Small Area Estimation

1
Small Area Estimation

• An Introduction

Prepared by Margarita F Guerrero (UNSIAP)
2
Topics Covered

• What are small areas?
• Statistics for Small Areas
• Some Small Area Estimation (SAE) Methods
• Two Illustrations

3
Examples of Small Areas

• Smaller geographical divisions
• Relative to whole country provinces
• Relative to province towns/municipalities
• Subpopulations of survey population
• Ethnic groups
• Women-headed households
• Age groups by sex by province

4
a Small Area (or Sub-domain) is

• a population for which inadequate or even no
  direct reliable information is available for the
  variable of interest
• Why does this happen, for example?
• In intercensal years, direct population counts
  are often not available for many small areas
• A sample survey designed for a large population
  may include only a small number of elements or
  even no element from the small area of interest

5
Small Area Statistics

• Statistics for small areas
• Some examples
• Population of municipalities
• Poverty incidence in ethnic minority communities
• Proportion of currently married women currently
  using a modern method of contraception in
  province A

6
Sources of Statistics for Small Areas

• Census
• Local (e.g., province, village) government
  conducts its own survey to collect data
• Design nationwide surveys to provide reliable
  estimates for small areas (sufficient sample
  size)
• Use estimation techniques that will give reliable
  statistics by combining available data sources in
  some way or small area estimation (SAE).

7


8
(No Transcript)
9
Major Approaches to SAE

• Demographic Methods
• Synthetic and Composite Estimation, without
  auxiliary information
• Synthetic and Composite Estimation, with
  auxiliary information

10
SAE Demographic Methods

• For estimating population (P) of small area
• Vital Rates (VR) Techniques
• Components Method
• Sample Regression Method
• Data requirements
• Current data from administrative records
• Data from most recent census

11
Logic of VR (1)
12
Logic of VR (2)
13
Logic of VR (3)
14
Estimated Population in small area is the average
of the two estimates
15
Example 1. Govindarajulu (1999)
Data bt 400, dt 35 from vital statistics
office. From the 1990 census R10 2, R20 1.8.
Assume R10 r10 2 and R20 r20 1.8. From
the census data the state rates are
16
Synthetic and Composite Estimation (without
auxiliary information) -1
yij value of the survey variable for the jth
unit in the ith local area (j 1, , Ni and i
1, , m)
Suppose you have sampled ni ? 0 units in the ith
local area whose values are yij (j 1, , ni).
In ith local area
17
Synthetic and Composite Estimation (without
auxiliary information) -2
Synthetic estimate of overall mean (weighted
mean of direct estimates)
Composite Estimate
18
Synthetic and Composite Estimation (without
auxiliary information) -3

• Question how to choose the weights, wi?
• One way
• if Ni is known,

19
Example 2
A small county has 500 families. A random sample
of 50 families has been drawn. Among other facts
and figures, monthly overall expenditure
(averaged over part 5 years) has been noted for
the sampled families. It is observed that 15
families in the sample reside in owned houses/
apartments and the rest reside in rented houses/
apartments. It is natural that these two groups
have different expenditures. We need two separate
estimates of monthly expenditures. The data are
20
Suppose it is known that 40 of families own
their residences in the county as a whole. Find a
composite estimate for owners expenditure. Let i
1 denote the owners.
Synthetic estimate
Using relative size as weights
Composite estimate
21
Estimating Poverty Incidence in Small Areas

• Viet Nam
• Source Country Report, GSO Viet Nam, UNSIAP
  First Regional Course on Poverty Measurements

22
Basis of Method Regression

• A model fitting procedure used to identify a
  functional relationship between the variable of
  interest (R) and the symptomatic variables rj.
• Symptomatic variables are characteristics
  whose variations are strongly related to changes
  in the population

23
SAE of HH Expenditure

• Step 1 Select symptomatic variables from census
  and household survey (VLSS)
• Step 2 Fit regression model for estimating
  expenditure from survey data.
• Step 3 Estimate expenditure for all households
  using census data.

24
Select symptomatic variables

• 1998 VLSS has good data on per capita
  expenditures but for only 5999 households
• 1999 Census did not collect expenditures/ incomes
  but covered 16.7 mil households
• 33 common variables in VLSS Census (17 are
  useful for predicting expenditures)

25
Common Variables Selected

• Household size
• Proportion of children and elderly people in
  household
• Proportion of females in household
• Highest level of education completed by head
• Highest level of education completed by spouse
• Head from ethnic minority
• Occupation of head
• Housing (type of house, roof, floor, toilet,
  living area)
• Main source of drinking water and electric
  lighting
• TV and/or radio ownership
• Region of residence (7 regions)

26
Regression Analysis
Run regression on VLSS data using common
variables where ln(yi) is the logarithm of
per capita expenditure for household i Xi is a
matrix of the common variables ? is a vector of
coefficients ?I is a normally distributed error
term
27
Regression Results(Rural Areas)
28
Estimate expenditure for all HHs
Use coefficients from VLSS regressions and
indicators from Census (Xic) to predict
expenditures for each Census household
29
(No Transcript)
30
Estimate Poverty Incidence

• Use predicted expenditures for each Census
  household to estimate the poverty incidence and
  poverty headcounts at the small area level
  (provincial or district level)

31
NATIONAL POVERTY MAP
32
RURAL POVERTY MAP
URBAN POVERTY MAP
33
OVERLAY OF ETHNIC MINORITIES
RURAL POVERTY MAP WITH ETHNIC MINORITY OVERLAY
Rural ethnic minority of population
50 to 100 (12) 25 to 50 (13)
10 to 25 (17) 0 to 10
(19)
Poverty Headcount ( of individuals) 60 to
100 (14) 45 to 60 (19) 25 to 45
(22) 0 to 25 (6) Rural ethnic
minority_ 50 to 100 (12) 25
to 50 (13) 10 to 25 (17) 0
to 10 (19)
34
RURAL POVERTY MAP WITH STORMS TYPHOONS OVERLAY
STORMS AND TYPHOONS BY PROVINCE 1996-1999