# Modelling of rent prices - which interpolation method should I choose?

I have national dataset of ~1,4 million households. There I have information about rent, size (number of rooms and m2) and some additional characteristics of each household.

I'd like to use this data to create surface of rent prices for the whole country and use this information as a proxy for estimation of values of remaining ~1.5 million households that are owned or do not have rent information.

Couple of questions here:

Is such approach appropriate for the this kind of problem at all?

Which method of interpolation would be most suitable to use here?

Also, would it be possible to take information about, for instance the size of the household into account?

I'm on ArcGIS 9.3 with ArcInfo license.

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It seems like Computer Aided Mass Appraisal (CAMA) systems would need to do something similar. I wonder how they handle it. en.wikipedia.org/wiki/Computer_Assisted_Mass_Appraisal –  Kirk Kuykendall Jan 18 '11 at 19:03

The idea is good but the proposed implementation may be too simplistic to be credible. Rents are a property of economic systems. Besides being influenced by location, they are related to other economic variables in important ways: state of the local (and national) economy, local housing prices, availability of capital, employment rates, etc. To do a good job you need an econometric model. It might benefit from having some spatial lag terms, but before such complications are considered you need to include many of these economic covariates.

Having said that, your ability to succeed depends on the relationships between the data you do have and the rents you want to predict. If your data are a representative sample of the entire country and are geographically dispersed--think of houses as raisins on a cookie and you have data about every other raisin in the cookie--then a relatively simple model might suffice. If your data are geographically focused--maybe you have information about raisins on the right side of the cookie and you want to make predictions for the raisins on the left side--then the problem is a more difficult one.

A good point of departure would be to fit a conventional linear econometric model of rents to household characteristics and gross spatial characteristics (such as state or county tax policies), compute the residuals, and begin exploring the residuals spatially (using variography, spatial kernel smooths, etc) to capture the geographic effects.

Suitable software is available as add-ons to R.

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@whubber The link to document describing variography seems to be dead. Is there a chance to update it? –  radek Dec 14 '12 at 12:27
Thanks, @radek. It is surprisingly difficult to find an exposition of variography on the Web that is introductory yet accurate and is not just a software manual. I found a recent PhD thesis that--judging from its abstract and introduction--appears to be clear and thorough and starts from a relatively elementary point. –  whuber Dec 14 '12 at 16:17
@whubber Thanks a lot! –  radek Dec 14 '12 at 16:55

As a very gentle introduction to topics on spatial regression I would highly recommend checking out the GeoDa workbook (chapters 22 to 25 will be of most interest). Even if you don't want to use the software it is a very comprehensive overview of spatial regression.

Will the built in regression functions in ArcMap handle that much data (not that any software would have a difficult time with that many points?)

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(+1) 1.4 million points is no problem for regression. (The effort in least squares algorithms, for example, is typically proportional to the cube of the number of variables. Setting up the equations requires only one fast scan through the dataset.) The real problem is that 1.4 million cases will have a rich and detailed structure: a good analysis would be extremely labor intensive. (This dataset could generate loads of PhD theses in economics, I'm sure.) The trick therefore is to do just as much work as is needed to obtain sufficiently accurate and defensible answers for the task at hand. –  whuber Jan 18 '11 at 15:05
@whuber , thank you for the clarification. –  Andy W Jan 18 '11 at 16:03

I've seen similar work done for house prices using hedonic modelling. See http://scholar.google.com/scholar?hl=en&q=hedonic+price+geography for examples.

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(+1) I agree the literature on hedonic models of house pricing are largely applicable to this question. I reframed from suggesting it though as an individual who is not familiar with regression may find the work of all those econometricians daunting (I know I do at times!) Theory wise though it would be a good literature to check up on, especially for covariates of interest. –  Andy W Jan 18 '11 at 19:27