Example

The transitional frequency matrix#3452#> is a special form of contingency table. It has the general form given in table 3.1.

Table 3.1: General structure of a transitional frequency matrix

	$X(t+1)$
	1	2	...	m	total
$X(t)$ = 1	$n_{11}$	$n_{12}$	...	$n_{1m}$	$n_{1+}$
2	$n_{21}$	$n_{22}$	...	$n_{2m}$	$n_{2+}$
...	...	...	...	...	...
m	$n_{m1}$	$n_{m2}$	...	$n_{mm}$	$n_{m+}$
total	$n_{+1}$	$n_{+2}$	...	$n_{+m}$	$n_{++}$

For our subject example, where $m=6$, the empirical transitional frequency matrix#3453#> is displayed in table 3.2 (in bold are the highest frequencies for each row).

Table 3.2: Transition frequency matrix of stress

	$STRE(t+1)$
	1	2	3	4	5	6
$STRE(t)$ = 1	12	9	7	4	1
2	8	45	21	6	5	2
3	7	19	42	13	1	1
4	4	8	10	7	3	3
5	1	5	2	3	2	1
6	1	1	2	1	2	1

It should be noted that transitions are counted from state at time $t$ to state at time $t+1$. Why not counting from time $t-1$ to time $t$? With empirical data, depending on whether one looks forwards or backwards, an observation is missing respectively at the end or the beginning of the sequence. But since missing values are typically not accounted for, the two types of transitional matrices are equivalent.