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Table 7 Best bicycle-difference scenario mixed-effects models for each health unit level. Beta coefficient estimate (Estimate), Standard Error (SE), Confidence Interval (CI), t-statistic (t), and p-value (p) reported for each fixed effect. Variance (σ2), between subject variance (τ00), and interclass correlation coefficient (ICC) reported for random effects of each model. Mean Average Error (MAE) and Root Mean Square Error (RMSE) reported as prediction accuracy assessments for each model

From: Exploring country-wide equitable government health care facility access in Uganda

  Health Center II Health Center III
Estimate SE CI t p Estimate SE CI t p
(Intercept) −55.42 3.35 −61.99 –−48.86 −16.54 < 0.001 −40.55 2.64 −45.72 –−35.38 −15.38 < 0.001
Poverty − 101.74 5.83 − 113.17 –−90.31 −17.44 < 0.001 −84.59 4.54 −93.48 –−75.69 −18.64 < 0.001
Population Density 95.74 5.89 84.19–107.30 16.24 < 0.001 91.61 4.59 82.62–100.60 19.97 < 0.001
Interaction 188.73 26.81 136.18–241.29 7.04 < 0.001 221.43 20.86 180.54–262.32 10.61 < 0.001
Random Effects
σ2 1118.22 676.78
τ00 119.50 SubRegion 74.02 SubRegion
ICC 0.1 0.1
MAE 24.88 19.65
RMSE 34.22 26.21
R2 0.24 0.30
  Health Center IV General Hospital
  Estimate SE CI t p Estimate SE CI t p
(Intercept) −91.24 3.84 −98.76 – −83.71 −23.76 < 0.001 − 174.03 9.37 − 192.39 –− 155.67 −18.58 < 0.001
Poverty − 123.33 8.06 − 139.12 –−107.54 −15.31 < 0.001 − 228.60 15.24 − 258.47 –− 198.73 − 15.00 < 0.001
Population Density 151.75 8.00 136.08–167.43 18.97 < 0.001 194.28 15.40 164.09–224.47 12.61 < 0.001
Interaction       −330.01 70.03 − 467.27 –−192.75 −4.71 < 0.001
Random Effects
σ2 2153.57 7620.12
τ00 155.30 SubRegion 938.09 SubRegion
ICC 0.07 0.11
MAE 36.64 66.81
RMSE 46.68 86.18
R2 0.28 0.21
  Regional Referral Hospital National Referral Hospital
  Estimate SE CI t p Estimate SE CI t p
(Intercept) − 354.7 15.21 − 384.52 – − 324.89 −23.32 < 0.001 − 1427.98 163.75 − 1748.93 –− 1107.04 −8.72 < 0.001
Poverty       − 341.30 42.98 −425.53 –− 257.07 −7.94 < 0.001
Population Density 706.79 25.92 655.98–757.59 27.27 < 0.001 326.25 43.40 241.19–411.31 7.52 < 0.001
Interaction       − 1360.50 196.74 − 1746.12 –− 974.89 −6.92 < 0.001
Random Effects
σ2 25,098.17 59,736.23
τ00 2464.05 SubRegion 294,736.58 SubRegion
ICC 0.09 0.83
MAE 119.80 202.78
RMSE 155.26 253.47
R2 0.28 0.85