{"title":"个体水平的概率和聚类水平的比例:在二元结果的非膨胀多层次模型中实现可解释的第 2 层估计。","authors":"Timothy Hayes","doi":"10.1037/met0000646","DOIUrl":null,"url":null,"abstract":"<p><p>Multilevel models allow researchers to test hypotheses at multiple levels of analysis-for example, assessing the effects of both individual-level and school-level predictors on a target outcome. To assess these effects with the greatest clarity, researchers are well-advised to cluster mean center all Level 1 predictors and explicitly incorporate the cluster means into the model at Level 2. When an outcome of interest is continuous, this unconflated model specification serves both to increase model accuracy, by separating the level-specific effects of each predictor, and to increase model interpretability, by reframing the random intercepts as unadjusted cluster means. When an outcome of interest is binary or ordinal, however, only the first of these benefits is fully realized: In these models, the intuitive cluster mean interpretations of Level 2 effects are only available on the metric of the linear predictor (e.g., the logit) or, equivalently, the latent response propensity, <i>y</i><sub>ij</sub>∗. Because the calculations for obtaining predicted probabilities, odds, and <i>OR</i>s operate on the entire combined model equation, the interpretations of these quantities are inextricably tied to individual-level, rather than cluster-level, outcomes. This is unfortunate, given that the probability and odds metrics are often of greatest interest to researchers in practice. To address this issue, I propose a novel rescaling method designed to calculate cluster average success proportions, odds, and <i>OR</i>s in two-level binary and ordinal logistic and probit models. I apply the approach to a real data example and provide supplemental R functions to help users implement the method easily. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":" ","pages":""},"PeriodicalIF":7.6000,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Individual-level probabilities and cluster-level proportions: Toward interpretable level 2 estimates in unconflated multilevel models for binary outcomes.\",\"authors\":\"Timothy Hayes\",\"doi\":\"10.1037/met0000646\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Multilevel models allow researchers to test hypotheses at multiple levels of analysis-for example, assessing the effects of both individual-level and school-level predictors on a target outcome. To assess these effects with the greatest clarity, researchers are well-advised to cluster mean center all Level 1 predictors and explicitly incorporate the cluster means into the model at Level 2. When an outcome of interest is continuous, this unconflated model specification serves both to increase model accuracy, by separating the level-specific effects of each predictor, and to increase model interpretability, by reframing the random intercepts as unadjusted cluster means. When an outcome of interest is binary or ordinal, however, only the first of these benefits is fully realized: In these models, the intuitive cluster mean interpretations of Level 2 effects are only available on the metric of the linear predictor (e.g., the logit) or, equivalently, the latent response propensity, <i>y</i><sub>ij</sub>∗. Because the calculations for obtaining predicted probabilities, odds, and <i>OR</i>s operate on the entire combined model equation, the interpretations of these quantities are inextricably tied to individual-level, rather than cluster-level, outcomes. This is unfortunate, given that the probability and odds metrics are often of greatest interest to researchers in practice. To address this issue, I propose a novel rescaling method designed to calculate cluster average success proportions, odds, and <i>OR</i>s in two-level binary and ordinal logistic and probit models. I apply the approach to a real data example and provide supplemental R functions to help users implement the method easily. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>\",\"PeriodicalId\":20782,\"journal\":{\"name\":\"Psychological methods\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":7.6000,\"publicationDate\":\"2024-02-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Psychological methods\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://doi.org/10.1037/met0000646\",\"RegionNum\":1,\"RegionCategory\":\"心理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PSYCHOLOGY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Psychological methods","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1037/met0000646","RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PSYCHOLOGY, MULTIDISCIPLINARY","Score":null,"Total":0}
Individual-level probabilities and cluster-level proportions: Toward interpretable level 2 estimates in unconflated multilevel models for binary outcomes.
Multilevel models allow researchers to test hypotheses at multiple levels of analysis-for example, assessing the effects of both individual-level and school-level predictors on a target outcome. To assess these effects with the greatest clarity, researchers are well-advised to cluster mean center all Level 1 predictors and explicitly incorporate the cluster means into the model at Level 2. When an outcome of interest is continuous, this unconflated model specification serves both to increase model accuracy, by separating the level-specific effects of each predictor, and to increase model interpretability, by reframing the random intercepts as unadjusted cluster means. When an outcome of interest is binary or ordinal, however, only the first of these benefits is fully realized: In these models, the intuitive cluster mean interpretations of Level 2 effects are only available on the metric of the linear predictor (e.g., the logit) or, equivalently, the latent response propensity, yij∗. Because the calculations for obtaining predicted probabilities, odds, and ORs operate on the entire combined model equation, the interpretations of these quantities are inextricably tied to individual-level, rather than cluster-level, outcomes. This is unfortunate, given that the probability and odds metrics are often of greatest interest to researchers in practice. To address this issue, I propose a novel rescaling method designed to calculate cluster average success proportions, odds, and ORs in two-level binary and ordinal logistic and probit models. I apply the approach to a real data example and provide supplemental R functions to help users implement the method easily. (PsycInfo Database Record (c) 2024 APA, all rights reserved).
期刊介绍:
Psychological Methods is devoted to the development and dissemination of methods for collecting, analyzing, understanding, and interpreting psychological data. Its purpose is the dissemination of innovations in research design, measurement, methodology, and quantitative and qualitative analysis to the psychological community; its further purpose is to promote effective communication about related substantive and methodological issues. The audience is expected to be diverse and to include those who develop new procedures, those who are responsible for undergraduate and graduate training in design, measurement, and statistics, as well as those who employ those procedures in research.