Statistical methods for real estate data

prof. RNDr. Beáta Stehlíková, CSc.

2013

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Informationis currently besides financial, energy,material resources

the main factor of progress.

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How to obtain new knowledge?

We want to answer the question:How to obtain new information, new knowledge from data?

Talk only about one method of spatial statistics

Why spatial statistics ?Methods of spatial statistics are for spatial

data

Real estate data contain very often information about the geographic location – there are spatial data

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Variable and data

A variable - a characteristic of population or sample that is of interest for us.

Data - the actual values of variables

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Different kinds of data

Cross-sectional data are data on one or more variables collected at a single point in time

Time series data data are collected over a period of time on one or more variables

Panel data – the same cross-section over time

Obs Price (SEK) Living Area 1 600 000 80 2 750 000 95 3 675 000 75 4 825 000 84 . . .

200 925 000 96

Obs. Year Index GDP 1 1981 101 900 2 1982 105 1050 3 1983 110 1200 .

20 1999 250 8500

in real estate

Types of data (scale)

We have said that data - the actual values of variables

Types of data: Interval data are numerical observations Ordinal data are ordered categorical observations Nominal data are categorical observations

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Types of data (scale)

Knowing the type of data (scale) is necessary to properly

select the technique to be used when analyzing data.

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Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful

information is produced.

Descriptive statistics

Descriptive statistics

Descriptive statistics

graphical techniques (histogram)numerical descriptive measures

Mean (average) Median (middle value) Mode (most frequently ) Variance Standard deviation

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Descriptive statistics are not enough

Average (17,8) Standard deviation (4,7) Coefficient of variation

(26,4 %) n=25 1

4

0

11

9

6,1 10,1 14,1 18,1 22,1

2

10

0

12

1

0

2

4

6

8

10

12

9,8 13,8 17,8 21,8 25,8

It is necessary to know

the probability distribution

Consider two data sets A and B

A

B

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Second example

Consider two large data sets A and B

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The location information

It is not possible to identify differences between data sets without we take into account the location information

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The location information

Variograms quantify changes in values in the space

there is no there is spatial autocorrelation

small distances

correspond to small changes in values

small distances

correspond to large

  changes in values

Spatial autocorrelation

The degree to which near and more distant things are interrelated

Measures of spatial autocorrelation attempt to deal with similarities

in the location of spatial objects and their attributes

Spatial autocorrelation

Positive (objects similar in location are similar in attribute)

Negative (objects similar in location are very different)

Zero (attributes are independent of location)

Spatial autocorrelation - measures.

Several measures available: Moran’s coefficient I, Geary’s C coefficient, Getis-Ord coefficient G.

These measures may be •“global” - they apply to the study region • or “local” - autocorrelation may exist in some parts of the region but not in others.

Moran’s coefficient I

varies between –1.0 and + 1.0 0 indicates no spatial autocorrelation [1/(n-1)]

(indicate random pattern) When autocorrelation is high, the I coefficient is

close to 1 or -1 Negative values I indicate negative

autocorrelation Positive values I indicate positive autocorrelation

(indicate a tendency toward clustering)

Regression analysis

is a technique for using data to identify relationships among variables and use these relationships to make predictions.

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Regression analyses that ignore spatial dependency can have

unstable parameter estimates and unreliable significance tests.

Solution: Spatial Autoregressive Models Lag model Spatial Error model

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Spatial Models

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SPATIAL LAG SPATIAL ERROROrdinary Least Squares

No influence from neighbors

Dependent variable influenced by

neighbors

Residuals influenced by neighbors

Y = β0 + Xβ Y = β0 + λ WY + Xβ + ε Y = β0 + Xβ + ρWε + ξ

Lag model controls spatial autocorrelation in the dependent variable

Error model controls spatial autocorrelation in the residuals, thus it controls autocorrelation in

the dependent and the independent variables

Software GeoDa

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Compare different spatial models

Neither R2 nor Adjusted R2 can be used to compare different spatial regression models

We can used Akaike Information Criteria (the smaller the AIC value the better the model)

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Example

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dependent variable y – price of dwellingindependent variable x – living area

Classical regression analysis

Residuals

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Moran´s I = 0.193022

Significance:P value= 0.03140<0.05

This indicate positive spatial autocorrelation

between residuals.

Spatial error model

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Local Moran’s coefficients

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Which values produce spatial autocorrelation ?

Spatial statistics

Methods of spatial statistics very use full for data with the location information

The art of looking for beauty,and science looking for true.

Spatial statistics will help us find the truewhen we use the right methods

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