Weighting

• Why weight?
  • Make the sample reflect its reference population
  • Re-impose equal probability of selection
• In panel studies equiprobability of selection comes under special strain: persons in the sample leave the sample, in ways that are not random - attrition
• In the longitudinal context equiprobability of selection becomes redefined as equiprobability of survival
• Thus we weight to take account of the fact that certain categories of people `attrite' more than others
• We apply weights proportional to the groups' relative rates of attrition

• This implies a multi-stage weighting procedure:
  1. Weight the Wave 1 sample to compensate for clustering, sample design and actual data-collection achievement.
  2. For each wave thereafter, calculate the group-specific attrition rate (for a special meaning of `group')
  3. For each wave, calculate a weight which is the product of the last wave's weight, multiplied by the group's relative attrition rate (w.r.t the average)
  4. Thus we `chain' weights: $\omega_i = \omega_1 \prod_{j=2}^{j=i} \theta_j$
• `Groups' are defined as cells in a multi-way table, constructed from variables chosen by an automated procedure which searches for significant interactions (i.e., significant differences in attrition rates for certain combinations of values).

• The BHPS has multiple weights:
  • longitudinal versus cross-sectional
  • individual versus household
  • enumerated versus respondent (hhd or ind)
• Longitudinal weights are recommended for analyses using more than one wave
• Cross-sectional weights are appropriate when single waves are used as cross-sectional surveys
• Longitudinal weights attempt to restore the representativity of the sample to 1991 (or 1999 and 2001 for the new panels)
• Cross-sectional weights attempt to restore the representativity of the sample to the year of data collection
• Longitudinal weights exclude all new entrants except children who have `aged' into the sample
• Longitudinal weights exclude persons with incomplete records (one gap and you're out: other designs are possible)
• Cross-sectional weights attempt to compensate for the non-random selection of new individuals into the sample
• Use household or individual weights according to the level of analysis
• Most analyses use respondent weights
• There exist additional ECHP weights to deal with the extra subsample from wave 7
• There also exist additional weights for the Scottish and Welsh panel surveys, incorporated from wave 9

• The recommendation is to use the longitudinal weight of the latest data
• Thus for a crosstabulation of ajbstat and cjbstat use clrwght, the wave 3 longitudinal respondent weight
• For a crosstabulation of jbstat at $t-1$ and $t$, use the $t$ weight:

    ID  Wave  EMP  PEMP   Weight
     1    2    3     2    blrwght
     1    3    3     3    clrwght
     1    4    2     3    dlrwght
     1    5    2     2    elrwght
     1    6    2     2    flrwght
     1    7    1     2    glrwght
     1    8    3     1    hlrwght
     1    9    3     3    ilrwght
  

• In this example code like the following will work:

  compute wgt = 0.
  if wave = 2 wgt = blrwght.
  if wave = 3 wgt = clrwght.
  if wave = 4 wgt = dlrwght.
  if wave = 5 wgt = elrwght.
  if wave = 6 wgt = flrwght.
  if wave = 7 wgt = glrwght.
  if wave = 8 wgt = hlrwght.
  if wave = 9 wgt = ilrwght.
  weight by wgt.
  

• Weight variables:
  

  wLEWGHT	Longitudinal enumerated individual weight
  wLRWGHT	Longitudinal individual respondent weight
  wXHWGHT	Household weight (cross-sectional)
  wXRWGHT	Cross-sectional respondent weight
  wXEWGHT	Cross-sectional enumerated individual weight
  wXRWGHTE	ECHP X-sectional respondent weight (W7+)
  wXEWGHTE	ECHP X-sectional enumerated indv weight (W7+)
  wXRWTSW1	X-sectional respondent weight including Scot/Wales
  wXEWTSW1	X-sectional enumerated indv weight including Scot/Wales
  wXRWTSW2	X-sectional respondent weight Scot/Wales only
  wXEWTSW2	X-sectional enumerated indv weight Scot/Wales only
  wLRWTSW1	Longitudinal respondent weight including Scot/Wales
  wLEWTSW1	Longitudinal enumerated indv weight including Scot/Wales
  wLRWTSW2	Longitudinal respondent weight Scot/Wales only
  wLEWTSW2	Longitudinal enumerated indv weight Scot/Wales only

• For a fuller discussion see Vol A of the documentation:
  http://www.iser.essex.ac.uk/ulsc/bhps/doc/vola/wgimp.php