Understand results
Read exported workbooks with uncertainty, response scales, and the current model boundaries in view.
The six exported result sections
Use Download All Tables after a completed run to preserve the full workbook. Each result section is a worksheet. Exporting only the currently visible table can omit outputs needed for later interpretation.
| Worksheet | What it contains | Start by checking |
|---|---|---|
| model.evaluation | Model evaluation and complexity measures | Completed model identity, DIC, WAIC, LS, eff/pd2 |
| local.prediction | Observed and predicted responses with uncertainty | Spatial/time keys, y, predict_y, response scale |
| summary.random.effects | Posterior summaries of modeled random effects | Component names, means, quantiles |
| time.coefficients | Temporal coefficient summaries | time_index, explain_variable, posterior quantiles |
| space.coefficients | Spatial coefficient summaries | Shared map ID and predictor-specific columns |
| STVPI | Spatiotemporal contribution estimates | Component definitions, percentage scale, uncertainty |
The source prose sometimes describes coefficients as a wide table, while its temporal plotting code uses a long table with explain_variable. Inspect the exported headers; the companion script checks the illustrated schema and stops if required fields are absent.
Model evaluation: compare like with like
DIC and WAIC assess model fit with a complexity penalty. Lower values generally support a better comparison within the same response, observations, and likelihood; do not compare the raw values across the three unrelated cases. eff and pd2 are effective-parameter measures used in the source output. Lower complexity alone does not make a model more useful.
The manual labels LS as a logarithmic predictive score and describes values closer to zero as favorable under its exported convention. Check the score definition and sign before extending that rule to other software or score implementations. A single score does not replace examining residual structure, uncertainty, missingness, and predictive validation.
If model variants use different predictor sets with different missing-value handling, record which observations informed each fit. A visually attractive coefficient map is not a model diagnostic.
Coefficients and credible intervals
Read the posterior mean alongside the 95% credible interval (2.5th–97.5th posterior quantiles) and the 50% credible interval (25th–75th quantiles). These intervals summarize uncertainty under the fitted Bayesian model; they are not conventional frequentist confidence intervals.
| Response family | Coefficient scale | Interpretation caution |
|---|---|---|
| Continuous log-Gaussian | Log response | Confirm the transformation and whether a column is a component or a combined coefficient |
| Binary logistic | Log odds | A coefficient is not a percentage-point change in probability |
| Count Poisson | Log modeled mean | A coefficient is not directly a change in the number of cases |
Spatial and temporal components describe different dimensions of variation. Check whether an output field is a random-effect component, a local combined coefficient, or a response-scale prediction before combining or exponentiating it. Standardizing X changes the comparison unit. Keep signs, magnitudes, variable scaling, and posterior uncertainty together in your explanation.
For temporal displays, translate time_index to the intended calendar: 1–21 means 2000–2020 for HALE; 1–12 means months of 2020 for COVID-19; 1–12 means 2012–2023 for hepatitis B. A LOESS curve is a visual smoother and adds no posterior certainty.
For spatial maps, join on ISO_A3, gb, or GEOID, according to the case. Do not append coefficient rows to a map by position. Use an intentional legend, show NA areas, and state whether color scales are shared across predictors.
Read the contribution component labels
| Source label | How to read it |
|---|---|
space.X | Spatial component associated with predictor X. |
time.X | Temporal component associated with predictor X. |
space.time.X | Combined spatiotemporal contribution associated with predictor X under the exported definition. |
space.all / time.all | Aggregate spatial / temporal components when supplied. |
space.time.all | Aggregate modeled spatiotemporal component when supplied. |
residual | Residual component when included in the fitted response family. |
Here X is a placeholder for an actual predictor name, such as PD. The source charts show several views of the same modeled decomposition. Do not sum every displayed row as though all rows were mutually exclusive parts: aggregate, combined, and individual components can overlap. Read the export and the method definition together before comparing denominators.
STVPI: contribution within the model
The Spatiotemporal Variance Partitioning Index decomposes modeled variation into spatial, temporal, and combined components as defined by the model. It supports comparing relative contributions of explanatory factors and reporting their posterior uncertainty. Use the exported component labels and the method reference when describing each part of a chart.
The source plotting examples express proportions as percentages. A stored 0.20 is displayed as 20%; do not divide it by 100 again. If your export stores values directly as percentages, adjust the display format rather than guessing from the column name. Preserve the workbook values.
Spatiotemporal contribution helps identify patterns that may inform subsequent causal research. It does not establish causal attribution, eliminate confounding, or show what would happen under an intervention. State the outcome, predictor set, neighborhood, missingness handling, and model assumptions when reporting rankings.
Prediction columns and response scales
| Column | Meaning in the source workflow |
|---|---|
| y | Observed response, including any NA entries |
| predict_y | Predicted value or mean on the exported response scale |
| fill_y | Outcome field completed with model predictions where observations are missing |
| predict_0.025quant / predict_0.975quant | Response-scale 95% interval in the continuous example |
| predict_0.25quant / predict_0.75quant | Response-scale 50% interval in the continuous example |
| y_mean and other unprefixed summaries | Model-specific summaries; inspect their scale and definition before using them |
For the continuous case, the manual already back-transforms the predict_ fields. For binary outcomes, predicted probabilities belong on [0, 1]. For counts, inspect whether the prediction is a response-scale mean. Do not apply another log or exponential transformation just to make a plotted value look plausible.
Use available observed/predicted pairs for descriptive accuracy. Exclude rows with missing outcomes from such evaluation; an imputed value is not an independent observed truth. For forecasts, future predictor information and a valid hold-out scheme matter. The illustrated desktop workflow alone does not establish a validated forecasting protocol.
A practical reporting checklist
- Software version, response family, response field, and research question.
- Geographic units, period, sources, map definition, and ID matching.
- Predictors and their scaling, transformations, missingness, and selection rationale.
- Neighborhood specification and any differences from the default.
- Model evaluation, coefficient means, and credible intervals.
- Available contribution components and the limits on their interpretation.
- Prediction scale, validation design, metrics, and uncertainty.
- Saved input, checked data, settings, workbook, and figure-generation script.
Continue to R visualization to create the displays, or to Troubleshooting if an output is missing or unexpected.
Method references
The supplied manual cites the following foundations. Consult the papers for model definitions and assumptions; this practical guide does not replace them.
- Song, C., Shi, X., & Wang, J. (2020). Spatiotemporally Varying Coefficients (STVC) model: a Bayesian local regression to detect spatial and temporal nonstationarity in variables relationships. Annals of GIS, 26(3), 277–291.
- Song, C., et al. (2019). Exploring spatiotemporal nonstationary effects of climate factors on hand, foot, and mouth disease using Bayesian STVC model in Sichuan, China. Science of the Total Environment, 648, 550–560.
- Song, C., et al. (2022). Spatiotemporal disparities in regional public risk perception of COVID-19 using Bayesian STVC series models across Chinese cities. International Journal of Disaster Risk Reduction, 77, 103078.
- Wan, Q., et al. (2022). Spatiotemporal heterogeneity in associations of national population ageing with socioeconomic and environmental factors at the global scale. Journal of Cleaner Production, 373, 133781.
- Song, C., & Tang, X. (2025). User’s Guide for the BSTVC R Package.