In nmmarquez/PointPolygon: Evaluate Point and Polygon Data Simulatneously

knitr::opts_chunk$set(echo = FALSE, warning = FALSE, message = FALSE, fig.height=4, dev='svg')

library(ggplot2)
samplePlots <- readRDS(
    "~/Documents/PointPolygon/demo/plotsForPresent.Rds")

resultsPlotsDR <- readRDS(
    "~/Documents/PointPolygon/demo/aggplotsDR.Rds")

resultsPlots <- readRDS(
    "~/Documents/PointPolygon/demo/aggplots.Rds")

Background

• For countries without comprehensive Vital Registration data accurate use of survey data is essential for estimating child mortality
• Data come to us at different spatial resolutions and if we believe the true underlying data generating process is continuous then administrative data is problematic for traditional geospatial models
• How can we effectively/accurately incorporate different spatial resolution data into geospatial models

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Data Example

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Data Example

• Historically incomplete VR for child births and deaths
• Number of surveys on complete birth history (CBH)
• DHS 2007 & 2013: Complete Spatial information given for CBH
• MICS 2014: Cluster location removed for CBH know only up to stratification

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Previous Approaches

• Golding et al 2017 (Resampling)
  • Pros: Uses all available data, applicable for all contexts
  • Cons: May distort the estimation of spatial correlation
• Utazi et al 2018 (RHS Integration with ICAR)
  • Pros: Uses all available data, applicable for all contexts
  • Cons: Built in ecological fallacy and strange non linearity
• Wilson et al 2018 (MCMC in INLA)
  • Pros: Correctly captures the data generating process
  • Cons: Slow to implement and potential privacy issues
• No substantive cross comparison between models evaluating performance

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New Proposal: Mixture Model

$$Y_i \sim \text{Binomial}(p_{s_i, t_i}, N_i) \ \text{logit}(p_{s_i, t_i}) = \boldsymbol{\beta \cdot X_{s_i, t_i}} + \omega(s_i, t_i) \ \boldsymbol{\omega} \sim \mathcal{GP}(\boldsymbol{0}, \mathcal{M} \otimes\text{AR1}) \ \boldsymbol{\omega}~\dot \sim~ \text{GMRF}(\boldsymbol{0}, Q^\mathcal{M} \otimes Q^\text{AR1}) \ \kappa \sim \text{Log Normal}(0, 10) \ \tau \sim \text{Log Normal}(0, 10) \ \rho \sim \text{Logit Normal}(0, 10)$$

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New Proposal: Mixture Model

$$Y^\star_i ~\dot \sim ~ \begin{cases} \text{Binomial}(p_{s_{j_1}, t_i}, N_i) \times q_{s_{j_1}}\ \vdots \ \text{Binomial}(p_{s_{j_J}, t_i}, N_i) \times q_{s_{j_J}} \ \end{cases} \text{for } j \in \mathcal{A}i \ \text{logit}(p{s_j, t_i}) = \boldsymbol{\beta \cdot X_{s_j, t_i}} + \omega(s_j, t_i) \ \boldsymbol{\omega}~\dot \sim~ \text{GMRF}(\boldsymbol{0}, Q^\mathcal{M} \otimes Q^\text{AR1}) \ \kappa \sim \text{Log Normal}(0, 10) \ \tau \sim \text{Log Normal}(0, 10) \ \rho \sim \text{Logit Normal}(0, 10)$$

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New Proposal Alternative: Riemann

$$Y^\star_i ~\dot \sim ~ \text{Binomial}(\sum_{j \in \mathcal{A}} p_{s_{j}, t_i} \times q_{s_{j}, t_i}, N_i)\ \text{logit}(p_{s_j, t_i}) = \boldsymbol{\beta \cdot X_{s_j, t_i}} + \omega(s_j, t_i) \ \boldsymbol{\omega}~\dot \sim~ \text{GMRF}(\boldsymbol{0}, Q^\mathcal{M} \otimes Q^\text{AR1}) \ \kappa \sim \text{Log Normal}(0, 10) \ \tau \sim \text{Log Normal}(0, 10) \ \rho \sim \text{Logit Normal}(0, 10)$$

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Model Requirements

• Covariate space for entire area must be known
• Must have a good sampling frame of population for time of sample
  • If known use enumeration areas
  • Population Raster is sufficient
• Relatively Large RAM requirements

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Model Comparison Framework: Simulated Field and Sampling

• Simulate a 2D Matern covariance process GP as the spatial field (1x1 grid)
• Add in a covariate to the field which either is
  • Spatially clustered
  • Spatially correlated
  • At random
• Sample from the field with known location
• Sample from the field with unknown location up to a polygon

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Model Comparison Framework: Simulated Field

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Model Comparison Framework: Simulated Field Variation

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Model Comparison Framework: Sampling

samplePlots$mixPlot

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Model Comparison Framework: Sampling

samplePlots$ovPlot

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Model Comparison Framework: Candidate Models

• Mixture Model
• Utazi Model
• Riemann Model
• Resampling Model
• Ignore Polygon Model
• Location Known Model (for Reference)

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Model Results

samplePlots$results

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Model Results

samplePlots$resultsSD

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Model Comparison Framework: Evaluation

• RMSE of the probability field $\frac{\text{RMSE}{\text{Utazi}} - \text{RMSE}{\text{Model}}}{\text{RMSE}_{\text{Utazi}}}$
• Coverage of CI across the field
• Bias
• Bias for Dissimilarity Measure
• Breakdown results by spatial range and covariate types

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Model Results

resultsPlots$rmseRelative

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Model Results

resultsPlots$coverage

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Model Results

resultsPlots$bias

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Model Results

resultsPlots$dissDiff

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Simulation DR Context

• Simulate spatial-temporal field over 6 years across the DR ~(5x5km grid)
• Sample using DHS 2013 and MICS 2014 location information
• Simulate cluster locations for MICS within known stratification (Region/urbanicity)
• DHS: 370 clusters with 3256 person-years of data
• Mics: 684 clusters of data with ~25,000 person years of data
• No Utazi model

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Dominican Republic Sampling

samplePlots$fieldDR

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Dominican Republic Sampling

samplePlots$fieldDR2

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Dominican Republic Sampling

samplePlots$reg

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Dominican Republic Sampling

samplePlots$regUR

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Model Results

samplePlots$drResults

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Model Results

samplePlots$drProvError

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Model Results

resultsPlotsDR$rmseRelative

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Model Results

resultsPlotsDR$rmseProvRelative

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Model Results

resultsPlotsDR$bias

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Model Results

resultsPlotsDR$provcoverage

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Model Results

resultsPlotsDR$dissDiff

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Notes on Runtime

resultsPlotsDR$runtime

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Conclusion

• New model provides significant improvement over IHME resampling
• Most tested models offer some improvement over resampling
• Reduction of standard errors compared to ignoring data (35% at province)
• Cost of implementation for mixture model is high (runtime & RAM)
• Riemann model offers a compromise in performance and resources

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Limitations

• No model miss-specification tests
• Unclear how different results are when applied to actual data
• Should test other countries
• Need to vary temporal auto correlation

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class: inverse, center, middle

Questions??

nmmarquez/PointPolygon documentation built on Dec. 10, 2020, 1:15 a.m.