Order of transitions in model specification

[andkov]

Workshop slides

Using example from workshop slides ( ss. 60-61)

The logic of the above ordering is as follows:

List only legal components of transitions, start with the first category. For each category, first list OUTGOING transition, then INCOMING transitions. Do not repeat components. Sort by ascending.

Specific steps

1. FROM category 1 (q12 and q15)
2. INTO category 1 ( q21)
3. FROM category 2 (q23, q25)
4. INTO category 2 (q32)
5. FROM category 3 ( q34, q35)
6. INTO category 3 (q43)
7. FROM category 4(q45)

   Vignette

Using the examples I from the ELECT vignette, the order of the transition components is specified as follows:

Example I

qnames <- c("q12","q13","q21","q23")

In case of 4 categories, the logic of ordering the transition components into model specification can be summarized as:

List only legal components of transitions, start with the first category. For each category, first list OUTGOING transition, then INCOMING transitions. Do not repeat components. Sort by ascending.

Application to current case

4-category case: A

qnames <- c("q12", "q13","q14","q21", "q23", "q24","q32", "q34")

4-category case: B

qnames <- c("q12", "q13","q14","q21", "q31", "q23", "q24","q32", "q34")

[andkov]

@GracielaMuniz , @ivacukic , @jochinho does this logic agree with your notes/understanding of the process?

[andkov]

There are three alternative formulation to express the same algorithm:

1. For those transitions r -> s in the model (as defined by the Q matrix), the presentation order is (r,s) starting with the lowest possible r and then moving on with the second entry s changing from low to highest before moving to the next candidate for r."
2. For each category, first list OUTCOMING following by INCOMING entries, without repeats in ascending order.
3. "[List all legal] off-diagonal entries of the Q matrix across the rows from left to right [from top to bottom]."