% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/interpret_cfa_fit.R
\name{interpret_gfi}
\alias{interpret_gfi}
\alias{interpret_agfi}
\alias{interpret_nfi}
\alias{interpret_nnfi}
\alias{interpret_cfi}
\alias{interpret_rfi}
\alias{interpret_ifi}
\alias{interpret_pnfi}
\alias{interpret_rmsea}
\alias{interpret_srmr}
\alias{interpret.lavaan}
\alias{interpret.performance_lavaan}
\title{Interpret of CFA / SEM Indices of Goodness of Fit}
\usage{
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")

\method{interpret}{lavaan}(x, ...)

\method{interpret}{performance_lavaan}(x, ...)
}
\arguments{
\item{x}{vector of values, or an object of class \code{lavaan}.}

\item{rules}{Can be the name of a set of rules (see below) or custom set of
\code{\link[=rules]{rules()}}.}

\item{...}{Currently not used.}
}
\description{
Interpretation of indices of fit found in confirmatory analysis or structural
equation modelling, such as RMSEA, CFI, NFI, IFI, etc.
}
\details{
\subsection{Indices of fit}{
\itemize{
\item \strong{Chisq}: The model Chi-squared assesses overall fit and the discrepancy
between the sample and fitted covariance matrices. Its p-value should be >
.05 (i.e., the hypothesis of a perfect fit cannot be rejected). However, it
is quite sensitive to sample size.
\item \strong{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;
\code{"byrne1994"}).
\item \strong{NFI/NNFI/TLI}: The (Non) Normed Fit Index. An NFI of 0.95, indicates the
model of interest improves the fit by 95\\% relative to the null model. The
NNFI (also called the Tucker Lewis index; TLI) is preferable for smaller
samples. They should be > .90 (Byrne, 1994; \code{"byrne1994"}) or > .95
(Schumacker & Lomax, 2004; \code{"schumacker2004"}).
\item \strong{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; \code{"hu&bentler1999"}) or .90 (Byrne, 1994; \code{"byrne1994"}).
\item \strong{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.
\item \strong{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.
\item \strong{PNFI}: the Parsimony-Adjusted Measures Index. There is no commonly
agreed-upon cutoff value for an acceptable model for this index. Should be >
0.50.
\item \strong{RMSEA}: The Root Mean Square Error of Approximation is a
parsimony-adjusted index. Values closer to 0 represent a good fit. It should
be < .08 (Awang, 2012; \code{"awang2012"}) or < .05 (Byrne, 1994; \code{"byrne1994"}).
The p-value 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.
\item \strong{RMR/SRMR}: the (Standardized) Root Mean Square Residual represents the
square-root 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; \code{"byrne1994"}).
}

See the documentation for \code{\link[lavaan:fitmeasures]{fitmeasures()}}.
}

\subsection{What to report}{

For structural equation models (SEM), Kline (2015) suggests that at a minimum
the following indices should be reported: The model \strong{chi-square}, the
\strong{RMSEA}, the \strong{CFI} and the \strong{SRMR}.
}
}
\note{
When possible, it is recommended to report dynamic cutoffs of fit
indices. See https://dynamicfit.app/cfa/.
}
\examples{
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))

\dontshow{if (require("lavaan") && interactive()) withAutoprint(\{ # examplesIf}
# Structural Equation Models (SEM)
structure <- " ind60 =~ x1 + x2 + x3
               dem60 =~ y1 + y2 + y3
               dem60 ~ ind60 "

model <- lavaan::sem(structure, data = lavaan::PoliticalDemocracy)

interpret(model)
\dontshow{\}) # examplesIf}
}
\references{
\itemize{
\item Awang, Z. (2012). A handbook on SEM. Structural equation modeling.
\item Byrne, B. M. (1994). Structural equation modeling with EQS and EQS/Windows.
Thousand Oaks, CA: Sage Publications.
\item 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, 56-83.
\item 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), 1-55.
\item Kline, R. B. (2015). Principles and practice of structural equation
modeling. Guilford publications.
\item Schumacker, R. E., and Lomax, R. G. (2004). A beginner's guide to
structural equation modeling, Second edition. Mahwah, NJ: Lawrence Erlbaum
Associates.
\item Tucker, L. R., and Lewis, C. (1973). The reliability coefficient for
maximum likelihood factor analysis. Psychometrika, 38, 1-10.
}
}
\keyword{interpreters}
