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Table 6 Best walking 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) 74.11 2.50 69.21–79.01 29.66 < 0.001 99.44 5.21 89.23–109.66 19.08 < 0.001
Poverty 102.20 8.56 85.43–118.98 11.94 < 0.001 203.81 10.07 184.07–223.54 20.24 < 0.001
Population Density − 261.91 8.68 − 278.93 –− 244.90 −30.17 < 0.001 − 288.61 10.18 − 308.56 –− 268.66 −28.35 < 0.001
Interaction − 628.20 39.88 − 706.36 –− 550.04 −15.75 < 0.001 − 725.85 46.34 − 816.67 –− 635.03 −15.66 < 0.001
Random Effects
σ2 2532.11 3345.50
τ00 59.85 SubRegion 286.93 SubRegion
ICC 0.02 0.08
MAE 33.71 43.97
RMSE 48.76 58.96
R2 0.45 0.45
  Health Center IV General Hospital
  Estimate SE CI t p Estimate SE CI t p
(Intercept) 198.92 7.25 184.71–213.13 27.44 < 0.001 357.85 17.55 323.46–392.24 20.39 < 0.001
Poverty 282.95 16.53 250.56–315.34 17.12 < 0.001 485.22 30.37 425.71–544.74 15.98 < 0.001
Population Density − 431.04 16.72 − 463.80 – − 398.28 −25.79 < 0.001 − 523.27 30.13 − 582.32 – − 464.22 −17.37 < 0.001
Interaction − 403.72 76.22 − 553.12 –− 254.32 −5.30 < 0.001      
Random Effects
σ2 9087.88 30,371.98
τ00 545.83 SubRegion 3289.19 SubRegion
ICC 0.06 0.1
MAE 75.86 134.15
RMSE 97.89 172.46
R2 0.39 0.26
  Regional Referral Hospital National Referral Hospital
  Estimate SE CI t p Estimate SE CI t p
(Intercept) 726.66 32.19 663.56–789.76 22.57 < 0.001 2806.11 326.60 2165.99–3446.23 8.59 < 0.001
Poverty       770.02 94.14 585.50–954.53 8.18 < 0.001
Population Density − 1593.59 51.83 − 1695.18 –− 1492.00 −30.74 < 0.001 − 821.41 95.07 − 1007.74 –−635.07 −8.64 < 0.001
Interaction       1689.33 430.99 844.59–2534.06 3.92 < 0.001
Random Effects
σ2 100,144.94 286,676.04
τ00 11,077.07 SubRegion 1,172,295.43 SubRegion
ICC 0.1 0.8
MAE 237.56 432.30
RMSE 310.62 557.29
R2 0.35 0.83