Probability-weighted option for order of decreasing difficulty (ODD) matching in LIAM2

[richard....@gmail.com]

Trails with Australian data suggest that ODD matching gives synthetic marriages with a standard deviation of 3.2 years for couple age differences, compared with the 5.62 years for actual couples.

 

These unrealistically low age differences can be improved by adding a probability-weighted option to ODD matching in LIAM2.  Column (2) of the following table shows hypothetical matching probabilities for 10 potential marriage partners.  Case 8 has the highest probability, and would be selected under ODD matching.

 

Column (3) shows cumulative probabilities, obtained by summing the probabilities in (2).  Select a random number between 0 and 1 (say 0.38683), and multiply by the last entry in (3), giving 0.83684.  Case 6 is the first one whose cumulative toal exceeds 0.83684, and is selected.  This is probability-weighting, as used in stochastic matching.

 

The Australian data suggest that oribaility-weighting gives slightly too high standard deviations of couple age differences.  Better results were obtained by using squares of probabilities, as in column (4).  Multiplying 0.38683 by the last entry in (40 gives 0.30657, again leading to the selection of case 6.

 

Using probability-weighting does increase runtimes.  ODD matching for 34803 couples, spread over 48 areas, took 1.2 seconds, while probability-weighted ODD matching took 3,5 seconds.

 

I would be happy to provide further deatils of our tests.

 

Richard Cumpston

 

 

Case	Probability	Summed	Summed
	of match	probabilities	squares of
			probabilities
(1)	(2)	(3)	(4)
1	0.01331	0.01331	0.00018
2	0.21452	0.22784	0.04620
3	0.38957	0.61741	0.19796
4	0.17942	0.79683	0.23015
5	0.03270	0.82953	0.23122
6	0.36187	1.19140	0.36218
7	0.46178	1.65318	0.57542
8	0.46311	2.11629	0.78989
9	0.05132	2.16761	0.79252
10	0.00037	2.16798	0.79252

[Gaëtan de Menten]

Hello,

Thanks a lot for sharing your findings and for starting a discussion on
methodologies used in Liam2 (which is always a good thing in my opinion).

On 09/01/2014 21:57, richard....@gmail.com wrote:
> Trails with Australian data suggest that ODD matching gives synthetic
> marriages with a standard deviation of 3.2 years for couple age
> differences, compared with the 5.62 years for actual couples.
> These unrealistically low age differences can be improved by adding a
> probability-weighted option to ODD matching in LIAM2. Column (2) of the
> following table shows hypothetical matching probabilities for 10
> potential marriage partners. Case 8 has the highest probability, and
> would be selected under ODD matching.

It is not entirely clear to me what you have done exactly: did you
actually use Liam2 in your tests? If so, did you already implement this
new option or are you planning to do so? In any case, if you need any
advice or have any trouble implementing it, do not hesitate to ask for help.

Ga�tan

> Column (3) shows cumulative probabilities, obtained by summing the
> probabilities in (2). Select a random number between 0 and 1 (say
> 0.38683), and multiply by the last entry in (3), giving 0.83684. Case 6

> is the first one whose cumulative total exceeds 0.83684, and is

> selected. This is probability-weighting, as used in stochastic matching.

> The Australian data suggest that probability-weighting gives slightly too

> high standard deviations of couple age differences. Better results were
> obtained by using squares of probabilities, as in column (4).

> Multiplying 0.38683 by the last entry in (4) gives 0.30657, again

> leading to the selection of case 6.
> Using probability-weighting does increase runtimes. ODD matching for
> 34803 couples, spread over 48 areas, took 1.2 seconds, while
> probability-weighted ODD matching took 3,5 seconds.

> I would be happy to provide further details of our tests.

> Case Probability Summed Summed
> of match probabilities squares of
> probabilities
> (1) (2) (3) (4)
> 1 0.01331 0.01331 0.00018
> 2 0.21452 0.22784 0.04620
> 3 0.38957 0.61741 0.19796
> 4 0.17942 0.79683 0.23015
> 5 0.03270 0.82953 0.23122
> 6 0.36187 1.19140 0.36218
> 7 0.46178 1.65318 0.57542
> 8 0.46311 2.11629 0.78989
> 9 0.05132 2.16761 0.79252
> 10 0.00037 2.16798 0.79252

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[richard cumpston]

Gaetan

 

I have written a program in C# to evaluate seven different matching methods

• stable marriage algorithm
• stochastic
• ODD
• ODD with probability weighting
• Inagaki ordered matching
• wobbled ordered matching
• SBAM (as presented by Stephensen and Markeprand at the IMA conference).

Results from the first 6 of these methods were included in my presentation on matching methods at the conference.  The results from SBAM are not encouraging, and I have asked Stephenson and Markeprand for suggestions.

 

I would be happy to provide the program to you, but would have to make substantial changes to keep the data confidential.

 

Hugh Sarjeant and I have no knowledge of Python, and are committed to some short-term development goals for our own synthesis and microsimulation programs.  We would be happy to comment on any test results you obtained from probability-weighted ODD matching.

 

 

Richard Cumpston

Director, Australian Projections Pty Ltd

Mobile 0433 170 276

On Wed, Jan 15, 2014 at 2:00 AM, Gaëtan de Menten <gdm@plan.be> wrote:

Hello,

Thanks a lot for sharing your findings and for starting a discussion on methodologies used in Liam2 (which is always a good thing in my opinion).

On 09/01/2014 21:57, richard....@gmail.com wrote:

Trails with Australian data suggest that ODD matching gives synthetic
marriages with a standard deviation of 3.2 years for couple age
differences, compared with the 5.62 years for actual couples.
These unrealistically low age differences can be improved by adding a
probability-weighted option to ODD matching in LIAM2.  Column (2) of the
following table shows hypothetical matching probabilities for 10
potential marriage partners.  Case 8 has the highest probability, and
would be selected under ODD matching.

It is not entirely clear to me what you have done exactly: did you actually use Liam2 in your tests? If so, did you already implement this new option or are you planning to do so? In any case, if you need any advice or have any trouble implementing it, do not hesitate to ask for help.

Gaėtan

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[Howard Redway]

I was interested in your comparison but have not been able to find a copy of the paper you presented at the conference.  Unfortunately neither I nor any of my colleagues were able to attend.  Is the paper available elsewhere or would you be able to send me a copy?

You may recall that I have a matching algorithm that I call ODD (I presented this in a paper Data Fusion by Statistical Matching at Canberra in 2003).  I am not sure if your code used the same underlying approach.

A second paper A Match Made In Silicon: Marriage Matching Algorithms for Dynamic Microsimulation was presented at the IMA Ottawa conference in 2009.  This compared several partnership matching algorithms.  The results were inconclusive which is why I am particularly interested in your paper.

Howard Redway

[richard cumpston]

Howard

 

Attached is the presentation and underlying paper.

 

I have your 2009 paper.  Where could I get a copy of the 2003 paper?

Richard Cumpston

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[Howard Redway]

Thanks Richard

I look forward to reading the paper and presentation.

Papers from the 2003 Canberra conference no longer appear to be available.  Attached is a copy of my paper.  

The method was developed for matching records to create the base data for one of our models.  It has only been applied to partnership matching in an experimental context..

Since 2003 I have added some enhancements to allow the inclusion of records with missing values and apply weightings to the distance functions.

My code is implemented in SAS.

Howard