kommunikasjon: communicating accuracy of register statistics

Communicating Accuracy of Register Statistics

Thomas Laitila

Statistics Sweden and Örebro university

Presentation at Nordiskt Statistikermöte, Bergen, 2013

Outline

Why - Why measure accuracy?

Criteria - Criteria on measures of uncertainty of register statistics

CIm - Confidence Image

Example

Discussion

Bergen, 2013 2 Thomas Laitila

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?


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


Why - Induction

Assumptions

Evidence

Area of concern

Statement


Why - Induction, example

Ignorable nonresponse

Sample of units

Swedish labor market

Estimate of rate of unemployment


Why - Induction, another example

Register on units

Swedish labor market

Estimate of rate of unemployment

Derived variables


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.


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.


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


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


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


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!


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!!!


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.


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


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


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)


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.


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.


Thanks for Your attention!

Request of paper Laitila (2012) [email protected]

Bergen, 2013 Thomas Laitila 21

kommunikasjon: communicating accuracy of register statistics

Technology

uncertainty bergen

induction statistics

inductive inference

cim laitila

unemployment bergen

old statistics

register a2

available register