4. ESTIMATING BIAS IN MULTIVARIATE RELATIONSHIPS 
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structure of the regression results did not change very much. The relative magnitude of the 
coefficients and their level of significance was stable. The Heckman results were situated 
between the survey and the validation sample and a low total bias was estimated. Though the 
bias correction generally tended to be only slight, the Heckman method appeared to work on 
the secure side. No correction was outside the expected range. 
Due to the fact that the general frame of this thesis is limited, I cannot describe other 
applications of corrections in detail. I will, therefore, only briefly mention tests with 
propensity weights. Taking the same data and the presented selection equation, I checked the 
same regression with weights calculated by the inverse of the predicted probability for sample 
participation. Though some estimates were corrected, it turned out that others were far out of 
range between the panel and the total sample, even in the extreme bias example. So Brehm's 
(1993:119-121) statement that weighting is no solution to the problem of nonresponse in 
multivariate analyses was verified. 
The decision as to whether a correction method is required and which one is useful 
depends upon the purpose of the regression model. If a precise prediction is needed, then the 
exact coefficient estimate in numbers is important and the danger of bias is relevant. If we are 
more interested in explaining the structure of interrelated variables - and this is often the case 
in sociological models - we focus on the interpretation of the relative importance of the 
coefficients and not on the absolute number. The efficiency of the Heckman correction 
depends upon a well specified selection equation (also the propensity weights method) which 
is more difficult to specify in the nonresponse problem. The income regression example 
showed that the interpretation of the significant effects was essentially unaltered.