moreFitIndices | R Documentation |
Calculate more fit indices that are not already provided in lavaan.
moreFitIndices(object, fit.measures = "all", nPrior = 1)
object |
The lavaan model object provided after running the |
fit.measures |
Additional fit measures to be calculated. All additional fit measures are calculated by default |
nPrior |
The sample size on which prior is based. This argument is used
to compute |
See nullRMSEA
for the further details of the computation of
RMSEA of the null model.
Gamma-Hat (gammaHat
; West, Taylor, & Wu, 2012) is a global
goodness-of-fit index which can be computed (assuming equal number of
indicators across groups) by
\hat{Γ} =\frac{p}{p + 2 \times \frac{χ^{2}_{k} - df_{k}}{N}},
where p is the number of variables in the model, χ^{2}_{k} is
the χ^2 test statistic value of the target model, df_{k} is
the degree of freedom when fitting the target model, and N is the
sample size (or sample size minus the number of groups if mimic
is
set to "EQS"
).
Adjusted Gamma-Hat (adjGammaHat
; West, Taylor, & Wu, 2012) is a
global fit index which can be computed by
\hat{Γ}_\textrm{adj} = ≤ft(1 - \frac{K \times p \times (p + 1)}{2 \times df_{k}} \right) \times ≤ft( 1 - \hat{Γ} \right),
where K is the number of groups (please refer to Dudgeon, 2004, for
the multiple-group adjustment for adjGammaHat
).
The remaining indices are information criteria calculated using the
object
's -2 \times log-likelihood, abbreviated -2LL.
Corrected Akaike Information Criterion (aic.smallN
; Burnham &
Anderson, 2003) is a corrected version of AIC for small sample size, often
abbreviated AICc:
\textrm{AIC}_{\textrm{small}-N} = AIC + \frac{2q(q + 1)}{N - q - 1},
where AIC is the original AIC: -2LL + 2q (where q = the number of estimated parameters in the target model). Note that AICc is a small-sample correction derived for univariate regression models, so it is probably not appropriate for comparing SEMs.
Corrected Bayesian Information Criterion (bic.priorN
; Kuha, 2004) is
similar to BIC but explicitly specifying the sample size on which the prior
is based (N_{prior}) using the nPrior
argument.
\textrm{BIC}_{\textrm{prior}-N} = -2LL + q\log{( 1 + \frac{N}{N_{prior}} )}.
Bollen et al. (2014) discussed additional BICs that incorporate more terms from a Taylor series expansion, which the standard BIC drops. The "Scaled Unit-Information Prior" BIC is calculated depending on whether the product of the vector of estimated model parameters (\hat{θ}) and the observed information matrix (FIM) exceeds the number of estimated model parameters (Case 1) or not (Case 2), which is checked internally:
\textrm{SPBIC}_{\textrm{Case 1}} = -2LL + q(1 - \frac{q}{\hat{θ}^{'} \textrm{FIM} \hat{θ}}), or
\textrm{SPBIC}_{\textrm{Case 2}} = -2LL + \hat{θ}^{'} \textrm{FIM} \hat{θ},
Bollen et al. (2014) credit the HBIC to Haughton (1988):
\textrm{HBIC}_{\textrm{Case 1}} = -2LL - q\log{2 \times π},
and proposes the information-matrix-based BIC by adding another term:
\textrm{IBIC}_{\textrm{Case 1}} = -2LL - q\log{2 \times π} - \log{\det{\textrm{ACOV}}},
Stochastic information criterion (SIC; see Preacher, 2006, for details) is similar to IBIC but does not subtract the term q\log{2 \times π} that is also in HBIC. SIC and IBIC account for model complexity in a model's functional form, not merely the number of free parameters. The SIC can be computed by
\textrm{SIC} = -2LL + \log{\det{\textrm{FIM}^{-1}}} = -2LL - \log{\det{\textrm{ACOV}}},
where the inverse of FIM is the asymptotic sampling covariance matrix (ACOV).
Hannan–Quinn Information Criterion (HQC; Hannan & Quinn, 1979) is used for model selection, similar to AIC or BIC.
\textrm{HQC} = -2LL + 2k\log{(\log{N})},
Note that if Satorra–Bentler's or Yuan–Bentler's method is used, the fit indices using the scaled χ^2 values are also provided.
A numeric
lavaan.vector
including any of the
following requested via fit.measures=
gammaHat
: Gamma-Hat
adjGammaHat
: Adjusted Gamma-Hat
baseline.rmsea
: RMSEA of the default baseline (i.e., independence) model
gammaHat.scaled
: Gamma-Hat using scaled χ^2
adjGammaHat.scaled
: Adjusted Gamma-Hat using scaled χ^2
baseline.rmsea.scaled
: RMSEA of the default baseline (i.e.,
independence) model using scaled χ^2
aic.smallN
: Corrected (for small sample size) AIC
bic.priorN
: BIC with specified prior sample size
spbic
: Scaled Unit-Information Prior BIC (SPBIC)
hbic
: Haughton's BIC (HBIC)
ibic
: Information-matrix-based BIC (IBIC)
sic
: Stochastic Information Criterion (SIC)
hqc
: Hannan-Quinn Information Criterion (HQC)
Sunthud Pornprasertmanit (psunthud@gmail.com)
Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)
Aaron Boulton (University of Delaware)
Ruben Arslan (Humboldt-University of Berlin, rubenarslan@gmail.com)
Yves Rosseel (Ghent University; Yves.Rosseel@UGent.be)
Bollen, K. A., Ray, S., Zavisca, J., & Harden, J. J. (2012). A comparison of Bayes factor approximation methods including two new methods. Sociological Methods & Research, 41(2), 294–324. doi: 10.1177/0049124112452393
Burnham, K., & Anderson, D. (2003). Model selection and multimodel inference: A practical–theoretic approach. New York, NY: Springer–Verlag.
Dudgeon, P. (2004). A note on extending Steiger's (1998) multiple sample RMSEA adjustment to other noncentrality parameter-based statistic. Structural Equation Modeling, 11(3), 305–319. doi: 10.1207/s15328007sem1103_1
Kuha, J. (2004). AIC and BIC: Comparisons of assumptions and performance. Sociological Methods Research, 33(2), 188–229. doi: 10.1177/0049124103262065
Preacher, K. J. (2006). Quantifying parsimony in structural equation modeling. Multivariate Behavioral Research, 43(3), 227-259. doi: 10.1207/s15327906mbr4103_1
West, S. G., Taylor, A. B., & Wu, W. (2012). Model fit and model selection in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 209–231). New York, NY: Guilford.
miPowerFit
For the modification indices and their
power approach for model fit evaluation
nullRMSEA
For RMSEA of the default independence model
HS.model <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit <- cfa(HS.model, data = HolzingerSwineford1939) moreFitIndices(fit) fit2 <- cfa(HS.model, data = HolzingerSwineford1939, estimator = "mlr") moreFitIndices(fit2)
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