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Table 2 Summary of parameter estimates obtained after multiple imputation of simulated missing data

From: Estimating range of influence in case of missing spatial data: a simulation study on binary data

Data 1 N Intercept (SD) RMeSE 2 Covariate 3 (SD) RMeSE 2 σ 2 (SD) RMeSE 2 Range 4 (SD) RMeSE 1
MCAR          
5% 998 -4.3 (0.32) 0.046 0.62 (0.053) 0.0095 0.49 (0.22) 0.031 13.2 (5.3) 1.0
10% 998 -4.3 (0.33) 0.071 0.62 (0.055) 0.015 0.49 (0.23) 0.042 13.4 (5.5) 1.4
15% 998 -4.3 (0.33) 0.090 0.62 (0.057) 0.019 0.48 (0.23) 0.055 13.3 (5.8) 1.6
25% 997 -4.3 (0.35) 0.12 0.63 (0.060) 0.025 0.46 (0.24) 0.077 13.2 (6.0) 2.1
50%5 924 -4.3 (0.38) 0.22 0.62 (0.066) 0.042 0.40 (0.28) 0.13 15.1 (9.2) 3.6
75%5 571 -4.2 (0.39) 0.37 0.62 (0.069) 0.069 0.44 (0.38) 0.18 15.2 (15.0) 4.2
MAR0 OR=1/3          
5% 1000 -4.3 (0.32) 0.054 0.62 (0.053) 0.012 0.49 (0.22) 0.038 13.4 (5.4) 1.3
10% 1000 -4.3 (0.33) 0.091 0.64 (0.056) 0.021 0.47 (0.22) 0.047 13.1 (5.4) 1.3
15% 1000 -4.3 (0.33) 0.10 0.64 (0.057) 0.022 0.46 (0.23) 0.058 13.1 (5.6) 1.5
25% 1000 -4.3 (0.35) 0.13 0.64 (0.060) 0.026 0.46 (0.24) 0.064 13.9 (6.4) 2.4
50%5 990 -4.3 (0.37) 0.20 0.65 (0.064) 0.041 0.42 (0.25) 0.10 14.1 (7.4) 2.7
75%5 846 -4.3 (0.39) 0.31 0.65 (0.068) 0.060 0.41 (0.30) 0.14 15.0 (9.9) 3.6
MAR0 OR=3          
5% 1000 -4.1 (0.33) 0.17 0.58 (0.056) 0.047 0.46 (0.24) 0.067 14.7 (6.7) 2.3
10% 1000 -4.2 (0.33) 0.084 0.61 (0.056) 0.018 0.47 (0.23) 0.051 13.5 (5.9) 1.6
15% 1000 -4.3 (0.33) 0.10 0.62 (0.057) 0.021 0.46 (0.25) 0.076 13.4 (6.2) 1.5
25% 986 -4.2 (0.34) 0.13 0.61 (0.059) 0.027 0.41 (0.27) 0.11 14.5 (7.3) 2.7
50%5 821 -4.0 (0.35) 0.25 0.58 (0.063) 0.047 0.36 (0.29) 0.15 14.9 (11.0) 3.8
75%5 536 -4.0 (0.37) 0.32 0.58 (0.067) 0.069 0.44 (0.52) 0.19 16.1 (20.3) 4.6
MAR1 OR=1/3          
5% 1000 -4.8 (0.34) 0.48 0.72 (0.059) 0.096 0.50 (0.23) 0.033 12.6 (5.0) 1.1
10% 1000 -4.9 (0.38) 0.61 0.75 (0.065) 0.12 0.51 (0.24) 0.041 12.4 (5.1) 1.2
15% 1000 -5.1 (0.38) 0.85 0.79 (0.066) 0.17 0.52 (0.25) 0.052 12.1 (5.0) 1.5
25% 1000 -5.4 (0.40) 1.08 0.84 (0.071) 0.22 0.53 (0.26) 0.060 11.2 (4.7) 1.9
50%5 1000 -5.6 (0.45) 1.30 0.88 (0.080) 0.26 0.54 (0.29) 0.081 10.5 (4.6) 2.5
75%5 995 -5.8 (0.51) 1.52 0.93 (0.090) 0.30 0.52 (0.32) 0.093 10.5 (5.2) 2.8
MAR1 OR=3          
5% 1000 -4.1 (0.33) 0.17 0.57 (0.055) 0.051 0.46 (0.24) 0.069 14.5 (6.7) 2.4
10% 990 -4.0 (0.33) 0.28 0.54 (0.057) 0.079 0.43 (0.25) 0.087 15.4 (8.0) 2.9
15% 934 -3.9 (0.33) 0.39 0.52 (0.058) 0.10 0.42 (0.26) 0.10 15.8 (8.7) 3.4
25% 880 -3.7 (0.34) 0.54 0.45 (0.058) 0.17 0.44 (0.30) 0.10 14.6 (8.0) 2.8
50%5 644 -3.4 (0.34) 0.85 0.36 (0.059) 0.26 0.46 (0.35) 0.14 15.7 (11.2) 3.7
75%5 566 -3.1 (0.33) 1.18 0.25 (0.062) 0.37 0.57 (0.50) 0.16 13.6 (12.6) 3.6
MNAR OR=1/3          
5% 1000 -4.2 (0.31) 0.064 0.62 (0.052) 0.0087 0.49 (0.22) 0.026 13.2 (5.3) 0.9
10% 1000 -4.2 (0.32) 0.092 0.62 (0.053) 0.011 0.49 (0.22) 0.038 13.3 (5.3) 1.2
15% 1000 -4.1 (0.32) 0.17 0.62 (0.054) 0.015 0.48 (0.22) 0.045 13.4 (5.6) 1.4
25% 1000 -4.1 (0.33) 0.22 0.62 (0.056) 0.018 0.46 (0.23) 0.064 13.7 (6.0) 1.8
50%5 972 -3.7 (0.33) 0.62 0.60 (0.057) 0.033 0.40 (0.23) 0.12 14.7 (7.3) 2.8
75%5 727 -3.3 (0.34) 0.98 0.59 (0.061) 0.051 0.34 (0.24) 0.18 15.4 (10.1) 3.9
MNAR OR=3          
5% 1000 -4.4 (0.32) 0.097 0.63 (0.055) 0.014 0.47 (0.22) 0.045 13.0 (5.3) 1.3
10% 1000 -4.5 (0.34) 0.18 0.63 (0.056) 0.023 0.49 (0.24) 0.057 13.6 (5.9) 1.8
15% 1000 -4.5 (0.40) 0.26 0.63 (0.061) 0.028 0.47 (0.25) 0.074 13.6 (6.3) 2.3
25% 983 -4.7 (0.40) 0.39 0.64 (0.067) 0.040 0.45 (0.29) 0.11 13.3 (7.0) 3.0
50%5 727 -5.0 (0.45) 0.46 0.64 (0.080) 0.046 0.50 (0.46) 0.14 13.9 (11.8) 3.6
75%5 485 -5.3 (0.55) 0.98 0.63 (0.096) 0.10 1.16 (5.5) 0.67 15.9 (27.3) 4.5
  1. 1Simulation scenarios described in the Methods section.
  2. 2Square root of the median of (est. incomplete data - est. complete data) 2.
  3. 3log(Herd size).
  4. 4Range of influence in km.
  5. 5Precision of prior distribution of hyperpar. changed from 0.001 to 0.1.
  6. All results are medians of N data sets.