By Ian Birnbaum
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Additional resources for An Introduction to Causal Analysis in Sociology
However, we can improve this notion of 'best' by assuming further than U is normally distributed for each set of values of the explicit variables in the equation. e. MV unbiased) in the set of all possible estimators. If U is conditionally normal, however, then they are indeed MV unbiased overall. This is not the only reason for assuming U normal, however; if we wish to make hypothesis tests, then this assumption is necessary. The assumption is not as arbitrary as it seems, and the interested reader is referred to Birnbaum ( 1979) for the theory underlying the assumption of normality.
Paradoxically, however, if we return to the hypothetical experiment interpretation then it is possible to rescue these parameters as causal measures and to dissolve the objection. L Standardised Unear Models Let us confme our attention initially to a single population. l, we see that P4 1 , for instance, can be interpreted as the number of a 4 's by which X4 will change for a change of a 1 in X 1 , all other causes constant. Hence,p4 1 , P42 and P4J are standardised path regression coefficients.
3 Now, a change of one unit in X 1 with X 2 and non-intervening implicit effects constant gives an effect (b4 1 + b43b31) on X4. The size of the regression coefficient has changed (and could indeed now be zero) because X 3 has become an intervening explicit variable which cannot be controlled for in this equation. This explains why we often wish to make explicit, variables which are implicit - intervening - if we suspect they have impQrtant effects then their inclusion can greatly elucidate the effect of the other explicit variables.