Table 6.
Test for differential response by sector
| Less than primary education | Primary education completed | |||||||
|---|---|---|---|---|---|---|---|---|
| North | East | South | West | North | East | South | West | |
| Males | ||||||||
| Log likelihood: rural | -2459.77 | -1874.81 | -947.86 | -598.91 | -391.29 | -471.61 | -387.01 | -125.49 |
| Log likelihood: urban | -561.68 | -377.78 | -394.38 | -228.74 | -762.63 | -600.70 | -661.10 | -586.81 |
| Log likelihood sum (unrestricted model, LU) | -3021.45 | -2252.59 | -1342.24 | -827.65 | -1153.92 | -1072.30 | -1048.11 | -712.29 |
| Log likelihood restricted model (LR) | -3025.87 | -2256.75 | -1347.63 | -833.03 | -1155.66 | -1081.02 | -1050.42 | -716.86 |
| X2-first stage test statistic: -2*( LR-LU) | 8.83 | 8.32 | 10.78 | 10.74 | 3.49 | 17.43 | 4.63 | 9.14 |
| Sample size | 4069 | 2713 | 1888 | 1168 | 1544 | 1306 | 1443 | 918 |
| P-value (8 degrees of freedom)1 | 0.36 | 0.40 | 0.21 | 0.22 | 0.90 | 0.03 | 0.80 | 0.33 |
| Log likelihood partially-restricted model (LRα) | n.a. | n.a. | n.a. | n.a. | n.a. | -1072.72 | n.a. | n.a. |
| X2-test statistic for cut-point shift: -2*( LRα-LU) | n.a. | n.a. | n.a. | n.a. | n.a. | 0.84 | n.a. | n.a. |
| P-value (2 degrees of freedom)2 | n.a. | n.a. | n.a. | n.a. | n.a. | 0.659 | n.a. | n.a. |
| X2-test statistic for g (.) function: -2*( LR-LRα) | n.a. | n.a. | n.a. | n.a. | n.a. | 16.59 | n.a. | n.a. |
| P-value (6 degrees of freedom)3 | n.a. | n.a. | n.a. | n.a. | n.a. | 0.011 | n.a. | n.a. |
| Females | ||||||||
| Log likelihood: rural | -2810.45 | -2102.21 | -1320.54 | -801.73 | -79.89 | -56.35 | -169.58 | -18.70 |
| Log likelihood: urban | -1183.61 | -801.69 | -876.94 | -551.19 | -307.07 | -291.29 | -329.00 | -330.72 |
| Log likelihood sum (unrestricted model, LU) | -3994.06 | -2903.90 | -2197.49 | -1352.93 | -386.96 | -347.64 | -498.58 | -349.42 |
| Log likelihood restricted model (LR) | -3998.27 | -2911.38 | -2210.64 | -1360.39 | -391.51 | -365.76 | -503.08 | -354.41 |
| X2-first stage test statistic: -2*( LR-LU) | 8.42 | 14.97 | 26.32 | 14.93 | 9.09 | 36.24 | 9.00 | 9.98 |
| Sample size | 5522 | 3553 | 3091 | 2009 | 546 | 445 | 767 | 477 |
| P-value (8 degrees of freedom)1 | 0.39 | 0.06 | 9.27 × 10-04 | 0.06 | 0.33 | 1.59 × 10-05 | 0.34 | 0.27 |
| Log likelihood partially-restricted model (LRα) | n.a. | n.a. | -2205.52 | n.a. | n.a. | -355.21 | n.a. | n.a. |
| X2-test statistic for cut-point shift: -2*( LRα-LU) | n.a. | n.a. | 16.08 | n.a. | n.a. | 15.14 | n.a. | n.a. |
| P-value (2 degrees of freedom)2 | n.a. | n.a. | 0.0003 | n.a. | n.a. | 0.0005 | n.a. | n.a. |
| X2-test statistic for g (.) function: -2*( LR-LRα) | n.a. | n.a. | 10.24 | n.a. | n.a. | 21.10 | n.a. | n.a. |
| P-value (6 degrees of freedom)3 | n.a. | n.a. | 0.115 | n.a. | n.a. | 0.002 | n.a. | n.a. |
16 parameters for Ho (α) and 3 cut-points (τ) were estimated the unrestricted model for two subgroups (9 × 2 = 18); 6 parameters for Ho (α), 1 parameters for membership (θ) and 3 cut-points (τ) were estimated for the restricted model. The degree of freedom is equal to the difference in the number of estimated parameters between these two models (18-10 = 8).
2 16 parameters, including 6 parameters for Ho (α) for the two subgroups (6 × 2 = 12), 1 parameters for membership (θ) and 3 cut-points (τ) were estimated for the partially-restricted model. The degree of freedom is equal to the difference of number of estimated parameters between unrestricted and partially-restricted models (18-16 = 2).
3 The degree of freedom is equal to the difference of number of estimated parameters between partially-restricted models and restricted models (16-10 = 6).