View source: R/interpret_cfa_fit.R
interpret_gfi  R Documentation 
Interpretation of indices of fit found in confirmatory analysis or structural equation modelling, such as RMSEA, CFI, NFI, IFI, etc.
interpret_gfi(x, rules = "byrne1994")
interpret_agfi(x, rules = "byrne1994")
interpret_nfi(x, rules = "byrne1994")
interpret_nnfi(x, rules = "byrne1994")
interpret_cfi(x, rules = "byrne1994")
interpret_rfi(x, rules = "default")
interpret_ifi(x, rules = "default")
interpret_pnfi(x, rules = "default")
interpret_rmsea(x, rules = "byrne1994")
interpret_srmr(x, rules = "byrne1994")
## S3 method for class 'lavaan'
interpret(x, ...)
## S3 method for class 'performance_lavaan'
interpret(x, ...)
x 
vector of values, or an object of class 
rules 
Can be the name of a set of rules (see below) or custom set of

... 
Currently not used. 
Chisq: The model Chisquared assesses overall fit and the discrepancy between the sample and fitted covariance matrices. Its pvalue should be > .05 (i.e., the hypothesis of a perfect fit cannot be rejected). However, it is quite sensitive to sample size.
GFI/AGFI: The (Adjusted) Goodness of Fit is the proportion of variance
accounted for by the estimated population covariance. Analogous to R2. The
GFI and the AGFI should be > .95 and > .90, respectively (Byrne, 1994;
"byrne1994"
).
NFI/NNFI/TLI: The (Non) Normed Fit Index. An NFI of 0.95, indicates the
model of interest improves the fit by 95\
NNFI (also called the Tucker Lewis index; TLI) is preferable for smaller
samples. They should be > .90 (Byrne, 1994; "byrne1994"
) or > .95
(Schumacker & Lomax, 2004; "schumacker2004"
).
CFI: The Comparative Fit Index is a revised form of NFI. Not very
sensitive to sample size (Fan, Thompson, & Wang, 1999). Compares the fit of a
target model to the fit of an independent, or null, model. It should be > .96
(Hu & Bentler, 1999; "hu&bentler1999"
) or .90 (Byrne, 1994; "byrne1994"
).
RFI: the Relative Fit Index, also known as RHO1, is not guaranteed to vary from 0 to 1. However, RFI close to 1 indicates a good fit.
IFI: the Incremental Fit Index (IFI) adjusts the Normed Fit Index (NFI) for sample size and degrees of freedom (Bollen's, 1989). Over 0.90 is a good fit, but the index can exceed 1.
PNFI: the ParsimonyAdjusted Measures Index. There is no commonly agreedupon cutoff value for an acceptable model for this index. Should be > 0.50.
RMSEA: The Root Mean Square Error of Approximation is a
parsimonyadjusted index. Values closer to 0 represent a good fit. It should
be < .08 (Awang, 2012; "awang2012"
) or < .05 (Byrne, 1994; "byrne1994"
).
The pvalue printed with it tests the hypothesis that RMSEA is less than or
equal to .05 (a cutoff sometimes used for good fit), and thus should be not
significant.
RMR/SRMR: the (Standardized) Root Mean Square Residual represents the
squareroot of the difference between the residuals of the sample covariance
matrix and the hypothesized model. As the RMR can be sometimes hard to
interpret, better to use SRMR. Should be < .08 (Byrne, 1994; "byrne1994"
).
See the documentation for fitmeasures()
.
For structural equation models (SEM), Kline (2015) suggests that at a minimum the following indices should be reported: The model chisquare, the RMSEA, the CFI and the SRMR.
When possible, it is recommended to report dynamic cutoffs of fit indices. See https://dynamicfit.app/cfa/.
Awang, Z. (2012). A handbook on SEM. Structural equation modeling.
Byrne, B. M. (1994). Structural equation modeling with EQS and EQS/Windows. Thousand Oaks, CA: Sage Publications.
Fan, X., B. Thompson, and L. Wang (1999). Effects of sample size, estimation method, and model specification on structural equation modeling fit indexes. Structural Equation Modeling, 6, 5683.
Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 155.
Kline, R. B. (2015). Principles and practice of structural equation modeling. Guilford publications.
Schumacker, R. E., and Lomax, R. G. (2004). A beginner's guide to structural equation modeling, Second edition. Mahwah, NJ: Lawrence Erlbaum Associates.
Tucker, L. R., and Lewis, C. (1973). The reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 110.
interpret_gfi(c(.5, .99))
interpret_agfi(c(.5, .99))
interpret_nfi(c(.5, .99))
interpret_nnfi(c(.5, .99))
interpret_cfi(c(.5, .99))
interpret_rmsea(c(.07, .04))
interpret_srmr(c(.5, .99))
interpret_rfi(c(.5, .99))
interpret_ifi(c(.5, .99))
interpret_pnfi(c(.5, .99))
# Structural Equation Models (SEM)
structure < " ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3
dem60 ~ ind60 "
model < lavaan::sem(structure, data = lavaan::PoliticalDemocracy)
interpret(model)
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