Table 5. Estimation of available ARIMAX models for each series.
| Syphilis | Model | Covariates | AIC | AICC | SBC |
|---|---|---|---|---|---|
| Primary | ARIMAX(0,0,0)×(0,0,0) | Secondary, Tertiary, Latent, Secondary*Tertiary | -451.83 | -451.32 | -442.1 |
| ARIMAX(1,0,0)×(0,0,0) | Secondary, Tertiary, Latent, Secondary*Tertiary | -469.62 | -468.85 | -457.47 | |
| ARIMAX(0,0,1)×(0,0,0) | Secondary, Tertiary, Latent, Secondary*Tertiary | -461.87 | -461.1 | -449.72 | |
| ARIMAX(0,0,1)×(1,0,0) | Secondary, Tertiary, Latent, Secondary*Tertiary | -472.02 | -470.93 | -457.43 | |
| ARIMAX(1,0,0)×(0,0,1) | Secondary, Tertiary, Latent, Secondary*Tertiary | -470.54 | -469.45 | -455.95 | |
| ARIMAX(0,0,0)×(1,0,1) | Secondary, Tertiary, Latent, Secondary*Tertiary | -470.54 | -469.45 | -455.95 | |
| ARIMAX(1,0,0)×(1,0,1) | Secondary, Tertiary, Latent, Secondary*Tertiary | -471.67 | -470.2 | -454.65 | |
| Secondary | ARIMAX(0,0,0)×(0,0,0) | Primary, Latent, Primary*Latent | -346.31 | -346.01 | -339.02 |
| ARIMAX(1,0,0)×(0,0,0) | Primary, Latent, Primary*Latent | -376.06 | -375.55 | -366.34 | |
| ARIMAX(0,0,1)×(0,0,0) | Primary, Latent, Primary*Latent | -376.23 | -375.73 | -366.51 | |
| ARIMAX(1,0,0)×(1,0,0) | Primary, Latent, Primary*Latent | -447.15 | -446.38 | -435 | |
| ARIMAX(1,0,1)×(0,0,0) | Primary, Latent, Primary*Latent | -381.75 | -380.98 | -396.6 | |
| ARIMAX(,0,1)×(0,0,1) | Primary, Latent, Primary*Latent | -401.33 | -400.56 | -389.17 | |
| ARIMAX(1,0,0)×(0,0,1) | Primary, Latent, Primary*Latent | -402.89 | -402.12 | -390.74 | |
| ARIMAX(0,0,1)×(1,0,0) | Primary, Latent, Primary*Latent | -441.6 | -440.83 | -429.44 | |
| Tertiary | ARIMAX(0,0,0)×(0,0,0) | Primary, Latent | -892.12 | -891.97 | -887.26 |
| ARIMAX(1,0,0)×(0,0,0) | Primary, Latent | -900.95 | -900.65 | -893.66 | |
| ARIMAX(1,0,(3))×(0,0,0) | Primary, Latent | -902.55 | -902.04 | -892.83 | |
| ARIMAX(0,0,(3))×(0,0,0) | Primary, Latent | -897.93 | -897.63 | -890.64 | |
| ARIMAX(0,0,1)×(0,0,0) | Primary, Latent | -897.57 | -897.27 | -890.27 | |
| Latent | ARIMAX(0,0,0)×(0,0,0) | Primary, Secondary, Tertiary, Congenital, Primary*Secondary, Secondary*Congenital, Tertiary*Congential | -284.93 | -283.46 | -267.91 |
| ARIMAX(0,0,1)×(0,0,0) | Primary, Secondary, Tertiary, Congenital, Primary*Secondary, Secondary*Congenital, Tertiary*Congential | -283.52 | -281.6 | -264.08 | |
| ARIMAX(0,0,0)×(1,0,0) | Primary, Secondary, Tertiary, Congenital, Primary*Secondary, Secondary*Congenital, Tertiary*Congential | -253.77 | -251.85 | -234.32 | |
| ARIMAX(0,0,0)×(1,0,0) | Primary, Secondary, Tertiary, Congenital, Primary*Secondary, Secondary*Congenital, Tertiary*Congential | -348.89 | -346.97 | -327.01 | |
| ARIMAX(0,0,0)×(0,0,1) | Primary, Secondary, Tertiary, Congenital, Primary*Secondary, Secondary*Congenital, Tertiary*Congential | -304.83 | -302.91 | -285.39 | |
| Congenital | ARIMAX(0,0,0)×(0,0,0) | Primary,Secondary, Latent, Secondary*Latent | -672.88 | -672.37 | -663.25 |
| ARIMAX(0,0,1)×(0,0,0) | Primary,Secondary, Latent, Secondary*Latent | -682.67 | -681.9 | -670.63 | |
| ARIMAX(0,0,1)×(0,0,1) | Primary,Secondary, Latent, Secondary*Latent | -691.42 | -690.33 | -676.98 | |
| ARIMAX(1,0,0)×(0,0,1) | Primary,Secondary, Latent, Secondary*Latent | -695.71 | -694.62 | -681.27 | |
| ARIMAX(0,0,1)×(1,0,0) | Primary,Secondary, Latent, Secondary*Latent | -692.54 | -691.45 | -678.1 |
Note:
* means the interaction term. The final ARIMAX model selected is highlighted in bold.