predictor space? When I conduct a sensitivity analysis, I see that output reports sample units for populated neighborhoods, the minimum neighborhood size and then the average neighborhood size. Is this what I should be looking at for that particular model?

By trial, I have found settings (usually changing avg neighborhood size and min neighborhood size for estimate; all on Conservative setting or manual for "more conservative") where the xR2 is reduced (substantially) and a point in which the best predictors chosen by the best model change. Still not sure how to assess if I'm adequately sampling the predictor space. In all cases, I get an incomplete 3D graph (ie some portion missing data). Right now, it seems like my results and interpretation are very dependent on what settings I choose and I'm not confident that I'm not just fishing for a result that looks good since I don't have a priori assumptions as to what the best models should be both in xR2 or predictors.

Thank you for sticking with me through this.

On Tuesday, October 27, 2015 at 8:40:59 AM UTC-7, MarioVictor wrote:

[Bruce McCune]

To see how your sample is arranged in predictor space, select Graph | Scatterplot, then select two of the strongest predictors. If the sample points are strongly clustered it will be obvious. If more than two predictors are important, use Graph | Scatterplot Matrix.

If the sampling is clustered, then it makes sense that changing the overfitting settings can change which predictors are best, because it would be changing the problem from fitting clusters of points to trying to fit the whole surface.

-Bruce McCune

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[MarioVictor]

Thank you for your guidance. I'll try that!

On Tuesday, October 27, 2015 at 8:40:59 AM UTC-7, MarioVictor wrote: