Qualitative and Mixed Methods Inference

2023

1. Qualitative and Mixed Methods Inference

   Macartan Humphreys, and Alan Jacobs

   2023

   We have been developing approaches to better integrate qualitative and quantitative strategies and better integrate theoretical and empirical research. The core idea is to represent theories as causal models, use Bayesian models to update on these theories given some mixture of ’correlational’ and ’process’ data, and then query those models to infer causal relations for specific cases of interest. In 2023 Humphreys and Jacobs published *Integrated Inferences* with Cambridge University Press. Integrated Inferences provides strategies for using causal models to integrate inferences from qualitative and quantitative data and to better theoretical insights into qualitative work. The key strategy is to use Bayesian approaches to update simultaneously from cross-sectional information on causes and outcomes and process information about the operation of causal mechanisms.

2025

1. WP

   Making, Updating, and Querying Causal Models with CausalQueries

   Till Tietz, Lily Medina, Georgiy Syunyaev, and 1 more author

   2025

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   The R package ‘CausalQueries‘ can be used to make, update, and query causal models defined on binary nodes. Users provide a causal statement of the form ‘X -> M <- Y; M <-> Y‘ which is interpreted as a structural causal model over a collection of binary nodes. Then ‘CausalQueries‘ allows users to (1) identify the set of principal strata—causal types—required to characterize all possible causal relations between nodes that are consistent with the causal statement (2) determine a set of parameters needed to characterize distributions over these causal types (3) update beliefs over distributions of causal types, using a ‘stan‘ model plus data, and (4) pose a wide range of causal queries of the model, using either the prior distribution, the posterior distribution, or a user-specified candidate vector of parameters.

   @unpublished{cq_2025,
     author = {Tietz, Till and Medina, Lily and Syunyaev, Georgiy and Humphreys, Macartan},
     title = {Making, Updating, and Querying Causal Models with CausalQueries},
     journal = {Under review},
     year = {2025},
     status = {WP},
     proj = {inference},
     keywords = {methods, causal inference},
     proj.1 = {inference}
   }

2. JCI

   Bounds on the fixed effects estimand in the presence of heterogeneous assignment

   Macartan Humphreys

   2025

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   In many contexts, treatment assignment probabilities differ across strata or are correlated with some observable third variables. Regression with covariate adjustment is often used to account for these features. It is known however that in the presence of heterogeneous treatment effects this approach does not yield unbiased estimates of average treatment effects. But it is not well known how estimates generated in this way diverge from unbiased estimates of average treatment effects. Here I show that biases can be large, even in large samples. However I also find conditions under which the usual approach provides interpretable estimates and I identify a monotonicity condition that ensures that least squares estimates lie between estimates of the average treatment effects for the treated and the average treatment effects for the controls. The monotonicity condition can be satisfied for example with Roy-type selection and is guaranteed in the two stratum case.

   @unpublished{ols_2025,
     author = {Humphreys, Macartan},
     title = {Bounds on the fixed effects estimand in the presence of heterogeneous assignment},
     journal = {forthcoming, Journal of Causal Inference},
     year = {2025},
     status = {WP},
     proj = {inference},
     keywords = {methods, causal inference},
     proj.1 = {inference}
   }

2024

1. SMR

   Bounding causes of effects with mediators

   Philip Dawid, Macartan Humphreys, and Monica Musio

   Sociological Methods & Research, 2024

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   Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. We are interested in assessing whether an outcome in some case is due to the exposure. This ’probability of causation’ is of interest in comparative historical analysis where scholars use process tracing approaches to learn about causes of outcomes for single units by observing events along a causal path. The probability of causation is typically not identified, but bounds can be placed on it. Here, we provide a full characterization of the bounds that can be achieved in the ideal case that X and Y are connected by a causal chain of complete mediators, and we know the probabilistic structure of the full chain. Our results are largely negative. We show that, even in these very favorable conditions, the gains from positive evidence on mediators is modest.

   @article{dawid_204,
     author = {Dawid, Philip and Humphreys, Macartan and Musio, Monica},
     title = {Bounding causes of effects with mediators},
     journal = {Sociological Methods \& Research},
     year = {2024},
     pages = {4.91E+14},
     publisher = {SAGE Publications Sage CA: Los Angeles, CA},
     status = {peer},
     proj = {inference},
     keywords = {methods},
     proj.1 = {inference}
   }