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  • Glossary

Earlier and Later

Assumptions made about artifacts earlier and later than those in the data can greatly influence the outcome of any seriation. Feature values for earlier artifacts are essentially blank and like Blanks and Zeroes it is not always obvious how to interpret them. For example, we could assume that earlier feature values are simply unknown, or we could assume that earlier artifacts do not exist (and their features are absent) or we could assume that earlier artifacts do exist but the feature is absent or its value is zero.

The assumption made can have a big impact on the seriation we get. For example, consider the assumption that a feature is present but its value is unknown for earlier artifacts. For a unimodal seriation a best seriation would preferably have all artifacts possessing the feature to occur consecutively at the very beginning of the seriation. Otherwise, there would be a break in the occurrence of the feature between an interval earlier than the seriated artifacts and the ones in the seriation possessing the feature.

Whatever conventions we are using, we need to let OptiPath know by setting the feature parameters Earlier and Later in the Features table. Right clicking on the column brings up a popup menu that allows you to set all features with one click.

There are six available settings for Earlier and Later.

Present & Zero - a zero value (0) will be interpreted to mean the feature is present but has a value of zero. A Present & Zero data entry will be included in the computation of the transition penalty, and will be included in the computation of the distance, between the item and its preceding or succeeding item in the seriation.

Absent & Zero - a zero value (0) will be interpreted to mean the feature is absent and has a value of zero. An Absent & Zero data entry will be included in the computation of the transition penalty, and will be included in the computation of the distance, between the item and its preceding or succeeding item in the seriation.

Present & Unknown - a zero value (0) will be interpreted to mean the feature is present but its value is unknown. A Present & Unknown data entry will be included in the computation of the transition penalty, but will not be included in the computation of the distance, between the item and its preceding or succeeding item in the seriation.

Absent & Unknown - a zero value (0) will be interpreted to mean the feature is absent and its value is unknown. An Absent & Unknown data entry will be included in the computation of the transition penalty, but will not be included in the computation of the distance, between the item and its preceding or succeeding item in the seriation.

Unknown & Zero - a zero value (0) will be interpreted to mean the presence or absence of the feature is unknown but its value is presumed to be zero. An Unknown & Zero data entry will not be included in the computation of the transition penalty, but will be included in the computation of the distance, between the item and its preceding or succeeding item in the seriation.

Unknown - a zero value (0) will be interpreted to mean the presence or absence of the feature is unknown and its value is unknown. An Unknown data entry will not be included in the computation of either the transition penalty or the distance between the item and its preceding or succeeding item in the seriation.

The settings made for Earlier and Later in the Features table will appear in the EARLIER and LATER rows of the Artifacts (Assemblages), Data and Results tables.

Each setting for Blanks and Zeroes can lead to different results in seriation. For more information see Setting the Earlier, Later, Blanks, Zeroes and Transition Parameters.

Presence is Known or Unknown

There is an important difference between a feature being absent and its presence being unknown. A presence followed by an absence, or vice versa, incurs a transition penalty. However, a presence or an absence followed by an unknown, or vice versa, does not incur a transition penalty. For example, in Table 1 below, each Item's number indicates its ordinal position in the seriation. In this case, a transition penalty would be incurred for Feature A between EARLIER and Item 1, but not for Features B, C or D. If Zeroes were set to Present & Zero or Present & Unknown for Feature E, then a transition penalty would be incurred; otherwise not. Similarly a transition penalty would be incurred for Feature A and C between Item 6 and LATER, but not for Features B, D or E.

Table 1	Feature A	Feature B	Feature C	Feature D	Feature E
EARLIER	Absent & Zero	Present & Zero	Unknown	Unknown & Zero	Absent & Unknown
Item 1	5	10	10	10	0
Item 2		17	17	17	17
Item 3	0		17	23	30
Item 4	7	17		30	39
Item 5	5	13	13	39	23
Item 6	21	4	4	10	0
LATER	Absent & Unknown	Present & Unknown	Absent & Unknown	Present & Zero	Unknown & Zero

Value is Zero or Unknown

There is also an important difference between a value of zero and an unknown value. If the value of EARLIER or LATER is unknown, OptiPath does not include it in computing distances, but if the value is zero the feature is included in the distance computation. For example, in Table 1, Features A, B and D will contribute to the distance between EARLIER and Item 1, but Feature C will not. Whether or not Feature E contributes to the distance calculation will depend upon the Zeroes setting for Feature E. Features D will contribute to the distance between Item 6 and LATER, but Features A, B and C will not. Whether or not Feature E contributes to the distance calculation will depend upon the Zeroes setting for Feature E.