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In the presence of covariates, average marginal effects (AMEs) are often preferred over odds ratios, as AMEs yield a clearer substantive and causal interpretation. However, standard error computation of AMEs neglects sampling\u2010based uncertainty (i.e., covariate values are assumed to be fixed over repeated sampling), which leads to underestimation of AME standard errors in other generalized linear models (e.g., Poisson regression). In this paper, we present and compare approaches allowing for stochastic (i.e., randomly sampled) covariates in models for binary outcomes. In a simulation study, we investigated the quality of the AME and stochastic\u2010covariate approaches focusing on statistical inference in finite samples. Our results indicate that the fixed\u2010covariate approach provides reliable results only if there is no heterogeneity in interindividual treatment effects (i.e., presence of treatment\u2013covariate interactions), while the stochastic\u2010covariate approaches are preferable in all other simulated conditions. We provide an illustrative example from clinical psychology investigating the effect of a cognitive bias modification training on post\u2010traumatic stress disorder while accounting for patients' anxiety using an RCT.<\/jats:p>","DOI":"10.1111\/bmsp.12355","type":"journal-article","created":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T06:32:45Z","timestamp":1721802765000},"page":"141-166","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Average treatment effects on binary outcomes with stochastic covariates"],"prefix":"10.1111","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9166-400X","authenticated-orcid":false,"given":"Christoph","family":"Kiefer","sequence":"first","affiliation":[{"name":"Department of Psychological Methods and Evaluation Bielefeld University  Bielefeld Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4974-505X","authenticated-orcid":false,"given":"Marcella L.","family":"Woud","sequence":"additional","affiliation":[{"name":"Department of Clinical Psychology and Experimental Psychopathology, Institute of Psychology University of G\u00f6ttingen  G\u00f6ttingen Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3313-7084","authenticated-orcid":false,"given":"Simon E.","family":"Blackwell","sequence":"additional","affiliation":[{"name":"Department of Clinical Psychology and Experimental Psychopathology, Institute of Psychology University of G\u00f6ttingen  G\u00f6ttingen Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9716-878X","authenticated-orcid":false,"given":"Axel","family":"Mayer","sequence":"additional","affiliation":[{"name":"Department of Psychological Methods and Evaluation Bielefeld University  Bielefeld Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2024,7,24]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.3982\/ECTA12675"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/pst.1880"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/biostatistics\/kxh020"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/S2215\u20100366(21)00170\u2010X"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1037\/t02025-000"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1037\/apl0000251"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4818-1"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.20982\/tqmp.16.4.p248"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2005.08.046"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1037\/0022\u2010006X.66.3.549"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02288588"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/0471445428"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1037\/edu0000284"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0023584"},{"key":"e_1_2_11_16_1","volume-title":"Econometric analysis","author":"Greene W. 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