Mean and Mean-and-Variance Corrections With Big Data

Ke-hai Yuan, Ge Jiang, Miao Yang

Research output: Contribution to journalArticlepeer-review


Mean and mean-and-variance corrections are the 2 major principles to develop test statistics with violation of conditions. In structural equation modeling (SEM), mean-rescaled and mean-and-variance-adjusted test statistics have been recommended under different contexts. However, recent studies indicated that their Type I error rates vary from 0% to 100% as the number of variables p increases. Can we still trust the 2 principles and what alternative rules can be used to develop test statistics for SEM with “big data”? This article addresses the issues by a large-scale Monte Carlo study. Results indicate that empirical means and standard deviations of each statistic can differ from their expected values many times in standardized units when p is large. Thus, the problems in Type I error control with the 2 statistics are because they do not possess the properties to which they are entitled, not because of the wrongdoing of the mean and mean-and-variance corrections. However, the 2 principles need to be implemented using small sample methodology instead of asymptotics. Results also indicate that distributions other than chi-square might better describe the behavior of test statistics in SEM with big data.
Original languageEnglish (US)
Pages (from-to)214-229
Number of pages16
JournalStructural Equation Modeling
Issue number2
StatePublished - Mar 4 2018
Externally publishedYes


  • adjusted statistic
  • big data
  • chi-square distribution
  • relative multivariate kurtosis
  • rescaled statistic

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Modeling and Simulation
  • Sociology and Political Science
  • Economics, Econometrics and Finance(all)


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