Q. Construction of the causal model - regression analysis?
The construction of an explanatory model is a crucial step in the regression analysis. It should be defined with reference to the action theory of intervention. It is likely that different kinds of variable exist. In a number of cases, they may be specially created, for instance to take account of the fact that an individual has benefited from support or not (a dummy variable, taking values 0 or 1). A variable can also represent an observable characteristic (having a job or not) or an unobservable one (probability of having a job). The model may suppose that a particular variable develops in a linear, logarithmic, exponential or other way. All the explanatory models are constructed on the foundation of a model, like the following, for linear regression:
Y = β0 + β1X1 + β2X2 + .... + βkXk + ε, where
Y is the change that programme is primarily supposed to produce (for example employment of trainees)
X1-k are independent variables likely to describe the change.
β0-k are constants and
ε is the error term
Phenomena of co-linearity weaken the explanatory power. For instance, when questioning women about unemployment, if they have experienced periods of previous unemployment that are systematically longer than those of men, it won't be possible to separate the influence of the two explanatory factors: gender and duration of previous unemployment.