Stats, MR and Data: Rim Weighting Excel Macro

Update - 09/12/2015

I've updated the macro and put it into one Excel add-in. It's now available here.

Introduction

In a previous post I wrote about two methods to demographically weight a market research sample to make the sample represent a population. For example, if you had a sample of 1000 people to measure the average height of a certain country, you might want to weight the sample by age and gender so that the sample represented the population in those two variables (dimensions, fields) exactly.

In this post I'm going to detail a macro that can be used to rim weight a sample.

The algorithm for rim weighting is very simple. Graham Kalton and Ismael Flores-Cervantes give a very good explanation of rim weighting (and other demographic weighting methods) in an article for the Journal of Official Statistics. This website is well worth a look for other articles on running panels, weighting schemes and, it seems, everything else to do with statistics. Anyway, I give a short explanation below.

To give a concrete example and help with the explanation I'll use the example given in the previous blog entry.

	Gender
Age	Male	Female	Total
Young	30%	20%	50%
Old	25%	25%	50%
Total	55%	45%	100%

The above table shows the population proportions for age and gender. Let's assume the sample proportions are as below:

	Gender
Age	Male	Female	Total
Young	20%	35%	55%
Old	20%	25%	45%
Total	40%	60%	100%

The totals are called the marginal distributions or the rims.

Rim weighting is an iterative process. The first dimension's (in this case age) totals are used to calculate a weight such that the sample totals (40% and 60%) equal the population totals (55% and 45%). This weight is then adjusted so that the next dimension's (gender) sample totals equal the population totals for that dimension. This is one iteration.

The process is repeated until either all the sample totals equal the population totals or the number of iterations exceeds a predefined maximum.

Macro

Below is the (fairly complicated) macro. It assumes that you want to match population proportions and that the input data is of the form rim1, targets1, rim2, targets2.

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Sub rimOrdered()

'Rim weight with respect to ordering of rim

Dim totalRange As range

Dim rimRange() As range

Dim tarRange() As range

Dim weights() As Double

Dim factors() As Double

Dim iterations As Integer

Dim m As Integer

Dim weightCap As Double 'Upper limit for weight

Dim weightLow As Double 'Lower limit for weight

Dim convCrit As Double 'Convergence criterion

Dim testBoo As Boolean 'Boolean for convergence criteria

Dim totalRim As Double

Dim numberOfRims As Integer

Dim names() As String 'Name of rim

Dim colNumber() As Integer 'Column number of rim

Dim weff As Double 'Weighting effect

Dim sqWeights As Double

Dim currWkName As String

Dim rimIter As Integer

Dim tempCheck As Double

Dim startTime

Dim i, k, n As Integer

Dim rimw() As Dictionary

Dim tarw() As Dictionary

Dim actuals() As Dictionary

RimForm2.Show

If RimForm2.TextBox1.Enabled = False Then

RimForm2.Hide

Unload RimForm2

Exit Sub

End If

Set totalRange = range(RimForm2.RefEdit1.Value)

Application.ScreenUpdating = False

Application.Calculation = xlManual

startTime = Time

numberOfRims = RimForm2.ListBox2.ListCount

iterations = RimForm2.TextBox1.Value

weightCap = RimForm2.TextBox2.Value

weightLow = RimForm2.TextBox5.Value

convCrit = RimForm2.TextBox3.Value

currWkName = ActiveSheet.Name

'Calculate number of rows

totalRim = totalRange.Rows.Count - 1

'Redimension arrays

ReDim rimw(numberOfRims)

ReDim tarw(numberOfRims)

ReDim actuals(numberOfRims)

For n = 0 To numberOfRims - 1

Set rimw(n) = New Dictionary

Set tarw(n) = New Dictionary

Set actuals(n) = New Dictionary

ReDim rimRange(numberOfRims)

ReDim tarRange(numberOfRims)

ReDim factors(numberOfRims, totalRange.Rows.Count - 1)

ReDim weights(totalRange.Rows.Count - 1)

ReDim names(numberOfRims)

ReDim colNumber(numberOfRims)

'Define area of rim ranges

For i = 0 To RimForm2.ListBox2.ListCount - 1

names(i) = RimForm2.ListBox2.List(i)

For k = 1 To totalRange.Columns.Count

If totalRange.Cells(1, k).Value = names(i) Then

colNumber(i) = k

End If

Set rimRange(i) = range(Cells(2, colNumber(i)), Cells(totalRange.Rows.Count, colNumber(i)))

Set tarRange(i) = range(Cells(2, colNumber(i) + 1), Cells(totalRange.Rows.Count, colNumber(i) + 1))

