# Combining estimators from multiple rounds and multiple countries

As a rule, when combining estimators from multiple countries - in the single-round as well as in the multi-round case - population weights have to be used (see Table 4.1).

Example: Voter turnout^{2} |
Design weight | Population weight | |
---|---|---|---|

a) To examine data from a single country - whether a single variable or a cross-tabulation | Voter turnout in Germany | X | |

Voter turnout in Germany by age and gender | X | ||

b) To compare results for two or more countries separately - without using totals or averages | Compare voter turnout in France, Germany and the UK. | X | |

c) To combine countries - whether on a single variable or via a cross-tabulation | i) Voter turnout in Scandinavia. | X | X |

ii) Voter turnout in the EU. | X | X | |

iii) Voter turnout across all countries participating in the ESS. | X | X | |

iv) Compare voter turnout between EU member states and accession countries. | X | X | |

v) Voter turnout by age groups across all ESS participating countries. | X | X |

1 = Table based on [Ess06b]. The 'X'es in the table indicate that the weight should be used.

2 = % of respondents voting in the last election.

However, combining estimators from multiple rounds and multiple countries raises the question of how to account for possibly varying population weights1. Assuming, again, a constant population from which the samples in various rounds are taken, a combined population weight is simply the average of the single-round weights. This can be formalised in the following way. The multi-round population weight of a specific country is defined as

It is convenient, however, to rescale the single-round population weights to the sum of the weights. The rescaled population weight for country c in round r is thus

and the corresponding average population weight of rounds a in country c is defined as

To further combine multi-round estimators for multiple countries, average population weights have to be calculated for all countries under consideration. These must be used as explained in [Ess06b].

The combined multi-round multi-country estimator can be expressed as

### Example

Now assume we were interested in the question of how satisfied people are on average when living in countries with a relatively left-wing government. To answer this question, we combine the overall satisfaction scores (STFLIFE}) of Germany, the United Kingdom, and Portugal, which can be seen as fairly typical cases of European left-wing governments. However, such a grouping of countries requires us to take design into account as well as population weights.

We have already calculated the single-country multi-round estimates in the previous Chapter. What we need for the construction of the combined estimator are the single-country multi-round population weights of the three countries.

First of all, the population weights of each country in each round have to be rescaled. The original and the rescaled weights are shown in the following table.

Original | Rescaled | |||
---|---|---|---|---|

Country | Round I | Round II | Round I | Round II |

DE | 2.39 | 2.45 | 0.4540 | 0.4498 |

GB | 2.33 | 2.57 | 0.4416 | 0.4713 |

PT | 0.55 | 0.43 | 0.1044 | 0.0789 |

The average of the rescaled population weights for Germany, the United Kingdom, and Portugal from rounds one and two are 0.4519, 0.4564, and 0.0917, respectively.

The weighted sum of the multi-round single-country overall satisfaction score (STFLIFE) is then

_{1,2;DE,GB,PT} = (7.08*0.4519) + (7.22*0.4564) + (6.06*0.0917)= 7.05

#### Footnotes

- [1] Population weights may vary between rounds because countries drop out or because another one is added.

#### References

- [Ess06b] ESS (2006b).
*Weighting European Social Survey Data*. European Social Survey. http://ess.nsd.uib.no/streamer/?module=main&year=2007&country=null&download=%5CSurvey+documentation%5C2007%5C07%23ESS3+-+Weighting+ESS+Data%5CLanguages%5CEnglish%5CWeightingESS.pdf