class: center, middle, inverse, title-slide .title[ # Combining Case Studies and Regression ] .subtitle[ ## Multi-Method Research I ] .author[ ### <large>Jaye Seawright</large> ] .institute[ ### <small>IQMR 2025</small> ] .date[ ### June 26, 2025 ] --- class: center, middle <style type="text/css"> pre { max-height: 400px; overflow-y: auto; } pre[class] { max-height: 200px; } </style> --- ### Case Study Roles - Test Measurement - Test Causal Pathway Hypotheses - Account for Outliers - Test for Confounders - Test for Complexity --- ### Measurement  --- ### Measurement  --- ### Measurement  --- ### Measurement  --- ### Measurement  --- ### Measurement  --- ### Measurement Chong --- ### Measurement 1. Use in-depth exploration of one or a few cases for qualitative correspondence test. 2. Process trace the quantitative measurement process to form a theory for the causes of any errors. 3. Qualitatively examine a few other cases that would be likely to suffer from the same kinds of errors to test the theory. 4. Revise the coding for all relevant cases. --- ### Mechanisms? 1. Causal pathway 2. Unobservable cause 3. Easily observable cause 4. Bounded explanation 5. Universal explanation --- ### Mechanisms? 6. Highly contingent explanation 7. Explanation built on lawlike regularities 8. An analytic technique 9. A micro-level explanation of a macro-level phenomenon --- ### Process Tracing --- ### Causal Pathways and Overall Causal Effects - Is the causal pathway "isolated" from other causal factors? - Is the causal pathway "exhaustive"? - Could the causal pathway plausibly account for the whole estimated effect? ---  ---  ---  ---  ---  --- ### Do We Have to Explain Outliers? --- ### Is Salt Bad for You? --- ### Exploring Outliers <img src="media/freedmanpetiti.PNG" width="70%" style="display: block; margin: auto;" /> --- ### Omitted Variables Omitted Variables vs Confounders --- ### Confounders 1. Trace the causes of the cause, then forward to `\(Y\)`: triangular process-tracing design. 2. Examine the `\(X\)` to `\(Y\)` causal pathway for any influence by potential causes of the cause. --- ### Causal Complexity - Interaction terms - Substitutability - Spillover --- ### Diffusion Statistical models --- ### Diffusion Can process tracing help? --- ### Diffusion Elkins and the Brazilian constitutional assembly. --- ### Regression Roles - Testing generalizability - Causal pathways and models - Addressing measurement problems - Testing the "importance" of omitted variables --- ### Generalizability Data Quality Does the model capture the qualitative hypothesis? --- ### Generalizability Data Quality for Historical Data Sets: - Proximity of Observations - Transparency of Citations - Certainty of the Historical Record - Attention to Valid Comparison --- ### Generalizability Data Quality for Surveys: - Simple Questions - Framing Effects - Pre-Test Evidence --- ### Generalizability "Thick" Concepts: - Cannot be reduced to a single indicator without losing some important part of their meaning. - Multidimensional: no aspect of the concept is reducible to any of the others. --- ### Mediation `\(T_{i}\)` is 1 or 0 `\(Y_{i}(t)\)` --- ### Mediation `\(M_{i}(t)\)` `\(Y_{i}(t, m)\)` --- ### Mediation `\(\tau_{i} = Y_{i}(1, M_{i}(1)) - Y_{i}(0, M_{i}(0))\)` `\(\delta_{i}(t) = Y_{i}(t, M_{i}(1)) - Y_{i}(t, M_{i}(0))\)` `\(\zeta_{i}(t) = Y_{i}(1, M_{i}(t)) - Y_{i}(0, M_{i}(t))\)` --- ### Mediation Assumption of Sequential Ignorability: `\(\{Y_{i}(t,m), M_{i}(t^{'})\} \perp T_{i} | X_{i} = x\)` and `\(Y_{i}(t,m) \perp M_{i} | T_{i} = t^{'}, X_{i} = x\)` --- ### Mediation 1. Fit model for mediator, conditional on treatment, etc. 2. Fit model for observed outcome, conditional on treatment, mediator, etc. 3. Using the first model, simulate `\(M_{i}(0)\)` and `\(M_{i}(1)\)` for each case. --- ### Mediation 4. Using the second model, simulate `\(Y_{i}(0, M_{i}(0))\)`, `\(Y_{i}(0, M_{i}(1))\)`, `\(Y_{i}(1, M_{i}(0))\)`, and `\(Y_{i}(1, M_{i}(1))\)` for each case. 5. Use simulated values to compute `\(\tau_{i}\)`, `\(\delta_{i}(t)\)`, and `\(\zeta_{i}(t)\)` for each case. 6. Repeat steps 3, 4, and 5 many times, saving the calculated values for each repetition. --- ### Multi-Method Tests of Mediation Models - Case Selection - Qualitative Design Considerations --- ### Hands-On At [this website](https://jnseawright.github.io/practice-of-multimethod/Chapter-5.html), work through the exercises labeled *A simple regression example* and *Integrative case-study followup*.