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Table 6 Test for differential response by sector

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
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, L U) -3021.45 -2252.59 -1342.24 -827.65 -1153.92 -1072.30 -1048.11 -712.29
Log likelihood restricted model (L R) -3025.87 -2256.75 -1347.63 -833.03 -1155.66 -1081.02 -1050.42 -716.86
X 2 -first stage test statistic: -2*( L R-L U) 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 (L ) n.a. n.a. n.a. n.a. n.a. -1072.72 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. 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.
X 2-test statistic for g (.) function: -2*( L R-L ) 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, L U) -3994.06 -2903.90 -2197.49 -1352.93 -386.96 -347.64 -498.58 -349.42
Log likelihood restricted model (L R) -3998.27 -2911.38 -2210.64 -1360.39 -391.51 -365.76 -503.08 -354.41
X 2 -first stage test statistic: -2*( L R-L U) 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 (L ) n.a. n.a. -2205.52 n.a. n.a. -355.21 n.a. n.a.
X 2-test statistic for cut-point shift: -2*( L -L U) 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.
X 2-test statistic for g (.) function: -2*( L R-L ) 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.
  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).