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Table 5 Relevant variables and hypotheses

From: A note on testing for complementarity and substitutability in the case of multiple practices

n Variable Hypothesis
3 \( x_{1} x_{2} x_{3} \) \( \alpha_{12} + \alpha_{123} \ge 0 \)
\( x_{1} x_{2} (1 - x_{3} ) \) \( \alpha_{12} \ge 0 \)
4 \( x_{1} x_{2} x_{3} x_{4} \) \( \alpha_{12} + \alpha_{123} + \alpha_{124} + \alpha_{1234} \ge 0 \)
\( x_{1} x_{2} x_{3} (1 - x_{4} ) \) \( \alpha_{12} + \alpha_{123} \ge 0 \)
\( x_{1} x_{2} (1 - x_{3} )x_{4} \) \( \alpha_{12} + \alpha_{124} \ge 0 \)
\( x_{1} x_{2} (1 - x_{3} )(1 - x_{4} ) \) \( \alpha_{12} \ge 0 \)
5 \( x_{1} x_{2} x_{3} x_{4} x_{5} \) \( \alpha_{12} + \alpha_{123} + \alpha_{124} + \alpha_{125} + \alpha_{1234} + \alpha_{1235} + \alpha_{1245} + \alpha_{12345} \ge 0 \)
\( x_{1} x_{2} x_{3} x_{4} (1 - x_{5} ) \) \( \alpha_{12} + \alpha_{123} + \alpha_{124} + \alpha_{1234} \ge 0 \)
\( x_{1} x_{2} x_{3} (1 - x_{4} )x_{5} \) \( \alpha_{12} + \alpha_{123} + \alpha_{125} + \alpha_{1235} \ge 0 \)
\( x_{1} x_{2} (1 - x_{3} )x_{4} x_{5} \) \( \alpha_{12} + \alpha_{124} + \alpha_{125} + \alpha_{1245} \ge 0 \)
\( x_{1} x_{2} x_{3} (1 - x_{4} )(1 - x_{5} ) \) \( \alpha_{12} + \alpha_{123} \ge 0 \)
\( x_{1} x_{2} (1 - x_{3} )x_{4} (1 - x_{5} ) \) \( \alpha_{12} + \alpha_{124} \ge 0 \)
\( x_{1} x_{2} (1 - x_{3} )(1 - x_{4} )x_{5} \) \( \alpha_{12} + \alpha_{125} \ge 0 \)
\( x_{1} x_{2} (1 - x_{3} )(1 - x_{4} )(1 - x_{5} ) \) \( \alpha_{12} \ge 0 \)