An Introduction to Causal Analysis in Sociology - download pdf or read online

By Ian Birnbaum

ISBN-10: 0333261127

ISBN-13: 9780333261125

ISBN-10: 1349164666

ISBN-13: 9781349164660

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J t) + L ( 2 )( (J I ' (J 2' . . ' (J t) + · · · + L(n)(O 1, 02, ... 2 where the bracketed superscript (i) indicates the observation Xa = Xa;. Let us now apply the method of maximum likelihood to the path regression coefficients. 3 ;~: We know that k -I E(XkiX1, ... ,xk-d= l: h;X;+ck, i= I where Ck =E( Uk ), a constant. Note that ck consists of the effect of explicit variables when they are zero plus the average effect of implicit variables. We assume that for every configuration of X 1 , •..

We need theoretical reasons to assume this. If our theory leads us to strongly suspect this assumption, then we will need to use terms like cX 1 X2; cX2 is the direct effect of X1 which depends for its size on which value X 2 has. In this book, however, only linear models will be considered. Interactive models (as models with such terms as eX 1 X 2 are called) can be incorporated in the linear case by defming Y 1 , say, as X 1 X 2. It must be stressed, however, that problems may occur in estimation due to the effect known as multi-<:ollinearity where the linear regression equation in the sample of at least one of the explicit variables on the rest accounts for a very high proportion of the variance in that variable.

Now, given this normality, we can use a method of estimation which in many ways is more intuitively convincing than least squares, and which is certainly more general. This method is called maximum likelihood, and it has the advantage here of leading on directly to hypothesis testing. In the case of linear regression, as here, the estimates obtained are exactly the The Theory of Causal Analysis 45 same as those obtained using least squares. The method gives estimators which have certain optimum properties in large samples.

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An Introduction to Causal Analysis in Sociology by Ian Birnbaum


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