[R-sig-Geo] Running huge dataset with dnearneigh

[Roger Bivand]

On Mon, 1 Jul 2019, Jiawen Ng wrote:

> Dear Roger,
>
> Thank you so much for your detailed response and pointing out potential
> pitfalls! It has prompted me to re-evalutate my approach.
>
> Here is the context: I have some stores' sales data (this is my training
> set of 214 points), I would like to find out where best to set up new
> stores in UK. I am using a geodemographics approach to do this: Perform a
> regression of sales against census data, then predict sales on UK output
> areas (by centroids) and finally identify new areas with
> location-allocation models. As the stores are points, this has led me to
> define UK output areas by its population-weighted centroids, thus resulting
> in the prediction by points rather than by areas. Tests (like moran's I and
> lagrange multiplier) for spatial relationships among the points in my
> training set were significant hence this has led me to implement some
> spatial models (specifically spatial lag, error and durbin models) to
> account for the spatial relationships in the data.

I'm afraid that my retail geography is not very up to date, but also that 
your approach is most unlikely to yield constructive results.

Most retail stores are organised in large chains, so optimise costs 
between wholesale and retail. Independent retail stores depend crucially 
on access to wholesale stores, so anyway cannot locate without regard to 
supply costs. Some service activities without wholesale dependencies are 
less tied.

Most chains certainly behave strategically with regard to each other, 
sometimes locating toe-to-toe to challenge a competing chain 
(Carrefour/Tesco or their local shop variants), sometimes avoiding nearby 
competing chain locations to establish a local monopoly (think Hotelling).

Population density doesn't express demand, especially unmet demand well at 
all. Think food deserts - maybe plenty of people but little disposable 
income. Look at the food desert literature, or the US food stamp 
literature.

Finally (all bad news) retail is not only challenged by location shifting 
from high streets to malls, but critically by online shopping, which 
shifts the cost structures one the buyer is engaged at a proposed price to 
logistics, to complete the order at the highest margin including returns. 
That only marginally relates to population density.

So you'd need more data than you have, a model that explicitly handles 
competition between chains as well as market gaps, and some way of 
handling online leakage to move forward.

If population density was a proxy for accessibility (most often it isn't), 
it might look like the beginnings of a model, but most often we don't know 
what bid-rent surfaces look like, and then, most often different 
activities sort differently across those surfaces.

>
> I am quite unsettled and unclear as to which neighbourhood definition to go
> for actually. I thought of IDW at first as I thought this would summarise
> each point's relationship with their neighbours very precisely thus making
> the predictions more accurate. Upon your advice (don't use IDW or other
> general weights for predictions), I decided not to use IDW, and changed it
> to dnearneigh instead (although now I am questioning myself on the
> definition of what is meant by general weights. Perhaps I am understanding
> the definition of general weights wrong, if dnearneigh is still considered
> to be a 'general weights' method) Why is the use of IDW not advisable
> however? Is it due to computational reasons? Also, why would having
> thousands of neighbours be making no sense? Apologies for asking so many
> questions, I'd just like to really understand the concepts!
>

The model underlying spatial regressions using neighbours tapers 
dependency as the pairwise elements of (I - \rho W)^{-1} (conditional) and 
[(I - \rho W) (I - \rho W')]^{-1} (see Wall 2004). These are NxN dense 
matrices. (I - \rho W) is typically sparse, and under certain conditions 
leads to (I - \rho W)^{-1} = \sum_{i=0}^{\inf} \rho^i W^i, the sum of a 
power series in \rho and W. \rho is typically upward bounded < 1, so 
\rho^i declines as i increases. This dampens \rho^i W^i, so that i 
influences j less and less with increasing i. So in the general case IDW 
is simply replicating what simple contiguity gives you anyway. So the 
sparser W is (within reason), the better. Unless you really know that the 
physics, chemistry or biology of your system give you a known systematic 
relationship like IDW, you may as well stay with contiguity.

However, this isn't any use in solving a retail location problem at all.

