R: Fit Measures for a Latent Variable Model

fitMeasures {lavaan}

R Documentation

Fit Measures for a Latent Variable Model

Description

This function computes a variety of fit measures to assess the global fit of a latent variable model.

Usage

fitMeasures(object, fit.measures = "all",
            baseline.model = NULL, h1.model = NULL,
            fm.args = list(standard.test     = "default",
                           scaled.test       = "default",
                           rmsea.ci.level    = 0.90,
                           rmsea.close.h0    = 0.05,
                           rmsea.notclose.h0 = 0.08,
                           robust            = TRUE,
                           cat.check.pd      = TRUE),
            output = "vector", ...)
fitmeasures(object, fit.measures = "all",
            baseline.model = NULL, h1.model = NULL,
            fm.args = list(standard.test     = "default",
                           scaled.test       = "default",
                           rmsea.ci.level    = 0.90,
                           rmsea.close.h0    = 0.05,
                           rmsea.notclose.h0 = 0.08,
                           robust            = TRUE,
                           cat.check.pd      = TRUE),
            output = "vector", ...)

Arguments

object

An object of class lavaan.

fit.measures

If "all", all fit measures available will be returned. If only a single or a few fit measures are specified by name, only those are computed and returned.

baseline.model

If not NULL, an object of class lavaan, representing a user-specified baseline model. If a baseline model is provided, all fit indices relying on a baseline model (eg. CFI or TLI) will use the test statistics from this user-specified baseline model, instead of the default baseline model.

h1.model

If not NULL, an object of class lavaan, representing a user-specified alternative to the default unrestricted model. If h1.model is provided, all fit indices calculated from chi-squared will use the chi-squared difference test statistics from lavTestLRT, which compare the user-provided h1.model to object.

fm.args

List. Additional options for certain fit measures. The standard.test element determines the main test statistic (chi-square value) that will be used to compute all the fit measures that depend on this test statistic. Usually this is "standard". The scaled.test element determines which scaling method is to be used for the scaled fit measures (in case multiple scaling methods were requested). The rmsea.ci.level element determines the level of the confidence interval for the rmsea value. The rmsea.close.h0 element is the rmsea value that is used under the null hypothesis that rmsea <= rmsea.close.h0. The rmsea.notclose.h0 element is the rmsea value that is used under the null hypothesis that rsmsea >= rmsea.notclose.h0. The robust element can be set to FALSE to avoid computing the so-called robust rmsea/cfi measures (for example if the computations take too long). The cat.check.pd element is only used when data is categorical. If TRUE, robust values for RMSEA and CFI are only computed if the input correlation matrix is positive-definite (for all groups).

output

Character. If "vector" (the default), display the output as a named (lavaan-formatted) vector. If "matrix", display the output as a 1-column matrix. If "text", display the output using subsections and verbose descriptions. The latter is used in the summary output, and does not print the chi-square test by default. In addition, fit.measures should contain the main ingredient (for example "rmsea") if related fit measures are requested (for example "rmsea.ci.lower"). Otherwise, nothing will be printed in that section. See the examples how to add the chi-square test in the text output.

...

Further arguments passed to or from other methods. Not currently used for lavaan objects.

Details

When a scaled (or robust) test statistic is requested (for example, by using test = "satorra.bentler"), the function will also return fit indices based on the scaled chi-square statistic, rather than the standard version. These scaled versions of fit measures, such as CFI and RMSEA, are calculated in the same way as their standard counterparts, with the key difference being that the scaled chi-square statistic is used in place of the regular one. In the output of fitMeasures(), these appear with the .scaled suffix, or in the Scaled column of the summary() output.

However, this substitution-based approach—used in SEM software for many years—has since been shown to be incorrect. Improved versions of robust fit indices have been proposed, offering better theoretical properties. Although still under development and not yet implemented for all estimation settings, these improved robust fit measures are provided when available. They appear with a .robust suffix in the output of fitMeasures(), or in the Scaled column of the summary() output on a row labeled Robust. As a general recommendation, these newer robust versions should be used whenever available, in preference to the older scaled ones. See the references below for more details.

It is also worth noting that, for models involving ordered categorical data, robust fit indices are only computed if the underlying matrix of tetrachoric or polychoric correlations is positive definite. If this condition is not met—which is not uncommon in small samples—the robust measures are reported as NA.

Finally, in some situations (especially when the data contains missing values), computing these robust fit indices may be computationally intensive. To avoid long runtimes, the calculation of robust fit measures can be disabled by setting the robust argument to FALSE in the fm.args list.

Value

A named numeric vector of fit measures.

References

Brosseau-Liard, P. E., Savalei, V., & Li, L. (2012). An investigation of the sample performance of two nonnormality corrections for RMSEA. Multivariate behavioral research, 47(6), 904-930. doi:10.1080/00273171.2012.715252

Brosseau-Liard, P. E., & Savalei, V. (2014). Adjusting incremental fit indices for nonnormality. Multivariate behavioral research, 49(5), 460-470. doi:10.1080/00273171.2014.933697

Savalei, V. (2018). On the computation of the RMSEA and CFI from the mean-and-variance corrected test statistic with nonnormal data in SEM. Multivariate behavioral research, 53(3), 419-429. doi:10.1080/00273171.2018.1455142

Savalei, V. (2021). Improving fit indices in structural equation modeling with categorical data. Multivariate Behavioral Research, 56(3), 390-407. doi:10.1080/00273171.2020.1717922

Savalei, V., Brace, J. C., & Fouladi, R. T. (2023). We need to change how we compute RMSEA for nested model comparisons in structural equation modeling. Psychological Methods. doi:10.1037/met0000537

Zhang, X., & Savalei, V. (2023). New computations for RMSEA and CFI following FIML and TS estimation with missing data. Psychological Methods, 28(2), 263-283. doi:10.1037/met0000445

Examples

HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- cfa(HS.model, data = HolzingerSwineford1939)
fitMeasures(fit)
fitMeasures(fit, "cfi")
fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea"))
fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea"), 
            output = "matrix")
fitMeasures(fit, c("chisq", "df", "pvalue", "cfi", "rmsea"),
            output = "text")

## fit a more restricted model
fit0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE)
## Calculate RMSEA_D (Savalei et al., 2023)
## See https://psycnet.apa.org/doi/10.1037/met0000537
fitMeasures(fit0, "rmsea", h1.model = fit)

[Package lavaan version 0.6-21 Index]