Table 2 Spatial Markov dynamic transformation probability matrix
Spatial lag term categories | \({}^{{t}_{i}}\!\left/ \!{}_{{t}_{i+1}}\right.\) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
\(\mathrm{I}\) | 1 | \({P}_{{}^{11}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{12}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{13}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{14}\!\left/ \!{}_{1}\right.}\) |
2 | \({P}_{{}^{21}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{22}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{23}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{24}\!\left/ \!{}_{1}\right.}\) | |
3 | \({P}_{{}^{31}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{32}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{33}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{34}\!\left/ \!{}_{1}\right.}\) | |
4 | \({P}_{{}^{41}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{42}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{43}\!\left/ \!{}_{1}\right.}\) | \({P}_{{}^{44}\!\left/ \!{}_{1}\right.}\) | |
\(\mathrm{II}\) | 1 | \({P}_{{}^{11}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{12}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{13}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{14}\!\left/ \!{}_{2}\right.}\) |
2 | \({P}_{{}^{21}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{22}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{23}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{24}\!\left/ \!{}_{2}\right.}\) | |
3 | \({P}_{{}^{31}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{32}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{33}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{34}\!\left/ \!{}_{2}\right.}\) | |
4 | \({P}_{{}^{41}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{42}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{43}\!\left/ \!{}_{2}\right.}\) | \({P}_{{}^{44}\!\left/ \!{}_{2}\right.}\) | |
\(\mathrm{III}\) | 1 | \({P}_{{}^{11}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{12}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{13}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{14}\!\left/ \!{}_{3}\right.}\) |
2 | \({P}_{{}^{21}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{22}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{23}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{24}\!\left/ \!{}_{3}\right.}\) | |
3 | \({P}_{{}^{31}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{32}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{33}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{34}\!\left/ \!{}_{3}\right.}\) | |
4 | \({P}_{{}^{41}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{42}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{43}\!\left/ \!{}_{3}\right.}\) | \({P}_{{}^{44}\!\left/ \!{}_{3}\right.}\) | |
\(\mathrm{IV}\) | 1 | \({P}_{{}^{11}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{12}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{13}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{14}\!\left/ \!{}_{4}\right.}\) |
2 | \({P}_{{}^{21}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{22}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{23}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{24}\!\left/ \!{}_{4}\right.}\) | |
3 | \({P}_{{}^{31}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{32}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{33}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{34}\!\left/ \!{}_{4}\right.}\) | |
4 | \({P}_{{}^{41}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{42}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{43}\!\left/ \!{}_{4}\right.}\) | \({P}_{{}^{44}\!\left/ \!{}_{4}\right.}\) |