Sequence analysis is a form of association analysis where the items in an association rule have a time ordering. When you specify sequencecolumn, the association function performs sequence analysis. The function assumes items in the antecedent occurred before items in the consequent.
If relaxedordering=false (the default), the function assumes items in the antecedent and consequent are also time-ordered. That is, X1 occurred before X2, and so on, and Y1 occurred before Y2, and so on.
If relaxedordering=true, the function does not assume items in the antecedent and consequent are time-ordered. Relaxed ordering is appropriate when strictly ordered items are undesirable or impossible (for example, when customers purchased multiple items on the same day). In the Results Data, rules are ordered by name, for convenience.
The formulas for Lift and Z-score in Association Rule Measures use an Expected Value that does not account for ordered items. With n items in the antecedent and m in the consequent, the probability of correct ordering is n!m!/(n + m)!, regardless of the value of relaxedordering. This formula is the inverse of the combinatorial analysis formula for the number of permutations of n + m objects grouped such that n are alike and m are alike.
For strictly ordered sequence analysis, the rule has n + m objects. Saying that n are alike and m are alike corresponds to restricting the permutations to those that preserve the ordering of the n items in the antecedent and m in the consequent. That is, in both the antecedent and consequent, orderings other than the correct ordering are considered the same permutation. Because Lift is divided by the Expected Value, a factor of one half doubles Lift and increases Z-score.
Interpret the Lift and Z-score for sequence analysis cautiously, because the assumptions in calculating the independent probability of correct ordering are quite broad. For example, the function assumes that all combinations of ordering are equally likely to occur, and ignores time between occurrences.
For more control over the calculation of Lift and Z-score in sequence analysis, set orderingprobability to a constant. To ignore the probability of correct ordering in Lift and Z-score calculations, use orderingprobability=1.