RMSEA 90% CI

[Michael Filsecker]

hi there! A simple question: why does lavaan report RMSEA CI at the 90% and not at the 95%? Any particular reason for that?

Thank you!

Michael.

[Edward Rigdon]

Is tradition. Why use 95%? Is tradition.

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[Terrence Jorgensen]

why does lavaan report RMSEA CI at the 90% and not at the 95%? 

A hypothesis of (not-)close fit is a directional hypothesis.  

• H0: ε < .05 (close fit)
• H0: ε > .05 (not-close fit)

A two-tailed test with alpha = .10 has the same tail probabilities / critical values as a one-tailed test in either direction.  So the 2 confidence limits of a two-tailed 90% CI give you the single 95% confidence limit for either test (close or not-close fit).  

MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1(2), 130–149. https://doi.org/10.1037/1082-989X.1.2.130

MacCallum, R. C., Browne, M. W., & Cai, L. (2006). Testing differences between nested covariance structure models: Power analysis and null hypotheses. Psychological Methods, 11(1), 19–35. https://doi.org/10.1037/1082-989X.11.1.19

The same is provided for CRMR or SRMR from lavResiduals(), although it is not explicitly labeled as 90%.  The unbiased estimates (e.g., usrmr) are also provided.

Maydeu-Olivares, A. (2017). Assessing the size of model misfit in structural equation models. Psychometrika, 82(3), 533–558. https://doi.org/10.1007/s11336-016-9552-7

If you want a different alpha / confidence level, then you can set it with lavaan::fitMeasures(..., fm=)

> HS.model <- ' visual  =~ x1 + x2 + x3
+               textual =~ x4 + x5 + x6
+               speed   =~ x7 + x8 + x9 '
>
> fit <- cfa(HS.model, data=HolzingerSwineford1939)
> fitMeasures(fit, c("rmsea","rmsea.ci.lower","rmsea.ci.upper"))
         rmsea rmsea.ci.lower rmsea.ci.upper
         0.092          0.071          0.114
> ## for 99% confidence, request a 98% CI
> fitMeasures(fit, c("rmsea","rmsea.ci.lower","rmsea.ci.upper"),

>             fm = list(rmsea.ci.level = 0.98))
         rmsea rmsea.ci.lower rmsea.ci.upper
         0.092          0.062          0.122 

The p values can also be determined for a designated H0, using the fm= elements shown on the ?fitMeasures help page.  I don't think you can request different alpha / confidence level from lavResiduals(),  but it is a normal-theory CI, so it would be easy to construct it yourself from the SE provided. 

Terrence D. Jorgensen    (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen

 

[Michael Filsecker]

Dear Prof. Jorgensen,

thank you very, very much for your awesome reponse!

Have a good day,

Michael.