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An antecedent variable is a variable that occurs before the independent variable and the dependent variable.
For example, in politics, a special interest group may want to support a politician who backs their cause. The group would look for a candidate who supports their views and support his election. Once in office, the politician would then conduct policy that supports the interest group.
Thus, the variable relationship forumla would look like this:
Antecendent variable (interest in cause) -> Independent variable (interest group support) -> dependent varibale (policy decisions)