> I believe that both the train and test set has varying intensities. I was
> weighing the different neighbourhood methods: dnearneigh, knearneigh, using
> IDW etc. and I felt like each method would have its disadvantages -- its
> difficult to pinpoint which neighbourhood definition would be best. If one
> were to go for knearneigh for example, results may not be fair due to the
> inhomogeneity of the points -- for instance, point A's nearest neighbours
> may be within a few hundreds of kilometres while point B's nearest
> neighbours may be in the thousands. I feel like the choice of any
> neighbourhood definition can be highly debateable... What do you think?
>

When in doubt use contiguity for polygons and similar graph based methods 
for points. Try to keep the graphs planar (as few intersecting edges as 
possible - rule of thumb).


> After analysing my problem again, I think that predicting by output areas
> (points) would be best for my case as I would have to make use of the
> population data after building the model. Interpolating census data of the
> output area (points) would cause me to lose that information.
>

Baseline, this is not going anywhere constructive, and simply approaching 
retail location in this way is unhelpful - there is far too little 
information in your model.

If you really must, first find a fully configured retail model with the 
complete data set needed to replicate the results achieved, and use that 
to benchmark how far your approach succeeds in reaching a similar result 
for that restricted area. I think that you'll find that the retail model 
is much more successful, but if not, there is less structure in 
contemporary retail than I though.

