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Table 5 Test for differential response by education

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

  Rural Urban
  North East South West North East South West
Males         
Log likelihood: <primary -2459.77 -1874.81 -947.86 -598.54 -561.68 -377.78 -394.38 -228.74
Log likelihood: primary+ -391.29 -471.61 -387.01 -125.45 -762.63 -600.70 -661.10 -586.81
Log likelihood sum (unrestricted model, L U) -2851.06 -2346.41 -1334.88 -723.99 -1324.31 -978.48 -1055.47 -815.55
Log likelihood restricted model (L R) -2856.40 -2350.25 -1338.57 -729.46 -1325.46 -986.37 -1060.74 -817.75
X 2 -first stage test statistic: -2*( L R-L U) 10.67 7.68 7.39 10.94 2.29 15.77 10.53 4.41
Sample size 3793 2820 1832 1032 1820 1199 1499 1054
P- value (8 degrees of freedom) 1 0.22 0.47 0.50 0.21 0.97 0.05 0.23 0.82
Log likelihood partially-restricted model (L ) n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.
X 2-test statistic for cut-point shift: -2*( L -L U) n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.
P- value (2 degrees of freedom) 2 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.
X 2-test statistic for g (.) function: -2*( L R-L ) n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.
P- value (6 degrees of freedom) 3 n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a.
Females         
Log likelihood: <primary -2810.45 -2102.21 -1320.54 -801.73 -1183.61 -801.69 -876.94 -551.19
Log likelihood: primary+ -79.89 -56.35 -169.58 -18.70 -307.07 -291.29 -329.00 -330.72
Log likelihood sum (unrestricted model, L U) -2890.34 -2158.56 -1490.12 -820.43 -1490.68 -1092.98 -1205.94 -881.91
Log likelihood restricted model (L R) -2893.46 -2175.41 -1495.02 -825.57 -1494.84 -1098.79 -1213.65 -884.54
X 2 -first stage test statistic: -2*( L R-L U) 6.23 33.69 9.81 10.27 8.32 11.63 15.42 5.24
Sample size 4011 2692 2017 1221 2057 1306 1841 1265
P- value (8 degrees of freedom) 1 0.62 4.6 × 10-5 0.28 0.25 0.40 0.17 0.05 0.73
Log likelihood partially-restricted model (L ) n.a. -2167.19 n.a. n.a. n.a. n.a. n.a. n.a.
X 2-test statistic for cut-point shift: -2*( L -L U) n.a. 17.26 n.a. n.a. n.a. n.a. n.a. n.a.
P- value (2 degrees of freedom) 2 n.a. 0.0002 n.a. n.a. n.a. n.a. n.a. n.a.
X 2-test statistic for g (.) function: -2*( L R-L ) n.a. 16.43 n.a. n.a. n.a. n.a. n.a. n.a.
P- value (6 degrees of freedom) 3 n.a. 0.012 n.a. n.a. n.a. n.a. n.a. n.a.
  1. 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. 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. 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).