1. Objectives and Challenges 4. Sampling Weight · 2021. 4. 21. · Objectives and Challenges:...

Outline

1. Objectives and Challenges

2. Proposed Methodology

3. Sampling Approach

4. Sampling Weight

5. Implementation

6. Challenges

Introduction to adaptive sampling designs 1

Objectives and Challenges : Informal sector

• Informal sector is believed to account for a significant share of the

economy in many developing countries. • 55% of SSA’s GDP (AfDB 2013)

• The 2014 Zimbabwe LFS shows that about 94% of people employed

(in non-farm sector) are in informal employment (was 84% in 2011).• Official estimate of unemployment rate is 11%

• Means of livelihood for the poor and vulnerable segment of the society

• Policy making can’t ignore this sector - need to better understand their

operations and needs

• A better understanding requires better data,


Objectives and Challenges: Objectives

i. Collect in-depth information on the business environment facing

informal businesses

• Key business environment and performance indicators

• Information specific to the informal sector (e.g.,, barriers to

registration)

ii. To derive estimates of the TOTAL number of informal firms in

Harare


Objectives and Challenges : Challenges

• Non availability of sampling frame

• Units are expected to be clustered across the survey area

➢ Distribution expected to be heterogeneous within the survey area

• Construction of a list frame from other data sources not feasible.


Conduct a representative survey by using

a probability sample

Proposed Methodology (1)

1. Use of a spatial area frame:

➢ Meets the criteria of a good sampling frame (exhaustive, up-to-

date, i.e. Greig-Smith, 1962)

2. Stratified Adaptive Cluster Sampling (Thompson 1990,1991)

➢ Addresses the problem of clusterization as well as the heterogenous

distribution

Approach originally developed for Biostatistical applications, applications

on human populations rare.


Selection of a suitable sampling

approach to address both of the

challenges

THE PSU SAMPLING FRAME

Introduction to adaptive sampling designs

• Total number of PSUs

covering the are was

20510

• Frame was stratified

according to assumed density of final sampling

units in the area

• Sample sizes were 100,

200, 300 units, for high,

medium, low density areas respectively.

• Sample sizes were

derived through

simulation.

6

Proposed Methodology – Construction of the grid

1. Use of a shape file with area

boundaries and stratum identifiers➢ Stratification accounts for an

(expected) heterogeneous

distribution.

2. Appropriate cell size➢ Needs to balance expected

workload (i.e. number of final

sampling units) and area coverage.


Proposed Methodology – Determination of the sample

size


1. Analytical Solution not feasible.

➢ However relative efficiency of

ACS to SRS has been

demonstrated.

2. Use of empirical micro simulation

approach (Meindl & Tempel, 2016)➢ Construction of a synthetic population

including mean sales as the target

variable.

Stratum Number of units Av. units per square Mean sales

low 3679 4.39 1018.7815

medium 16223 7.14 1002.3281

high 12757 15.69 995.1539


size


1. Modify different population parameters

(i.e. distribution/density) of the population.

2. Modify different design parameters (i.e.

square, number of sampled starting

squares, expansion factor)

3. Repeat the design n times

4. Compare estimated outcome with the

(known) true population mean.

Implementation – Selection of the starting squares

1. Each starting square defines a

potential network.

2. Expansion of the starting square if a

(stratum) threshold level is found.

3. Survey all squares surrounding the

square responsible for the expansion.



size

• Simulation code is implemented into R’s shiny (Winston et al., 2017) web application.

• Results also include the (expected) expansion and therefore facilitate survey cost estimation.


Stratum Level Number of units Av. units per square Mean sales

low 0 38 7.6 1122.6063

medium 0 137 8.56 1003.1202

medium 1 29 7.25 865.1046

medium 2 30 6 921.7877

medium 4 7 3.5 1014.4759

high 0 366 17.43 1036.9261

high 1 242 17.29 1046.3947

high 2 96 16 887.846

high 3 66 22 997.4784

high 4 36 18 1069.0724

11

Proposed Methodology – Computations of Weight


1. Weights for the starting squares.

2. Weights for the squares subject to

expansion (i.e. the intersection

probability).

3. (Accounting for stratum overlap and edge units).

1. 𝑝0 =𝑛0

𝑁

2. 𝑝1 = 1− 𝑁−𝑚𝑖𝑛0

/ 𝑁𝑛0

Implementation – Sampling Design


1. Create the grid and a synthetic

population to test the design

2. Run a simulation based on the

provided parameters, to advise

on the sample size (i.e. number

of PSUs)

3. Provide estimates of the

expected workload.

