Example Guttman Scale response patterns for one item over four visits.
Notes: 1 indicates the item was answered correctly; 0 indicates it was incorrect. Patterns in the first five rows are consistent with the Guttman scale. NB: the first and fifth patterns (1111, 0000) do not represent decline since individuals with either pattern of responses to this item over the four visits either always or never exhibited the ability to answer correctly (respectively). Both patterns are consistent with a Guttman Model because each shows the expected consistency in what an item reflects about the individual's state/ability.
*indicates one example pattern of the 11 other possible outcomes for one item over four visits; none of these other patterns is consistent with a Guttman Model since the item is shown to have been correct after not being correct at an earlier visit. There are a total of 16 (24) patterns of right (1) and wrong (0) responses on this item, but only the first five response patterns in this table represent error-free measurement of decline for the item. The proportion of the sample that does not exhibit one of these five patterns over four years is the estimated measurement error for the item.
