semTools (version 0.5-1)

chisqSmallN: k-factor correction for \(chi^2\) test statistic

Description

Calculate k-factor correction for \(chi^2\) model-fit test statistic to adjust for small sample size.

Usage

chisqSmallN(fit0, fit1 = NULL, ...)

Arguments

fit0

The lavaan model object provided after running the cfa, sem, growth, or lavaan functions.

fit1

Optional additional '>lavaan model, in which fit0 is nested. If fit0 has fewer df than fit1, the models will be swapped, still on the assumption that they are nested.

…

Additional arguments to the lavTestLRT function.

Value

A numeric vector including the unadjusted (naive) chi-squared test statistic, the k-factor correction, the corrected test statistic, the df for the test, and the p value for the test under the null hypothesis that the model fits perfectly (or that the 2 models have equivalent fit).

Details

The k-factor correction (Nevitt & Hancock, 2004) is a global fit index which can be computed by:

$$ kc = 1 - \frac{2 \times P + 4 \times K + 5}{6 \times N}$$

where \(N\) is the sample size when using normal likelihood, or \(N - 1\) when using likelihood = 'wishart'.

References

Nevitt, J., & Hancock, G. R. (2004). Evaluating small sample approaches for model test statistics in structural equation modeling. Multivariate Behavioral Research, 39(3), 439--478. doi:10.1207/S15327906MBR3903_3

Examples

# NOT RUN {
HS.model <- '
    visual  =~ x1 + b1*x2 + x3
    textual =~ x4 + b2*x5 + x6
    speed   =~ x7 + b3*x8 + x9
'
fit1 <- cfa(HS.model, data = HolzingerSwineford1939)
## test a single model (implicitly compared to a saturated model)
chisqSmallN(fit1)

## fit a more constrained model
fit0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE)
## compare 2 models
chisqSmallN(fit1, fit0)

# }