{"title":"异方差多水平模型的精确标准误差:一种计算效率更高的折刀技术","authors":"Steffen Zitzmann, Sebastian Weirich, Martin Hecht","doi":"10.3390/psych5030049","DOIUrl":null,"url":null,"abstract":"In random-effects models, hierarchical linear models, or multilevel models, it is typically assumed that the variances within higher-level units are homoscedastic, meaning that they are equal across these units. However, this assumption is often violated in research. Depending on the degree of violation, this can lead to biased standard errors of higher-level parameters and thus to incorrect inferences. In this article, we describe a resampling technique for obtaining standard errors—Zitzmann’s jackknife. We conducted a Monte Carlo simulation study to compare the technique with the commonly used delete-1 jackknife, the robust standard error in Mplus, and a modified version of the commonly used delete-1 jackknife. Findings revealed that the resampling techniques clearly outperformed the robust standard error in rather small samples with high levels of heteroscedasticity. Moreover, Zitzmann’s jackknife tended to perform somewhat better than the two versions of the delete-1 jackknife and was much faster.","PeriodicalId":93139,"journal":{"name":"Psych","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Accurate Standard Errors in Multilevel Modeling with Heteroscedasticity: A Computationally More Efficient Jackknife Technique\",\"authors\":\"Steffen Zitzmann, Sebastian Weirich, Martin Hecht\",\"doi\":\"10.3390/psych5030049\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In random-effects models, hierarchical linear models, or multilevel models, it is typically assumed that the variances within higher-level units are homoscedastic, meaning that they are equal across these units. However, this assumption is often violated in research. Depending on the degree of violation, this can lead to biased standard errors of higher-level parameters and thus to incorrect inferences. In this article, we describe a resampling technique for obtaining standard errors—Zitzmann’s jackknife. We conducted a Monte Carlo simulation study to compare the technique with the commonly used delete-1 jackknife, the robust standard error in Mplus, and a modified version of the commonly used delete-1 jackknife. Findings revealed that the resampling techniques clearly outperformed the robust standard error in rather small samples with high levels of heteroscedasticity. Moreover, Zitzmann’s jackknife tended to perform somewhat better than the two versions of the delete-1 jackknife and was much faster.\",\"PeriodicalId\":93139,\"journal\":{\"name\":\"Psych\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Psych\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3390/psych5030049\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Psych","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/psych5030049","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Accurate Standard Errors in Multilevel Modeling with Heteroscedasticity: A Computationally More Efficient Jackknife Technique
In random-effects models, hierarchical linear models, or multilevel models, it is typically assumed that the variances within higher-level units are homoscedastic, meaning that they are equal across these units. However, this assumption is often violated in research. Depending on the degree of violation, this can lead to biased standard errors of higher-level parameters and thus to incorrect inferences. In this article, we describe a resampling technique for obtaining standard errors—Zitzmann’s jackknife. We conducted a Monte Carlo simulation study to compare the technique with the commonly used delete-1 jackknife, the robust standard error in Mplus, and a modified version of the commonly used delete-1 jackknife. Findings revealed that the resampling techniques clearly outperformed the robust standard error in rather small samples with high levels of heteroscedasticity. Moreover, Zitzmann’s jackknife tended to perform somewhat better than the two versions of the delete-1 jackknife and was much faster.