# nullRMSEA: Calculate the RMSEA of the null model In semTools: Useful Tools for Structural Equation Modeling

## Description

Calculate the RMSEA of the null (baseline) model

## Usage

 1 nullRMSEA(object, scaled = FALSE, silent = FALSE) 

## Arguments

 object The lavaan model object provided after running the cfa, sem, growth, or lavaan functions. scaled If TRUE, the scaled (or robust, if available) RMSEA is returned. Ignored if a robust test statistic was not requested. silent If TRUE, do not print anything on the screen.

## Details

RMSEA of the null model is calculated similar to the formula provided in the lavaan package. The standard formula of RMSEA is

RMSEA =√{\frac{χ^2}{N \times df} - \frac{1}{N}} \times √{G}

where χ^2 is the chi-square test statistic value of the target model, N is the total sample size, df is the degree of freedom of the hypothesized model, G is the number of groups. Kenny proposed in his website that

"A reasonable rule of thumb is to examine the RMSEA for the null model and make sure that is no smaller than 0.158. An RMSEA for the model of 0.05 and a TLI of .90, implies that the RMSEA of the null model is 0.158. If the RMSEA for the null model is less than 0.158, an incremental measure of fit may not be that informative."

## Value

A value of RMSEA of the null model (a numeric vector) returned invisibly.

## Author(s)

Ruben Arslan (Humboldt-University of Berlin, rubenarslan@gmail.com)

Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)

## References

Kenny, D. A., Kaniskan, B., & McCoach, D. B. (2015). The performance of RMSEA in models with small degrees of freedom. Sociological Methods Research, 44(3), 486–507. doi: 10.1177/0049124114543236

• miPowerFit For the modification indices and their power approach for model fit evaluation
• moreFitIndices For other fit indices
 1 2 3 4 5 6 HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) nullRMSEA(fit)