• Deductive view of the relationship between theory and research
• Epistemologically described as empiricism & realism
• Ontological position of objectivism
• Purposes:
  • Comparative studies
  • Association studies
  • Causal studies

• Common aspects:
  • Sampling
  • Bias
  • Counfunding
  • Counterfactuals
• Some methods:
  • Regression models
  • Multivariate regression analysis
  • Group comparison
  • Clustering
  • Dimensionality reduction (nMDS)
  • Principal component analysis (PCA)
  • Redundancy Analysis (RDA)
  • Canonical Correspondence Analysis (CCA)
  • Factor Analysis (FA)
  • Multiple Correspondence Analysis (MCA)
  • Time series analysis (TSA)

1. Research question
2. Selection of site or case
3. Research design: hypotheses
4. Data collection
5. Data analysis / interpretation
6. Writing findings

• Aim:
  • Test hypotheses
  • Constructing baselines
• Hypotheses
• Measurement / variables / observables
• Sampling:
  • Avoid bias
• Tests and errors

• Null-hypothesis: opposite of the question asked
• Unlikely = it occurs at most 5% of the time
• p-value < 0.05 unlikely to occur simply by chance
  • Type I errors: false positives
  • Type II errors: false negatives

1. Data cleaning
2. Visualization
   • Aggregate and understand patterns
   • Trends
   • Annomalies in data (outliers)

3. Analysis
   • Description (mean, variance)
   • Dependencies, correlations
   • Differences
4. Modelling
   • Prediction
   • Forecasting
   • Handling missing data

• Central tendencies and comparisons:
  • income between urban and rural areas
  • precipitation or food production
• Relationships between system components: income ~ farm size + distance to markets + number of working family members?
  food production ~ irrigation + soil features + fertilizer use?
• Relevant components or relationship strenghts

• Features of the data
• Normally distributed?
  • If not, are transformations needed?
• Homoscedasticity
• Sampling units

• Descriptive countable data (groups)
• Non-rankable: sex, color (nominal)
• Rankable: age class, group size (ordinal)
• Interesting features: quantiles, mode

• Cannot be counted: temperature
• Size and magnitud
• Higher information quality
• You can discretize but not the other way around

• Normality?:
  • Shapiro-Wilks test
• Good proxies parametric:
  • mean
  • median
  • variance
  • standard deviation
• Non-parametric

• Central tendency: mode
• Variability: NA
• Shape / distribution: NA
• Relationship: NA
• Group comparison: Chi square test

• Central tendency: mode, median
• Variability: min-max, semi-interquartile range, skewness
• Shape / distribution: Kolmogorov-Smirnoff test of continuity
• Relationships: Spearman rank
• Group comparison:
  • 2 groups: Mann-Whitney test
  • many groups: Kruskal-Wallis test

1. Central tendency
2. Variability

Examples: Gapminder data

1. Central tendency
2. Variability

Examples: experimental game with fishermen
Aim: How do they behave under different levels of threshold uncertainty

• Combination of several factors explain your dependent variable
• They can be: continuos, discrete (ordinal, nominal)
• Controling for…
• Account for interactions
• Which model is better?
  • AIC
  • BIC

Rocha et al. Cooperation in the Face of Thresholds, Risk, and Uncertainty

• Parametric: Several test available
• 2-groups:
  • t-test (one-sided, two-sided?)[p]
  • Mann-Whitney U test [np]
• Many groups:
  • ANOVA [p]
  • Kruskal Wallis [np]
• Which group differ? post-hoc tests (Tukey, Scheffé)

Who is different?

Rocha et al. Mapping Social Ecological Systems Archetypes

• Hierarchical
• k-means
• SOM
• PAM
• n-MDS[*]

• Euclidean
• Manhattan
• Jaccard
• Bray-Curtis

• Principal Component Analysis
• Redundancy Analysis
• Canonical Correspondence analysis
• Factor Analysis
• Multiple Correspondence Analysis
• Non-metric Multi-Dimensional Scaling [*]

• Linear:
  • based on regression tools
  • Independence assumption
  • Does badly with non-linear data
  • RDA & FA:
    • how much variance of independent variables is explained by dependent variables?
• Non-linear:
  • based on similarity
• Good practices:
  • Data normalization
    • transformation
    • 0 mean / 1SD

• Interpret plausible descriptions of sample data
• Hypothesis testing
  • Drivers
  • Treatments
  • Synchrony
• Forecasting
• Causality

• Multivariate autoregressive state-space models (MARSS)
• Vector autoregression, panel models (econometrics)
  • covariate data
    • continuous
    • discrete (nominal, ordinal)
  • drift term: deterministic dynamic
  • error term: stochastic random process
• Convergent cross-mapping

• Challenge of SDGs: how do we find context dependent solutions?
• There is no panaceas!!
• Social-ecological systems framework
  • 2-tier variables (n=53)
• Over 100 case study coded but local in temporal and spatial scales:
  • SES Library
  • SES Meta Analysis Database

To develop a data driven method to upscale Ostrom’s SES framework

• West African Sahel is vulnerable area due to:
  • wide-spread of poverty
  • recurrent droughts and dry spells
  • political upheaval
  • growing food demand
• Volta basin is 2/3 Ghana and Burkina Faso
  • N: dry, poor, subsistence agriculture
  • S: wet, rich, urbanization

Impact of water reservoirs in food security?

• Our findings are robust across time despite low data quality
• Dams make a difference in orange, purple, and green clusters.
• Variance in kilocalories is more relevant on the orange cluster. It means occasionally they do better off, but still a vulnerable group to yield loss.

• 256 participants from 4 fishing communities
• Largely depend on natural resources as main source of income
• History of regime shifts:
  • Mangroves collapse (1980s -90s)
  • Hypoxia events and fish deadzones

• Individual extraction: \[x_{i,t}\]
• Proportion of extraction: \[x_{i,t}/S_t\]

• Cooperation: \[C_{i,t} = \frac{x_{i,t}}{\frac{S_t - \theta}{N}}\]

• Diff-in-diff regression: \[\hat{Y_i} = \hat{\mu} + \hat{\gamma}G_i + \hat{\delta}T_i + \hat{\tau}G_iT_i\]

It’s harder to coordinate under treatments, but agreements increase the probability to coordinate and react to lower stock sizes by reducing fishing preasure. Agreements also reduce the variance of extraction and the variance of cooperation. Changes in fishing effort depends on treatments while changes in cooperation depends on context.