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Table 3 Test for differential response by region of residence

From: Measuring the health of the Indian elderly: evidence from National Sample Survey data

H0 Males Females
  Rural Urban Rural Urban
  Less than primary education Primary education completed Less than primary education Primary education completed Less than primary education Primary education completed Less than primary education Primary education completed
Log likelihood: North -2459.77 -391.29 -561.68438 -762.63 -2810.45 -79.89 -1183.61 -307.07
Log likelihood: East -1874.81 -471.61 -377.78396 -600.70 -2102.21 -56.35 -801.69 -291.29
Log likelihood: South -947.86396 -387.01 -394.37561 -661.10 -1320.54 -169.58 -876.94 -329.00
Log likelihood: West -598.91288 -125.49 -228.73973 -586.81 -801.73 -18.70 -551.19 -330.72
Log likelihood sum (unrestricted model, L U) -5881.35 -1375.40 -1562.58 -2611.23 -7034.94 -324.52 -3413.43 -1258.08
Log likelihood restricted model (L R) -5910.92 -1390.14 -1577.21 -2639.0483 -7083.58 -347.71777 -3446.14 -1284.52
X 2 -first stage test statistic: -2*(L R-L U) 59.14 29.49 29.25 55.64 97.28 46.39 65.41 52.88
Sample size 7694 1783 2144 3428 9465 476 4710 1759
P- value (24 degrees of freedom) 1 8.4 × 10 -5 0.202 0.211 0.0003 8.5.8 × 10 -11 0.004 1.1 × 10 -5 0.0006
Log likelihood partially-restricted model (L ) -5898.58 n.a. n.a. -26.18.29 -7067.62 -330.00 -3431.05 -1269.87
X 2-test statistic for cut-point differences: -2*( L -L U) 34.46 n.a. n.a. 14.13 65.36 10.95 35.24 23.59
P- value (6 degrees of freedom) 2 5.5 × 10 -6 n.a. n.a. 0.028 3.7 × 10-12 0.090 3.9 × 10 -6 0.0006
X 2-test statistics for g (.): -2*( L R-L ) 24.68 n.a. n.a. 41.51 31.92 35.44 30.17 29.29
P- value (18 degrees of freedom) 3 0.134 n.a. n.a. 0.001 0.022 0.008 0.036 0.045
  1. 16 parameters for Ho (α) and 3 cut-points (τ) were estimated the unrestricted model for four subgroups (9 × 4 = 36); 6 parameters for Ho (α), 3 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 (36-12 = 24).
  2. 2 30 parameters, including 6 parameters for Ho (α) for the four subgroups (6 × 4 = 24), 3 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 (36-30 = 6).
  3. 3 The degree of freedom is equal to the difference of number of estimated parameters between partially-restricted models and restricted models (30-12 = 18).