'Calculate factors for each of the rims

'Set up hashes

For n = 0 To numberOfRims - 1

For Each i In rimRange(n).Rows

If rimw(n).Exists(i.Value) Then

rimw(n).Item(i.Value) = rimw(n).Item(i.Value) + 1

actuals(n).Item(i.Value) = actuals(n).Item(i.Value) + 1

Else

rimw(n).Add i.Value, 1

actuals(n).Add i.Value, 1

End If

For n = 0 To numberOfRims - 1

For i = 1 To tarRange(n).Rows.Count

If Not tarw(n).Exists(rimRange(n)(i).Value) Then

tarw(n).Add rimRange(n)(i).Value, tarRange(n)(i).Value

End If

'Test that value already in target is the same for this cell

'i.e. that targets are consistent

'Test that tarw(n) adds up to 1

tempCheck = 0

For Each i In tarw(n).Keys

'Test for numeric values

If IsNumeric(tarw(n).Item(i)) Then

'If a non-numeric value is found then abort and display error message

tempCheck = tempCheck + (10 ^ CInt(RimForm2.TextBox4.Value)) * tarw(n).Item(i)

Else

MsgBox ("Rim " & n + 1 & ", Key " & i & " is not numeric")

Application.ScreenUpdating = True

Application.Calculation = xlAutomatic

Unload RimForm2

'Application.StatusBar = "Rim weighting macro aborted"

Exit Sub

End If

'If they don't display sum of targets and rim affected

If Int(tempCheck) <> (10 ^ CInt(RimForm2.TextBox4.Value)) And RimForm2.CheckBox1.Value = True Then

contvar = MsgBox("Rim " & n + 1 & " targets do not add to 100%" & vbCrLf & "They add to: " & tempCheck / (10 ^ (CInt(RimForm2.TextBox4.Value)) / 100) & "%" & vbCrLf & vbCrLf & "Do you wish to continue?", vbYesNo)

If contvar = vbNo Then

Application.ScreenUpdating = True

Application.Calculation = xlAutomatic

Unload RimForm2

'Application.StatusBar = "Rim weighting macro aborted"

Exit Sub

End If

'Set up initial weights

For i = 0 To totalRange.Rows.Count - 1

weights(i) = 1

'Calculate factor and iterate round the loop

'Factors

m = 0

m = m + 1

For n = 0 To numberOfRims - 1

For i = 0 To totalRange.Rows.Count - 2

weights(i) = weights(i) * totalRim * tarw(n)(rimRange(n)(i + 1).Value) / rimw(n)(rimRange(n)(i + 1).Value)

If weights(i) > weightCap Then weights(i) = weightCap

If weights(i) < weightLow Then weights(i) = weightLow

'Reset hashes

rimIter = n + 1

If rimIter = numberOfRims Then rimIter = 0

For Each i In rimw(rimIter).Keys

rimw(rimIter).Item(i) = 0

totalRim = 0

'Recalculate values in hashes

j = 0

For Each v In rimRange(rimIter).Rows

rimw(rimIter).Item(v.Value) = rimw(rimIter).Item(v.Value) + weights(j)

'Recalculate total sum of weights

totalRim = totalRim + weights(j)

j = j + 1

'Test convergence criterion

testBoo = True

For n = 0 To numberOfRims - 1

For Each i In rimw(n).Keys

If rimw(n).Item(i) = 0 Then

rimw(n).Item(i) = 0.0001

End If

If Abs(totalRim * tarw(n).Item(i) / rimw(n).Item(i) - 1) > convCrit Then

testBoo = False

End If

Loop Until m >= iterations Or testBoo

sqWeights = 0

'Display weights

Cells(1, totalRange.Columns.Count + 1).Value = "Weights"

For i = 2 To totalRange.Rows.Count

Cells(i, totalRange.Columns.Count + 1).Value = weights(i - 2)

'Calculate WEFF

sqWeights = sqWeights + (weights(i - 2) * weights(i - 2))

'Produce report

Worksheets.Add

Set sname = ActiveSheet

'Need to check that this doesn't already exist in the spreadsheet

Dim wkshtName As String

Dim wkshtThere As Boolean

Dim wkshtCount As Integer

wkshtName = currWkName & " Report"

wkshtCount = 1

wkshtThere = False

For wksht = 1 To ActiveWorkbook.Sheets.Count

If ActiveWorkbook.Sheets(wksht).Name = wkshtName Then

wkshtThere = True

End If

If wkshtThere = True Then

wkshtCount = wkshtCount + 1

wkshtName = currWkName & " Report" & wkshtCount

End If

Loop Until wkshtThere = False

sname.Name = wkshtName

If totalRim = 0 Then totalRim = 0.00001

Cells(1, 1).Value = "Number of iterations"

Cells(1, 2).Value = m

Cells(2, 1).Value = "WEFF"

Cells(2, 2).Value = (totalRange.Rows.Count - 1) * sqWeights / totalRim ^ 2

Cells(3, 1).Value = "Time taken"

stopTime = Time

Cells(3, 2).Value = Format((stopTime - startTime) * 24 * 60 * 60, "00")

Cells(1, 4).Value = "Ordered weighting"

