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If I have two sequences:

1: A-B-C-D
1: X-A-B-C-D

and I do:

library(TraMineR)
seqdist(sequence1, sequence2, method = "OM")

Will it then compare position 1, 2, 3, 4, 5 (in the 2nd sequence) and show that each position needs to be replaced, or is it smart enough to just insert the X at the front of the 1st sequence, and then shift the other markers so as to make the two sequences equal (aligned)?

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Yes, this is the whole advantage of optimal matching over Hamming distance. You can check it like this

library(TraMineR) 
myseq <- seqdef(c("a-b-c-d", "x-a-b-c-d"))
seqdist(myseq, method="OM", sm="CONSTANT")

The resulting distance is one, because it only insert x at the front and then shift the rest of the sequence.

If you use

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