Qual Quant (2012) 46:1547–1570
Testing structural equation models: the impact of error
variances in the data generating process
Randi Hammervold · Ulf Henning Olsson
Published online: 23 March 2011
© Springer Science+Business Media B.V. 2011
Abstract Yet another paper on ﬁt measures? To our knowledge, very few papers discuss
how ﬁt measures are affected by error variance in the Data Generating Process (DGP). The
present paper deals with this. Based upon an extensive simulation study, this paper shows
that the effects of increased error variance differ significantly for various ﬁt measures. In
addition to error variance the effects depend on sample size and severity of misspeciﬁcation.
The ﬁndings conﬁrm the general notion that good ﬁt as measured by the chi-square, RMSEA
and GFI etc. does not necessarily mean that the model is correctly speciﬁed and reliable.
One ﬁnding is that the chi square test may give support to misspeciﬁed models in situations
with a high level of error variance in the DGP, for small sample sizes. Another ﬁnding is
that the chi-square test looses power also for large sample sizes when the model is negligible
misspeciﬁed. Other results include incremental ﬁt indices as NFI and RFI which prove to be
more informative indicators under these circumstances. At the end of the paper we formulate
some guidelines for use of different ﬁt measures.
Keywords Fit measures · Error variance · Structural equation modeling · Chi-square test
A continuous stride has been fought between different researcher communities on the use
and interpretation of ﬁt indices. It is obvious that this is a difﬁcult issue. Our contribution will
focus on the indices RMSEA, GFI, NFI, RFI, CFI and SRMR, in addition to the chi-square
statistics, and on a speciﬁc source of “noise in the data”, namely variance in the error term.
Two important questions regarding what constitutes a good index (Bollen and Long 1993)
R. Hammervold (
Trondheim Business School, Sør-Trøndelag University College, 7004 Trondheim, Norway
U. H. Olsson
Norwegian School of Management, BI, 0442 Oslo, Norway