Communicating Accuracy of Register Statistics

1. Communicating Accuracy of
Register Statistics
Thomas Laitila
Statistics Sweden and Örebro university
Presentation at Nordiskt Statistikermöte, Bergen, 2013

2. Outline
Why - Why measure accuracy?
Criteria - Criteria on measures of uncertainty
of register statistics
CIm - Confidence Image
Example
Discussion
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3. Why - Some basic questions
• What is statistics (statistical inference
methods) all about?
• What is making statistics so special, why is it
of value to us?
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4. Why - Chatterjee (2003)
• There are two methods for deriving
statements – deduction and induction
• Statistics is a prolongation of epistemiology
(theory on knowledge and knowledge
building)
• Statistics provide with a method for inductive
inference
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5. Why - Induction
Assumptions
Evidence
Area of concern
Statement
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6. Why - Induction, example
Ignorable nonresponse
Sample of units
Swedish labor market
Estimate of rate of
unemployment
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7. Why - Induction, another example
Register on units
Swedish labor market
Estimate of rate of
unemployment
Derived variables
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8. Why - Induction and Evidence
• All evidence come with uncertainty of the
general
• Statements derived by induction are uncertain
• Example: Inductive statement – A man will
inevitably die
– Evidence - No man born for more than e.g. 150
years ago are still alive.
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9. Why - Why is statistical inference so
special?
• Statistics is the only theory yet, providing with
objective measures of uncertainty of inductive
inference.
• Objective measures of importance for general
communication of statistics.
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10. Why - Summing up
• Register statistics yield inductive statements
• Register statistics are thereby uncertain
• Statistical inference provide with objective
measurements of uncertainty
• Inference on register statistics should be
founded in statistical inference theory
• Do we have appropriate statistical tools?
Yes, and no
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11. Criteria - Approaches for statistical
inference on register statistics
• Model based methods
– Multivariate techniques
– Data mining methods
– Stochastic processes
– and more
• Sample surveys
– Use sample surveys as a complement for
measuring uncertainty
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12. Criteria – Criteria on a measure
a) Founded within statistical inference theory
• Interpretable and objective measures
b) Easy to interpret by users
• How easy is the interpretation of an ordinary
confidence interval?
c) Of low cost
d) Comparable with measures in sample surveys
• Comparability/coherency
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13. CIm – A new statistical tool
• Statistical inference methods centers around
– a point estimator, and
– its sampling distribution
• In register statistics, treating variables as fixed,
there is
– a point estimate, but
– its sampling distribution is degenerate
• One alley of finding appropriate tools for register
statistics is to develop statistical inference
procedures which are not based on the sampling
distribution of an estimator!
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14. CIm - Laitila (2012)
• Confidence Images
• Idéa: Use external information to restrict the
potential values of study variables (y1,y2,…,yN)
– This will restrict the potential values of the population
parameter of interest t=f(y1,y2,…,yN)
– The more information, the more t is restricted.
• Information can come in any form, as long it
comes with a measure of uncertainty
• We can use registers, sample surveys, old
statistics, google, facebook, whatever!!!
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15. Example - Estimation of total number
of cattle in Swedish farms
County N:o units N:o missing values Sum of y_k
1 18713 3817 393797
2 14321 2918 296944
3 12281 2475 261832
4 10836 2213 216535
5 8646 1763 185285
6 7233 1485 148029
Total 72030 14671 1502422
Table 1: Information1 in available register on farms (N=72030)
1) No measurement or coverage errors in the register.
Problem: Estimate the total number of cattle with an interval estimate
using the information in the register, which contains missing values.
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16. Example - Pieces of information
• A1: Available data in the register
• A2: The 100 largest farms are in the register
and the N:o cattle for the 100th largest farm is
553.
• A3: Table 2 (below)
• A4: A 95% CI of the proportion of farms with
zero cattle: 0.6 – 0.71
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17. In register In population
County y_k=0 y_k>=553 y_k>=100 y_k>=100
1 9108 29 1252 1288
2 6989 17 931 959
3 5960 21 784 800
4 5329 12 677 701
5 4196 10 581 601
6 3565 11 467 477
Total 35147 100 4692 4826
Table 2: Additional information (N:o units)
Example – Table 2
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18. Example – Calculated CIms
Information
Used
Confidence
Level
Lower
bound
Upper
bound
A1 - A2 100% 1502 9615
A1 - A3 100% 1516 3016
A1 – A4 95% 1516 2217
Table 3: Confidence intervals for the total number of cattle based
on information sets A1 – A4. (Thousands cattle, True value 1,56 million)
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19. Discussion
• Image instead of interval as the method may
not provide a “connected” interval of points.
The CIm may consist of e.g. separate disjoint
intervals
• The CIm can directly be generalized to
multivariate cases.
• Easy calculated in some cases, in others
calculation can be a most complicated thing.
Research needed here.
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20. Discussion
• The CIm fulfill all the four criteria listed above.
• Most interesting:
– Traditional confidence intervals are special cases
of Cims
– Any kind of information (data) can be used, as
long as there is a probability measure of its
certainty
• The CIm is a theory, there is a need for
methodological developments.
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21. Thanks for Your attention!
Request of paper Laitila (2012)
thomas.laitila@scb.se
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