Implements the "Dynamics" component of the CEnTR*IMPACT framework (Price, 2024). This function processes multidimensional assessment data to calculate domain-level scores using geometric means and computes a "Balance Score" (\(S_d\)) using the Gini coefficient. It is designed to measure the equitable distribution of effort and impact across the core domains of the CBPR Framework (Wallerstein & Duran, 2010; Wallerstein, et al., 2020).
Arguments
- dynamics_df
A data frame containing the assessment data. Required columns:
domain: Character or Factor. The broader category (e.g., "Partnerships").dimension: Character or Factor. The specific metric (e.g., "Trust").salience: Numeric. The importance of the dimension. Must be \(0 < x \le 1\).weight: Numeric. The observed intensity or presence. Must be \(0 < x \le 1\).
Value
An object of class dynamics_analysis containing:
dynamics_df: The processed input data frame with addeddimension_score.domain_df: A summary data frame with aggregated scores per domain.dynamics_score: A single numeric value representing the Balance Score (\(S_d\)), where 1 indicates perfect balance.
Details
The CEnTR*IMPACT framework uses this analysis to quantify "Developmental Balance." A higher Balance Score indicates that the project is maintaining a healthy equilibrium across its various dimensions, rather than over-indexing on just one area at the expense of others.
The Scoring Process:
Dimension Scoring: For each descriptor, weight (\(w_j\)) is multiplied by Smith's salience index (\(s_j\)). The dimension score is the geometric mean across all descriptors. $$s_{\text{dimension}} = \left(\prod_{j=1}^{n} (w_j \times s_j)\right)^{1/n}$$
Domain Scoring: Aggregates dimension scores within each domain using the geometric mean across all dimensions in the domain. $$s_{\text{domain}} = \left(\prod_{i=1}^{m} s_{\text{dimension},i}\right)^{1/m}$$
Dynamics Scoring: Calculated based on the inequality of all domain scores. $$S_{d} = 1 - \operatorname{Gini}(\{s_{\text{domain},k}\})$$
Dynamics Score Interpretation: The following rule of thumb (Haddad et al., 2024; Wang et al., 2020) is used to interpret the Dynamics Score (\(S_d\)):
\(S_d < 0.5\): Very Low Balance
\(0.50 \le S_d < 0.59\): Low Balance
\(0.60 \le S_d < 0.69\): Moderate Balance
\(0.70 \le S_d \le 0.79\): High Balance
\(S_d \ge 0.80\): Very High Balance
Handling Missing Data:
The function is permissive with partial datasets. If a domain is included in the
input but contains NA values for weights or salience, it is retained in
the output. However, if sufficient data is missing to prevent calculation, the
score will be NaN.
References
Haddad, C. N., Mahler, D. G., Diaz-Bonilla, C., Hill, R., Lakner, C., & Lara Ibarra, G. (2024). The World Bank's New Inequality Indicator: The Number of Countries with High Inequality. Washington, DC: World Bank. doi:10.1596/41687
Price, J. F. (2024). CEnTR*IMPACT: Community Engaged and Transformative Research – Inclusive Measurement of Projects & Community Transformation (CUMU-Collaboratory Fellowship Report). Coalition of Urban and Metropolitan Universities.
Wallerstein, N., & Duran, B. (2010). Community-Based Participatory Research Contributions to Intervention Research: The Intersection of Science and Practice to Improve Health Equity. American Journal of Public Health, 100(S1), S40–S46. doi:10.2105/AJPH.2009.184036
Wallerstein, N., et al. (2020). Engage for Equity: A Long-Term Study of Community-Based Participatory Research and Community-Engaged Research Practices and Outcomes. Health Education & Behavior, 47(3), 380–390. doi:10.1177/1090198119897075
Wang, H.-Y., Chou, W., Shao, Y., & Chien, T.-W. (2020). Comparison of Ferguson’s delta and the Gini coefficient used for measuring the inequality of data related to health quality of life outcomes. Health and Quality of Life Outcomes, 18(1), 111. doi:10.1186/s12955-020-01356-6
Examples
# 1. Generate synthetic data using the built-in generator
# We use a fixed seed to ensure the example is reproducible
df <- generate_dynamics_data(seed = 123)
# 2. Run the Dynamics analysis
result <- analyze_dynamics(df)
# 3. Inspect the global Balance Score (Sd)
# A score closer to 1.0 indicates high balance across domains
print(result$dynamics_score)
#> [1] 0.9763636
# 4. Inspect the domain-level scores
print(result$domain_df)
#> # A tibble: 5 × 2
#> domain domain_score
#> <ord> <dbl>
#> 1 Contexts 0.45
#> 2 Partnerships 0.45
#> 3 Research 0.44
#> 4 Learning 0.46
#> 5 Outcomes 0.4