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Table 4 Test for differential response by gender

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

  Less than primary education Primary education completed
  North East South West North East South West
Rural         
Log likelihood: Female -2810.45 -2102.21 -1320.54 -801.73 -79.89 -56.35 -169.58 -18.70
Log likelihood: Male -2459.77 -1874.81 -947.86 -598.91 -391.29 -471.61 -387.01 -125.49
Log likelihood sum (unrestricted model, L U) -5270.22 -3977.02 -2268.41 -1400.64 -471.18 -527.96 -556.59 -144.19
Log likelihood restricted model (L R) -5275.57 -3982.81 -2271.41 -1404.48 -474.22 -543.43 -558.48 -148.23
X 2 -first stage test statistic: -2*( L R-L U) 10.70 11.59 6.01 7.68 6.08 30.95 3.78 8.09
Sample size 7185 4827 3113 2034 619 685 736 219
P- value (8 degrees of freedom) 1 0.22 0.17 0.65 0.47 0.64 0.0001 0.88 0.43
Log likelihood partially-restricted model (L ) n.a. n.a. n.a. n.a. n.a. -535.07 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. 14.22 n.a. n.a.
P- value (2 degrees of freedom) 2 n.a. n.a. n.a. n.a. n.a. 0.001 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. 16.74 n.a. n.a.
P- value (6 degrees of freedom) 3 n.a. n.a. n.a. n.a. n.a. 0.010 n.a. n.a.
Urban         
Log likelihood: Female -1183.61 -801.69 -876.94 -551.19 -307.07 -291.29 -329.00 -330.72
Log likelihood: Male -561.68 -377.78 -394.38 -228.74 -762.63 -600.70 -661.10 -586.81
Log likelihood sum (unrestricted model, L U) -1745.30 -1179.47 -1271.32 -779.93 -1069.69 -891.99 -990.10 -917.53
Log likelihood restricted model (L R) -1746.76 -1183.38 -1283.50 -784.23 -1071.20 -895.77 -993.93 -919.59
X 2 -first stage test statistic: -2*( L R-L U) 2.92 7.83 24.37 8.58 3.01 7.57 7.67 4.13
Sample size 2406 1439 1866 1143 1471 1066 1474 1176
P- value (8 degrees of freedom) 1 0.94 0.45 0.002 0.38 0.93 0.48 0.47 0.85
Log likelihood partially-restricted model (L ) n.a. n.a. -1272.32 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. 2.00 n.a. n.a. n.a. n.a. n.a.
P- value (2 degrees of freedom) 2 n.a. n.a. 0.368 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. 22.37 n.a. n.a. n.a. n.a. n.a.
P- value (6 degrees of freedom) 3 n.a. n.a. 0.0010 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).