Best wishes,

Roger

> Thank you for the comments and the advice so far,  I would greatly welcome
> and appreciate additional feedback!
>
> Thank you so much once again!
>
> Jiawen
>
>
>
>
>
>
>
>
> On Sun, 30 Jun 2019 at 16:57, Roger Bivand <Roger.Bivand using nhh.no> wrote:
>
>> On Sat, 29 Jun 2019, Jiawen Ng wrote:
>>
>>> Dear Roger,
>>
>> Postings go to the whole list ...
>>
>>>
>>> How can we deal with a huge dataset when using dnearneigh?
>>>
>>
>> First, why distance neighbours? What is the support of the data, point or
>> polygon? If polygon, contiguity neighbours are preferred. If not, and the
>> intensity of observations is similar across the whole area, distance may
>> be justified, but if the intensity varies, some observations will have
>> very many neighbours. In that case, unless you have a clear ecological or
>> environmental reason for knowing that a known distance threshold binds, it
>> is not a good choice.
>>
>>> Here is my code:
>>>
>>> d <- dnearneigh(spdf,0, 22000)
>>> all_listw <- nb2listw(d, style = "W")
>>>
>>> where the spdf object is in the british national grid CRS:
>>> +init=epsg:27700, with 227,973 observations/points. The distance of
>> 22,000
>>> was decided by a training set that had 214 observations and the spdf
>> object
>>> contains both the training set and the testing set.
>>>
>>
>> This is questionable. You train on 214 observations - do their areal
>> intensity match those of the whole data set? If chosen at random, you run
>> into the spatial sampling problems discussed in:
>>
>>
>> https://www.sciencedirect.com/science/article/pii/S0304380019302145?dgcid=author
>>
>> Are 214 observations for training representative of 227,973 prediction
>> sites? Do you only have observations on the response for 214, and an
>> unobserved response otherwise? What are the data, what are you trying to
>> do and why? This is not a sensible setting for models using weights
>> matrices for prediction (I think), because we do not have estimates of the
>> prediction error in general.
>>
>>> I am using a Mac, with a processor of 2.3 GHz Intel Core i5 and 8 GB
>>> memory. My laptop showed that when dnearneigh command was run on all
>>> observations, around 6.9 out of 8GB was used by the rsession and that the
>>> %CPU used by the rsession was stated to be around 98%, although another
>>> indicator showed that my computer was around 60% idle. After running the
>>> command for a day, rstudio alerted me that the connection to the rsession
>>> could not be established, so I aborted the entire process altogether. I
>>> think the problem here may be the size of the dataset and perhaps the
>>> limitations of my laptop specs.
>>>
>>
>> On planar data, there is no good reason for this, as each observation is
>> treated separately, finding and sorting distances, and choosing those
>> under the threshold. It will undoubtedly slow if there are more than a few
>> neighbours within the threshold, but I already covered the inadvisability
>> of defining neighbours in that way.
>>
>> Using an rtree might help, but you get hit badly if there are many
>> neighbours within the threshold you have chosen anyway.
>>
>> On most 8GB hardware and modern OS, you do not have more than 3-4GB for
>> work. So something was swapping on your laptop.
>>
>>> Do you have any advice on how I can go about making a neighbours list
>> with
>>> dnearneigh for 227,973 observations in a successful and efficient way?
>>> Also, would you foresee any problems in the next steps, especially when I
>>> will be using the neighbourhood listw object as an input in fitting and
>>> predicting using the spatial lag/error models? (see code below)
>>>
>>> model <-  spatialreg::lagsarlm(rest_formula, data=train, train_listw)
>>> model_pred <- spatialreg::predict.sarlm(model, test, all_listw)
>>>
>>
>> Why would using a spatial lag model make sense? Why are you suggesting
>> this model, do you have a behavioural for why only the spatially lagged
>> response should be included?
>>
>> Why do you think that this is sensible? You are predicting 1000 times for
>> each observation - this is not what the prediction methods are written
>> for. Most involve inverting an nxn inverse matrix - did you refer to
>> Goulard et al. (2017) to get a good understanding of the underlying
>> methods?
>>
>>> I think the predicting part may take some time, since my test set
>> consists
>>> of 227,973 - 214 observations = 227,759 observations.
>>>
>>> Here are some solutions that I have thought of:
>>>
>>> 1. Interpolate the test set point data of 227,759 observations over a
>> more
>>> manageable spatial pixel dataframe with cell size of perhaps 10,000m by
>>> 10,000m which would give me around 4900 points. So instead of 227,759
>>> observations, I can make the listw object based on just 4900 + 214
>> training
>>> points and predict just on 4900 observations.
>>
>> But what are you trying to do? Are the observations output areas? House
>> sales? If you are not filling in missing areal units (the Goulard et al.
>> case), couldn't you simply use geostatistical methods which seem to match
>> your support better, and can be fitted and can predict using a local
>> neighbourhood? While you are doing that, you could switch to INLA with
>> SPDE, which interposes a mesh like the one you suggest. But in that case,
>> beware of the mesh choice issue in:
>>
>> https://doi.org/10.1080/03610926.2018.1536209
>>
>>>
>>> 2. Get hold of better performance machines through cloud computing such
>> as
>>> AWS EC2 services and try running the commands and models there.
>>>
>>
>> What you need are methods, not wasted money on hardware as a service.
>>
>>> 3. Parallel computing using the parallel package from r (although I am
>> not
>>> sure whether dnearneigh can be parallelised).
>>>
>>
>> This could easily be implemented if it was really needed, which I don't
>> think it is; better methods understanding lets one do more with less.
>>
>>> I believe option 1 would be the most manageable but I am not sure how and
>>> by how much this would affect the accuracy of the predictions as
>>> interpolating the dataset would be akin to introducing more estimations
>> in
>>> the prediction. However, I am also grappling with the trade-off between
>>> accuracy and computation time. Hence, if options 2 and 3 can offer a
>>> reasonable computation time (1-2 hours) then I would forgo option 1.
>>>
>>> What do you think? Is it possible to make a neighbourhood listw object
>> out
>>> of 227,973 observations efficiently?
>>
>> Yes, but only if the numbers of neighbours are very small. Look in Bivand
>> et al. (2013) to see the use of some fairly large n, but only with few
>> neighbours for each observation. You seem to be getting average neighbour
>> counts in the thousands, which makes no sense.
>>
>>>
>>> Thank you for reading to the end! Apologies for writing a lengthy one,
>> just
>>> wanted to fully describe what I am facing, I hope I didn't miss out
>>> anything crucial.
>>>
>>
>> Long is OK, but there is no motivation here for why you want to make 200K
>> predictions from 200 observations with point support (?) using weights
>> matrices.
>>
>> Hope this clarifies,
>>
>> Roger
>>
>>> Thank you so much once again!
>>>
>>> jiawen
>>>
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>>>
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>>
>> --
>> Roger Bivand
>> Department of Economics, Norwegian School of Economics,
>> Helleveien 30, N-5045 Bergen, Norway.
>> voice: +47 55 95 93 55; e-mail: Roger.Bivand using nhh.no
>> https://orcid.org/0000-0003-2392-6140
>> https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en
>>
>
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-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; e-mail: Roger.Bivand using nhh.no
https://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en