4. ESTIMATING BIAS IN MULTIVARIATE RELATIONSHIPS
67
had dropped out of the former wave. This information is not given in the initial sampling,
however. Census data is, therefore, often used to validate a sample. Weighting based on
census information has to cope with several other problems such as e.g. incompatible
definition of target groups", differing variable categories, incomparable interview situation,
etc. Another disadvantage is that such a weighting technique may be able to correct marginal
distributions, but that we cannot assess what happens in multivariate interdependencies"
Other approaches refer more strongly to the aspect of nonresponse. The underlying
idea is to find a weighting adjustment that reflects the different probability of response. One
strategy is to take classes which represent the ease with which a person is contacted in order
to construct weights as e.g. is done in the Politz-Simmons" procedure or weighting by the
number of necessary telephone calls.
Burton (1999) suggests weights based on attitudes according to his hypothesis that
nonrespondents differ from respondents in their attitudes and opinions.
The last approach I will mention here is weighting by the propensity to respond.
Firstly, a regression of a dichotomous variable (being a respondent versus not being one) on
explanatory variables is performed, then the inverse of the predicted probabilities will be
taken as weights. This is discussed by Little/Schenker" (1995) and Brehm (1993:118).
Persons with a low prognosis for response will get more weight by this method. A good
model is, therefore, necessary in order to predict who will be a respondent and who not. In
other words, one needs information about the excluded "dark chapter persons" as well.
Schnell (1997:249-250) discusses the method as an interesting alternative under the title
"propensity weights". Brehm" (1993) is more sceptical about the positive effect, particularly
in multivariate analyses. Little/Schenker (1995:47) mention high variances for weighted
estimates and general problems of variance estimation in such a case.
4.2 The Heckman Sample Selection Model
The fundamental idea of the Heckman model is to correct a possibly biased regression model
in the error term. The error adjustment is calculated on the basis of a previous model which
As already mentioned, the EGLHS sampled East German persons using the concept of their origin as the basis,
whereas the German microcensus samples according to the place of residence.
This is also mentioned by Schnell (1997:248).
ยป It uses informationon how often people could have been contacted. See: Brehm (1993:118).
Little/ Schenker (1995) Missing Data. In: Arminger/ Clogg/Sobel (1995) Handbook of Statistical Modeling for
the Behavioral Sciences. pp. 46-47.
* See critical discussion in Brehm (1993:118-121).