Bear F. Braumoeller
Assistant Professor, Department of Government, Harvard University

What Are Boolean Logit and Probit?

Boolean probit/logit are designed for situations in which

• the dependent variable, Y, is binary;
  
  
• the impact of the various causal mechanisms, or "causal paths," which together make the dependent variable occur cumulates in a Boolean fashion — i.e., A and B cause Y, or A and (B or C) cause Y; and
  
  
• the impact of each causal mechanism is determined by some vector of independent variables.
  
  

Example. Imagine that citizens in a democratic state might choose not to vote (Y=1) if they are ignorant (A) or if they are indifferent between the candidates (B) or if they both live far from a polling station (C) and lack transportation (D) — that is,

A or B or (C and D) cause Y.

Ignorance, in turn, might be captured by years of schooling (X1) and exposure to mass media like newspapers (X2) and television (X3); indifference might be captured by the difference between candidate evaluations (X4-X5); remoteness might be captured by physical distance from the nearest polling station (X6); and availability of transportation might be captured by household automobile ownership (X7).

Boolean logit and probit are maximum-likelihood techniques that are designed to test such hypotheses.

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