13

Implementation – Questionnaire and Navigation

1. Develop a “smart” questionnaire➢ Count the number of units

in the square

➢ Expand the square in line

with the predefined rule

➢ Show the enumerator the

correct boundary file on the

map

2. Create navigation files, which

can be used on the tablet.

3. Combine the two instruments,

such that they are usable even

in low skill environments.


Implementation – Monitoring and Adjustments


Fieldwork update

• 141 networks completed.

• 1840 informal firms listed

• 469 standard interviews completed; refusal rate of about 4%


Fieldwork update…


Completed squares and yield per square by strata.

Share of firms and response rate by strata

30

70

120

24

48

69

81 8087

43

114

46

13

6

-5

5

15

25

35

45

55

65

75

85

-10

10

30

50

70

90

110

130

High Medium Low

Sample Completed netwroks Completed Squares

Firms per square (av.) % resulted in expansion

56

28

16

59

25

16

5 62

0

10

20

30

40

50

60

70

High Medium Low

% firms found % long form quest. Refusal Rate (%)

Fieldwork update…

• Sectoral composition, based on data for 1017 listed and 261 interviewed

firms.


103[10%]

754[74%]

160

[16%]

43[16.5%]

175[67%]

43[16.5%]

0

100

200

300

400

500

600

700

800

Manufacturing Retail Services

Listed firms Interviewed

Some Descriptives


99% 4500 5400 Kurtosis 13.56255

95% 2000 4800 Skewness 3.055291

90% 1500 4500 Variance 715862.4

75% 600 4000

Largest Std. Dev. 846.0865

50% 250 Mean 555.6939

25% 100 25 Sum of Wgt. 245

10% 50 20 Obs 245

5% 35 20

1% 20 20

Percentiles Smallest

sales

************* SALES ****************

*************************************

*************************************

Some Descriptives


0

.00

05

.00

1.0

015

Den

sity

0 2000 4000 6000sales

kernel = epanechnikov, bandwidth = 111.0113

Kernel density estimate

0.1

.2.3

Den

sity

2 4 6 8 10ln_sales

kernel = epanechnikov, bandwidth = 0.3747

Kernel density estimate

Some Descriptives


0.2

.4.6

.8

Den

sity

0 5 10 15 20 25emp_total

Mean # of paid employee(s) : 1.24

Median # of paid employee(s) : 1.00

Mean # of unpaid employee(s) : 0.47

Median # of unpaid employee(s) : 0.00

Mean # of female employee(s) : 0.82

Median # of female employee(s) : 1.00

Some Descriptives


99% 41.96667 117.5833 Kurtosis 62.62024

95% 31.74167 42.15 Skewness 5.585522

90% 27.89167 41.96667 Variance 74.19437

75% 24.28333 40.98333


50% 20.25833 Mean 20.92051

25% 16.6 9.966666 Sum of Wgt. 260

10% 12.96667 8.033334 Obs 260

5% 11.90833 .5833333

1% 8.033334 .3666667


time

DURATION FOR LONGFORM

99% 12.76667 357.3167 Kurtosis 637.7595

95% 5.583333 49.91667 Skewness 24.90674

90% 4.308333 17.93333 Variance 190.3719

75% 3.366667 14


50% 2.616667 Mean 3.530686

25% 2.083333 1.1 Sum of Wgt. 680

10% 1.683333 1.1 Obs 680

5% 1.533333 .5833333

1% 1.166667 .45


time

DURATION FOR SHORTFORM

Some Descriptives


REFERENCES

Greig-Smith, P. (1964) Quantitative plant ecology. (2nd ed.) Butterworths, London.

Bernhard Meindl, Matthias Templ, Andreas Alfons, Alexander Kowarik, and with contributions from Mathieu Ribatet (2017). simPop: Simulation of Synthetic Populations for Survey Data Considering Auxiliary Information. R package version 0.6.0. URL https://CRAN.R-project.org/package=simPop.

Sudman, S., Sirken, M., Cowan, C. D. (1988). Sampling rare and elusive populations. Science240.4855: 991

Solomon, H., & Zacks, S. (1970). Optimal design of sampling from finite populations: A critical review and indication of new research areas. Journal of the American Statistical Association, 65(330), 653-677.

Thompson, S. K. (1990). Adaptive cluster sampling. Journal of the American Statistical Association, 85(412), 1050-1059.

Thompson, S. K. (1991). Stratified adaptive cluster sampling. Biometrika, 78(2), 389-397.

Winston Chang, Joe Cheng, JJ Allaire, Yihui Xie and Jonathan McPherson (2017). shiny: Web Application Framework for R. R package version 1.0.0. https://CRAN.R-project.org/package=shiny


Thank You!


1. Objectives and Challenges 4. Sampling Weight · 2021. 4. 21. · Objectives and Challenges:...

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