In sae4health: Small Area Estimation for Key Health and Demographic Indicators from Household Surveys

Unit-level (Cluster-level) Model

Unit-level models assume smoothing models for counts of events in each cluster (Wakefield, Okonek, and Pedersen 2020; Li et al. 2020). In terms of traditional Small Area Estimation literature, cluster-level models are a type of unit-level model. Currently, the app implements an unstratified model without taking into account the urban/rural stratification in the sampling design.

Let $Y_c$ be the number of events in cluster $c$, and $n_c$ be the number of individuals at risk, where $c= 1,\dots,C$. The unstratified model assumes the hierarchical structure:

$$Y_c \mid p_c,d\sim \textrm{BetaBinomial}(n_c,p_c,d),$$ $$p_c=\textrm{expit}(\alpha+e_{i[s_c]}+S_{i[s_c]}),$$

where $\alpha$ is the intercept, and $i[s_c]$ indexes the area within which the cluster $s_c$ resides. Similar to the area-level model, $e_i$ and $S_i$ are unstructured and structured spatial random effects with the same prior as before. The Beta-binomial distribution arise from a hierarchical model where the probability follows a $\text{Beta}(a, b)$ prior. The overdispersion parameter, $d=\frac{1}{\alpha+\beta+1}$, is between 0 and 1 and represent the the intracluster correlation between Bernoulli draws within cluster. The default prior for $d$ is $\text{logit}(d) \sim \text{Normal}(0,0.4)$.

The app implements the unit-level model via surveyPrev::clusterModel() function, with BYM2 model for the spatial random effects. The app currently only supports unstratified models. Please refer to surveyPrev package for stratified unit-level model.

sae4health documentation built on June 8, 2025, 10:43 a.m.