RMSEA value in anova and lavTestLRT function

[羅孟婷]

Hi lavaan group,

I found out that outputs from the anova and lavTestLRT function produce a "RMSEA" value 0.10573 (see below graphs), but was not able to locate information to explain what that is. I check my output, it is not the point estimate of RMSEA nor the upper or lower bound of 90% CI. 

Does anyone know what it is? Thanks!

[Shu Fai Cheung]

I believe it is simply RMSEA computed using the chi-square difference and model df difference:

library(lavaan)
#> This is lavaan 0.6-14
#> lavaan is FREE software! Please report any bugs.

# Adapted the example of cfa()
HS.model.1 <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '
fit.1 <- cfa(HS.model.1, data = HolzingerSwineford1939)
HS.model.2 <- ' visual  =~ x1 + x2 + x3
                textual =~ x4 + x5 + x6
                speed   =~ x7 + x8 + x9
                visual ~~ 0 * textual + 0 * speed
                textual ~~ 0 * speed'
fit.2 <- cfa(HS.model.2, data = HolzingerSwineford1939)

(lrt <- lavTestLRT(fit.2, fit.1))
#>
#> Chi-Squared Difference Test
#>
#>       Df    AIC    BIC   Chisq Chisq diff   RMSEA Df diff Pr(>Chisq)    
#> fit.1 24 7517.5 7595.3  85.305                                          
#> fit.2 27 7579.7 7646.4 153.527     68.222 0.26875       3  1.026e-14 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Compute RMSEA using Chi-square difference and the df difference
rmsea_self <- sqrt(((lrt[2, "Chisq"] - lrt[1, "Chisq"]) - 3) / (3 * nobs(fit.2)))
rmsea_self
#> [1] 0.268752

# The RMSEA from the output of lavTestLRT()
rmsea_lrt <- lrt[2, "RMSEA"]
rmsea_lrt
#> [1] 0.268752

# Check if they are the same
all.equal(rmsea_self, rmsea_lrt)
#> [1] TRUE

This is a new measure introduced in 0.6-13 (https://lavaan.ugent.be/history/dot6.html).

Also see:

https://github.com/yrosseel/lavaan/blob/a9a9088c7a7b59b6941d0f67d8f975a7e0b07f41/R/lav_test_LRT.R#L13

How it was computed:

https://github.com/yrosseel/lavaan/blob/a9a9088c7a7b59b6941d0f67d8f975a7e0b07f41/R/lav_test_LRT.R#L218-L220

Hope this helps.

Regards,

Shu Fai Cheung (張樹輝)

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[羅孟婷]

This is extremely helpful!!! Thank you for providing relevant resources as well. 

shufai...@gmail.com 在 2023年3月10日 星期五上午8:10:07 [UTC+8] 的信中寫道：

[Terrence Jorgensen]

Savalei, V., Brace, J. C., & Fouladi, R. T. (2023). We need to change how we compute RMSEA for nested model comparisons in structural equation modeling. Psychological Methods. https://doi.org/10.1037/met0000537

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Shu Fai Cheung (張樹輝)]

Thanks a lot for the reference!

-- Shu Fai

[羅孟婷]

Thanks!

Shu Fai Cheung (張樹輝) <shufai...@gmail.com> 於 2023年3月14日 週二 下午9:45寫道：

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