Table 2.
Estimated posterior mean differences in mean Hb concentration for the effects of selected explanatory variables from a final Bayesian hierarchical model (n = 1523)
| Variable | Mean | 95% credible intervala |
|---|---|---|
| Fixed part of the model | ||
| Intercept | 12.520 | (12.280–12.760) |
| Sex (Reference category: ‘Male’) Female | −0.183 | (−0.330 to −0.036)b |
| Age (Reference category: ‘10–12 years old’) | ||
| 13–15 years old | 0.222 | (0.064–0.377)b |
| > = 16 years old | 0.417 | (0.012–0.832)b |
| Classification of BMIZ (Reference category:’ Not wasted’) Wasted | −0.244 | (−0.544 to 0.062) |
| Classification of HAZ (Reference category:’ Not stunted’) Stunted | −0.347 | (−0.564 to −0.128)b |
| Intensity of hookworm infection (Reference category: ‘Not Infected’) | ||
| Lightly infected | 0.050 | (−0.102 to 0.197) |
| Moderately infected | −0.310 | (−1.048 to 0.419) |
| Heavily infected | −0.516 | (−1.277 to 0.233) |
| Intensity of Schistosoma mansoni infection (Reference category: ‘Not Infected’) | ||
| Lightly infected | −0.113 | (−0.417 to 0.189) |
| Moderately infected | 0.068 | (−0.268 to 0.414) |
| Heavily infected | −0.513 | (−0.942 to −0.097)b |
| Intensity of Trichuris trichiura infection (Reference category: ‘Not Infected’) | ||
| Lightly infected | 0.105 | (−0.121 to 0.336) |
| Moderately infected | 0.834 | (−0.195 to 1.857) |
| Heavily infected | 0.110 | (−2.649 to 2.890) |
| Intensity of Ascaris lumbricoides infection (Reference category: ‘Not Infected’) | ||
| Lightly infected | −0.164 | (−0.372 to 0.047) |
| Moderately infected | −0.206 | (−0.480 to 0.073) |
| Malaria spp infection (Reference category: ‘Not Infected’) Infected | −0.159 | (−0.315 to −0.009)b |
| Random part of the model | ||
| Level-2 (i.e. between schools) variance | 0.225 | (0.114–0.413) |
| Level-1 (i.e. between children within a school) variance | 2.031 | (1.889–2.186) |
BMIZ, Body Mass Index Z-score; HAZ, Height for Age Z-score.
95% Credible intervals (CIs) are different from classical 95% confidence intervals in various ways, some of which are: (i) in their interpretation: we say there is a 95% probability that the true parameter lies in a 95% credible interval where this is certainly not the interpretation of a 95% confidence interval. In a long series of 95% confidence intervals, 95% of those should contain the true parameter value – unlike the Bayesian interpretation we cannot give a probability for whether a particular confidence interval contains the true value; and (ii) credible intervals will generally be narrower due to the additional information provided by the prior (Spiegelhalter et al., 2004).
These are significant differences compared with the reference category in the sense that the probability is at least 95% that these parameters lie within the credible interval, which is significant.