Cited by 449Advanced Statistical Methods and ModelsStatistical Methods and Bayesian InferenceData Analysis with R

The DOI matches its Crossref record; 16 of the 18 references it cites were found in a registry or an index; none of the 16 sources its claims cite is checked for support yet.

influence.ME: Tools for Detecting Influential Data in Mixed Effects Models

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Abstract

influence.ME provides tools for detecting influential data in mixed effects models.The application of these models has become common practice, but the development of diagnostic tools has lagged behind.influence.ME calculates standardized measures of influential data for the point estimates of generalized mixed effects models, such as DFBETAS, Cook's distance, as well as percentile change and a test for changing levels of significance.influence.ME calculates these measures of influence while accounting for the nesting structure of the data.The package and measures of influential data are introduced, a practical example is given, and strategies for dealing with influential data are suggested.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper introduces influence.ME, an R package for detecting influential cases in generalized mixed effects models estimated with lme4, providing DFBETAS, Cook’s distance, percentile change, and a test for changing significance while accounting for nesting. In a 23-school example, deleting school 7472 changed the school-level structure effect from non-significant to significant.

Key findings

  • influence.ME calculates standardized influence measures for mixed effects models: DFBETAS, Cook’s distance, percentile change, and a significance-change test (`sigtest`), plus plotting and `exclude.influence` for deleting identified cases.
  • In the example with 519 students in 23 schools, the original model estimated the structure effect as -2.0950 (SE 1.3237, t = -1.583, not significant) and the homework effect as 2.3938 (SE 0.2771, t = 8.640).
  • The DFBETAS cut-off was 2/√23 = .41; school 7472 had a structure DFBETAS of 1.254990963, exceeding the cut-off. The Cook’s distance cut-off was 4/23 = .17; school 7472 had a Cook’s distance of 1.575002.
  • After excluding school 7472, the model used 496 observations in 22 groups and estimated the structure effect as -3.8949 (SE 1.4342, t = -2.716), now statistically significant. For lower-level observations, the Cook’s distance cut-off was 4/519 = .0077; students 88 and 89 exceeded it for the structure estimate, but `sigtest` showed no significance changes.

Methods

  • The paper describes the influence.ME package and demonstrates it with the `school23` data, a subset of NELS-88 containing 519 students nested in 23 schools, using a linear mixed model: `math ~ homework + structure + (1 | school.ID)` estimated with lme4.
  • The `influence` function iteratively deletes each higher-level group, or with `obs=TRUE` each lower-level observation, and re-estimates the model; the resulting `estex` object is passed to `dfbetas`, `cooks.distance`, `pchange`, `sigtest`, and plotting functions.
  • DFBETAS measures change in a single parameter standardized by the excluding-case standard error; Cook’s distance summarizes change across selected parameters; percentile change reports percentage change; `sigtest` compares test statistics after deletion to a user-specified value.

Limitations

  • Stated: the leverage measure was not developed for generalized mixed effects models, so the package emphasizes influence on point estimates; the Langford and Lewis `delete=FALSE` procedure does not work with factor variables; the `influence` function can evaluate higher-level cases or single observations but not both at once; lower-level detection is often infeasible with many lower-level observations; the procedure can be computationally intensive; no cut-off is provided for percentile change.
  • Evident: the worked example assumes math, homework, and structure are correctly measured at the interval level, and the paper does not report simulation or benchmark comparisons of the package’s performance.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.32614/rj-2012-011

Cites

16 of 16 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

41 No basis given · 24 Own interpretation · 16 Not checked yet · 12 Own result

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  • It may state two separate claims as one. 15
  • Probably not a substantial claim. 56
  • The quote only partly states this claim. 2
63 of 63
  • The paper relies on this without support.

    Diagnostic tools to evaluate fitted mixed effects models lag behind their increasing popularity.

    “Despite these models' increasing popularity, diagnostic tools to evaluate fitted models lag behind.”
  • The paper relies on this without support.

    Most existing procedures for detecting influential data do not account for the nesting structure of the data.

    “However, most existing procedures do not account for the nesting structure of the data.”
  • The paper relies on this without support.

    All cases used to estimate a regression model exert some level of influence on the regression parameters.

    “All cases used to estimate a regression model exert some level of influence on the regression parameters.”
  • The authors state this as an assumption.

    The math, homework, and structure variables were correctly measured at the interval level.

    “For the purpose of our example, we assume here that the math, homework, and structure variables were correctly measured at the interval level.”
  • The paper relies on this without support.

    The application of mixed effects models has become common practice, but the development of diagnostic tools lags behind.

    “The application of these models has become common practice, but the development of diagnostic tools lag behind.”
  • The paper relies on this without support.

    Overly influential data are a problem especially encountered in models based on a limited number of cases.

    “Since overly influential data are a problem especially encountered in models based on a limited number of cases, a straightforward remedy would be to observe more cases in the population of interest.”
  • The paper relies on this without support.

    If data are used to estimate too complex models, or if parameterization is incorrect, influential cases are more likely to occur.

    “If the data are used to estimate too complex models, or if parameterization is incorrect, influential cases are more likely to occur.”
  • The paper relies on this without support.

    In social science applications of mixed effects models, higher-level groups are often readily accessible cases such as schools and countries, making it possible to obtain additional measurements to remedy influential data.

    “However, in social science applications of mixed effects models, the higher-level groups are often readily accessible cases such as schools and countries.”
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Citations

Cites

Show all 18 references

Research works printed but not linked: 4

  1. R. Cook. Detection of influential observations in lin- ear regression. Technometrics, 19(1):15-18, 1977.
  2. M. J. Crawley. The R Book. Wiley, 2007.
  3. I. Kreft and J. De Leeuw. Introducing Multilevel Mod- eling. Sage Publications, 1998.
  4. T. Van der Meer, M. te Grotenhuis, and B. Pelzer. In- fluential cases in multilevel modeling. A method- ological comment. American Sociological Review, 75: 173-178, 2010. [p38, 40, 46]

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Metadata

Authors
Nieuwenhuis, R., Grotenhuis, M., & Pelzer, B.
Venue
The R Journal
Published
2012
Volume
4
Issue
2
Pages
38
ISSN
2073-4859 (ISSN-L)
OpenAlex
W1549371580
Cited by
442
References
18
Citations by year
2026: 29 · 2025: 36 · 2024: 45 · 2023: 38 · 2022: 64 · 2021: 63 · 2020: 33 · 2019: 28 · 2018: 24 · 2017: 26 · 2016: 22 · 2015: 17 · 2014: 12 · 2013: 5
FWCI
10.39
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • The R Journal (publishedVersion, cc-by)
  • Lincoln (University of Nebraska) (submittedVersion, cc-by)
  • Radboud Repository (Radboud University) (submittedVersion)
  • University of Twente Research Information (submittedVersion)
  • Radboud Repository (Radboud University) (submittedVersion, other-oa)
  • University of Twente Research Information (submittedVersion, other-oa)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Data Analysis with R
Keywords
mixed models, generalized linear mixed models, Cook's distance, nested data, influence diagnostics, R package

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