For n = 0 To numberOfRims - 1

Cells(4, (n + 1) * 6 - 5).Value = names(n)

p = 6

Cells(5, (n + 1) * 6 - 4).Value = "Actual"

Cells(5, (n + 1) * 6 - 3).Value = "Weighted"

Cells(5, (n + 1) * 6 - 2).Value = "Targets"

Cells(5, (n + 1) * 6 - 1).Value = "Difference"

For Each i In rimw(n).Keys

Cells(p, (n + 1) * 6 - 5).NumberFormat = "@"

Cells(p, (n + 1) * 6 - 5).Value = i

Cells(p, (n + 1) * 6 - 4).Value = actuals(n).Item(i) / (totalRange.Rows.Count - 1)

Cells(p, (n + 1) * 6 - 4).NumberFormat = "0.00%"

Cells(p, (n + 1) * 6 - 3).Value = rimw(n).Item(i) / totalRim

Cells(p, (n + 1) * 6 - 3).NumberFormat = "0.00%"

Cells(p, (n + 1) * 6 - 2).Value = tarw(n).Item(i)

Cells(p, (n + 1) * 6 - 2).NumberFormat = "0.00%"

Cells(p, (n + 1) * 6 - 1).Value = (totalRim * tarw(n).Item(i) / rimw(n).Item(i)) - 1

Cells(p, (n + 1) * 6 - 1).NumberFormat = "0.00%"

p = p + 1

'Sort bits

range(Cells(6, (n + 1) * 6 - 5), Cells(p - 1, (n + 1) * 6 - 1)).Sort Key1:=range(Cells(6, (n + 1) * 6 - 5), Cells(p - 1, (n + 1) * 6 - 1)).Columns(1), Header:=xlNo

Dim freqDist() As Integer

ReDim freqDist((weightCap - weightLow) * 10)

For i = 2 To totalRange.Rows.Count

freqDist(WorksheetFunction.Floor(weights(i - 2), 0.1) * 10) = freqDist(WorksheetFunction.Floor(weights(i - 2), 0.1) * 10) + 1

For i = weightLow To weightCap Step 0.1

Cells(i * 10 + 3, numberOfRims * 6 + 1).Value = i

Cells(i * 10 + 3, numberOfRims * 6 + 2).Value = freqDist(i * 10)

Application.ScreenUpdating = True

Application.Calculation = xlAutomatic

Unload RimForm2

End Sub

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What's missing here is the form required to specify the target area, the dimensions and the criteria for running the procedure. I'll add a link to the form when I think of somewhere to put it. The image below shows the listboxes defining the rims and targets:

From these the dictionary objects rimw and tarw are populated.

The next image shows the variables tab:

This tab allows you to define the maximum number of iterations and the weight caps.

The meat of the macro is shaded in grey. This is where the calculation of the weights actually happens.

Also the macro produces a report of the weighting giving a breakdown of how successful it was by each of the rims.

For example, the following input:

ID	Rim1	Target1	Rim2	Target2
1	A	0.75	C	0.5
2	A	0.75	C	0.5
3	A	0.75	D	0.5
4	B	0.25	D	0.5
5	B	0.25	D	0.5

produces:

Number of iterations	1
WEFF	1.09375
Time taken	0

Rim1					Rim2
	Actual	Weighted	Targets	Difference		Actual	Weighted	Targets	Difference
A	60.00%	75.00%	75.00%	0.00%	C	40.00%	50.00%	50.00%	0.00%
B	40.00%	25.00%	25.00%	0.00%	D	60.00%	50.00%	50.00%	0.00%

in the report.

Weights are placed in the column after the area specified in the first tab.

Conclusion

The macro above will calculate rim weights fairly rapidly for any number of dimensions/fields. You can specify convergence criteria, weight caps and the number of iterations.

Hopefully this will help somebody and all comments welcome - especially if they are suggestions for improvements.

In my next entry I'll explain what the WEFF is and how it affects the accuracy of the estimation.

8 comments:

Anonymous26 September 2013 at 08:02
Firstly nice blog. I am playing around with the macro and just wanted to know if you have had a chance to add a link to the form?
MJ Brookson4 January 2014 at 01:41
I've developed a macro as well that also allows for trimming weights, reports, and weighting multiple subsets at once. I'm busy converting it to a web application at www.spinnakerresearch.nl. We're still in beta so you can still get a free account.
Anonymous19 August 2015 at 07:54
First of all thank you for sharing this macro. It's very useful. Unfortunately I have to switch to English region settings in order to use it, since the macro breaks when decimals are indicated with commas instead of dots. Is it possible to fix this by altering the code? Thx.
PkPk4 December 2015 at 19:15
Hi thanks for sending this. I have been spending lots of time on this with formulas. Please can you repost the macro with all the fixes? I went to the websites above and could not access the updated macro. Thanks in advance

Saturday 22 June 2013

Rim Weighting Excel Macro

Update - 09/12/2015

Introduction

Macro

Conclusion

8 comments: