The obsession with weight in the modelling world

1
The obsession with weight in the modelling world
And its ancillary affects on Analysis
2
The basic

• The basic idea of sampling
• The reason behind complicating a good idea
• The implication when modelling data

3
How Sampling Works.
Now lets assume that we had some idea about the
picture we wanted to see. And we decide to
stratify the sample. In this case we decide to
sample different areas of the picture at
different rates, the backgroud, the dress, the
face, the hands, etc...
Imagine a well known picture Since a picture is
made up of points of colour (pixels), we will
sample the points of colour at different rates.
1 Random (systematic)
10 Random
3 Random
5 Random
2.5 Stratified
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How Sampling Works.
1
3
5
10
2.5 Stratified
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How does this affect modeling or analysis

• The sample is no longer simply random
• We purposefully biaised the sample to gain
  efficiencies to meet other goals
• This bias is corrected when we apply the design
  weights.

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Framework
If you were to analyse each stratum separately
Still there would be some difficulty associated
with the correction for non-response and final
callibration (post)
Each part can actually be treated as surveys each
with a simpler design
The sampling frame or design allows you to keep
all these part together in a cohesive way for
analysis.
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How to interpret sampling
The way we sample is reflected and corrected by
how we weight the data in the end.

• If you looked only at the parts we sampled
• You wouldnt get an accurate picture.
• All the parts would be there but not in the right
  proportions.

• The design weights compensate for the known
  distortions. The final weights include estimated
  distortions.

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What would you use to base the fundamental
multivariate relationships in your model or
analysis ?
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Steps to calculate the weights Basic overview

• At the survey design stage, some factors are used
  to determine the sample size required
• Probability of selection calculated
• First series of adjustments for non-response
• Post-stratification

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Factors to determine the sample size

• Characteristics to be estimated (small
  proportions)
• Required precision of the estimates (targetted
  CV)
• Variability of the data
• Expected non-response rate
• Size of the population

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Original design weight

• Once the sample is selected in each stratum,
  calculate the original weight
• Nh/nh, where  h  is the stratum
• Since the sample is selected from LFS, get
  original weight from LFS.
• Adjustments for the number of available children.

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Non-response adjustment

• Adjustments must be made to take into account the
  total non-response
• Characteristics of respondents vs non-respondents
  are analyzed
• Province, income, level of education of parents,
  depression scale of PMK, urban/rural, etc.

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Post-stratification

• Adjustment factor calculated in order to
  post-stratify the sample to known population
  counts, by
• Province, age, gender

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Final weight

• Wf Wi X Adj1 X Adj2
• Where
• Wf Final weight
• Wi initial weight
• Adj1 Non-response adjustment
• Adj2 Post stratification

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Link between analysis and the sample design
(weight)
Intelligence
Grade level
Childs Ability
Social environment
Teachers
School
Materials
Subject
Curriculum
Province
The proportion of kids in the sample being taught
the PEI curriculum is much larger than whats
found in the population
Province is a stratum
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Link between analysis and the sample design

• There are very few things in a childs life that
  is not related to where they live.
• In the city versus in a small village
• In a small province versus a large one
• what social/educational programs are offered
• what social support and services are offered
• regional cultural differences
• to name a few

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Weights for cycle 4

• Cross-sectional weights
• Longitudinal weights, including the converted
  respondents.
• Longitudinal weights, children introduced in C1
  and respondent to all cycles. NEW
• Not to mention the bootstrap weights, which are
  used for an entirely different purpose.

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Cross-sectional Weights

• Available for all cycles, up to Cycle 4.
• When are they used?
• Cycle 4 cross-sectional weights
• to represent the population aged 0-17 in 2000-01.
• Cycle 1 weights
• to represent the population aged 0-11 in 1994-95.

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Cross-sectional Weights - Cycle 4 - Warning

• In Cycle 4, children with a cross-sectional
  weight come from 4 different cohorts (introduced
  in 1994, 1996, 1998 and 2000).
• By 2000, the 1994 cohort has been around for 6
  years
• cross-sectional representativity decreases over
  time because of sample erosion and population
  change (immigration).

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Cross-sectional Weights - Cycle 5

• For Cycle 5 (2002-2003), no children aged 6 and
  7.
• In addition, the 1994 cohorts cross-sectional
  representativity has declined even further
  (erosion and immigration).
• As a result, cross-sectional weights will be
  calculated only for children aged 0-5.

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Cross-sectional weights in a nutshell

• Cross-sectional weights must be used when the
  analysis concerns a specific year, when you want
  a snapshot of the situation at a specific point
  in time.

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Longitudinal Weights

• Longitudinal weights represent the population of
  children at the time they were brought in to the
  survey.
• Children introduced in Cycle 1 longitudinal
  weights represent the population of children aged
  0-11 in 1994-95.

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Longitudinal Weights (continued)

• Children introduced in Cycle 2 longitudinal
  weights represent the population of children aged
  0-1 in 1996-97.
• Children introduced in Cycle 3 longitudinal
  weights represent the population of children aged
  0-1 in 1998-99.
• Children introduced in Cycle 4 longitudinal
  weights represent the population of children aged
  0-1 in 2000-01.

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When are longitudinal weights used?

• When you want to track a cohort of children
  introduced in a particular cycle and see how
  theyve developed over time.

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Longitudinal Weights - Cycle 4

• Something new in Cycle 4
• 2 sets of longitudinal weights
• Set 1 Weights for children who responded in
  their first cycle and in Cycle 4 (possible
  non-response in Cycle 2 or 3)
• Set 2 Weights for those introduced in cycle 1
  who responded in every cycle. NEW.

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Longitudinal Weights - Cycle 4

• Difference between the 2 sets of longitudinal
  weights
• To avoid total non-response in Cycle 2 or 3, the
  set of weights for those who responded throughout
  can be used.
• If youre only interested in the changes between
  Cycle 1 and Cycle 4 directly, the longitudinal
  weights including converted respondents can be
  used.

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Examples

• Following are real examples taken from the NLSCY
  data

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Weighting - Examples
Average weights in Cycle 4.
Prince Edward Island
7 1-year-olds
5-year-old
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Weighting - Examples
Average weights in Cycle 4 (continued)
Ontario
712 15-year-olds
15-year-old
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Example Proportion of children aged 0-17, by
province, Cycle 4, UNWEIGHTED

• 24 of Canadas children live in the Maritime
  provinces whereas in reality...

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Example Proportion of children aged 0-17, by
province, Cycle 4, WEIGHTED

• Whereas in reality7.3 of children live in the
  Maritime provinces.

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Number of children aged 0-15 by year of age,
Quebec, Cycle 3, unweighted

• The conclusion is obvious
• Huge increase in births in 1993 and 1997!!!!!

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Number of children aged 0-15 by year of age,
Quebec, Cycle 3, WEIGHTED

• So much for the pseudo baby boom...

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Conclusion

• To be obsessed with weights is a good thingwhere
  statistical analysis is concerned