lavaan (version 0.6-19)

lavTestLRT: LRT test

Description

LRT test for comparing (nested) lavaan models.

Usage

lavTestLRT(object, ..., method = "default", test = "default",
           A.method = "delta", scaled.shifted = TRUE,
           type = "Chisq", model.names = NULL)
anova(object, ...)

Value

An object of class anova. When given a single argument, it simply returns the test statistic of this model. When given a sequence of objects, this function tests the models against one another, after reordering the models according to their degrees of freedom.

Arguments

object

An object of class lavaan.

...

additional objects of class lavaan.

method

Character string. The possible options are "satorra.bentler.2001", "satorra.bentler.2010", "satorra.2000", and "standard". See details.

test

Character string specifying which scaled test statistics to use, in case multiple scaled test= options were requested when fitting the model(s). See details.

A.method

Character string. The possible options are "exact" and "delta". This is only used when method = "satorra.2000". It determines how the Jacobian of the constraint function (the matrix A) will be computed. Note that if A.method = "exact", the models must be nested in the parameter sense, while if A.method = "delta", they only need to be nested in the covariance matrix sense.

scaled.shifted

Logical. Only used when method = "satorra.2000". If TRUE, we use a scaled and shifted test statistic; if FALSE, we use a mean and variance adjusted (Satterthwaite style) test statistic.

type

Character. If "Chisq", the test statistic for each model is the (scaled or unscaled) model fit test statistic. If "Cf", the test statistic for each model is computed by the lavTablesFitCf function. If "browne.residual.adf" (alias "browne") or "browne.residual.nt", the standard chi-squared difference is calculated from each model's residual-based statistic.

model.names

Character vector. If provided, use these model names in the first column of the anova table.

Details

The anova function for lavaan objects simply calls the lavTestLRT function, which has a few additional arguments.

The only test= options that currently have actual consequences are "satorra.bentler", "yuan.bentler", or "yuan.bentler.mplus" because "mean.var.adjusted" and "scaled.shifted" are currently distinguished by the scaled.shifted argument. See lavOptions for details about test= options implied by robust estimator= options). The "default" is to select the first available scaled statistic, if any. To check which test(s) were calculated when fitting your model(s), use lavInspect(fit, "options")$test.

If type = "Chisq" and the test statistics are scaled, a special scaled difference test statistic is computed. If method is "satorra.bentler.2001", a simple approximation is used described in Satorra & Bentler (2001). In some settings, this can lead to a negative test statistic. To ensure a positive test statistic, we can use the method proposed by Satorra & Bentler (2010). Alternatively, when method="satorra.2000", the original formulas of Satorra (2000) are used. The latter is used for model comparison, when ... contain additional (nested) models. Even when test statistics are scaled in object or ..., users may request the method="standard" test statistic, without a robust adjustment.

References

Satorra, A. (2000). Scaled and adjusted restricted tests in multi-sample analysis of moment structures. In Heijmans, R.D.H., Pollock, D.S.G. & Satorra, A. (eds.), Innovations in multivariate statistical analysis: A Festschrift for Heinz Neudecker (pp.233-247). London, UK: Kluwer Academic Publishers.

Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66(4), 507-514. tools:::Rd_expr_doi("10.1007/BF02296192")

Satorra, A., & Bentler, P. M. (2010). Ensuring postiveness of the scaled difference chi-square test statistic. Psychometrika, 75(2), 243-248. tools:::Rd_expr_doi("10.1007/s11336-009-9135-y")

Examples

HS.model <- '
    visual  =~ x1 + b1*x2 + x3
    textual =~ x4 + b2*x5 + x6
    speed   =~ x7 + b3*x8 + x9
'
fit1 <- cfa(HS.model, data = HolzingerSwineford1939)
fit0 <- cfa(HS.model, data = HolzingerSwineford1939, 
            orthogonal = TRUE)
lavTestLRT(fit1, fit0)


## When multiple test statistics are selected when the model is fitted,
## use the type= and test= arguments to select a test for comparison.

## refit models, requesting 6 test statistics (in addition to "standard")
t6.1 <- cfa(HS.model, data = HolzingerSwineford1939,
            test = c("browne.residual.adf","scaled.shifted","mean.var.adjusted",
                     "satorra.bentler", "yuan.bentler", "yuan.bentler.mplus"))
t6.0 <- cfa(HS.model, data = HolzingerSwineford1939, orthogonal = TRUE,
            test = c("browne.residual.adf","scaled.shifted","mean.var.adjusted",
                     "satorra.bentler", "yuan.bentler", "yuan.bentler.mplus"))

## By default (test="default", type="Chisq"), the first scaled statistic
## requested will be used. Here, that is "scaled.shifted"
lavTestLRT(t6.1, t6.0)
## But even if "satorra.bentler" were requested first, method="satorra.2000"
## provides the scaled-shifted chi-squared difference test:
lavTestLRT(t6.1, t6.0, method = "satorra.2000")
## == lavTestLRT(update(t6.1, test = "scaled.shifted"), update(t6.0, test = "scaled.shifted"))

## The mean- and variance-adjusted (Satterthwaite) statistic implies
## scaled.shifted = FALSE
lavTestLRT(t6.1, t6.0, method = "satorra.2000", scaled.shifted = FALSE)

## Because "satorra.bentler" is not the first scaled test in the list,
## we MUST request it explicitly:
lavTestLRT(t6.1, t6.0, test = "satorra.bentler") # method="satorra.bentler.2001"
## == lavTestLRT(update(t6.1, test = "satorra.bentler"),
##               update(t6.0, test = "satorra.bentler"))
## The "strictly-positive test" is necessary when the above test is < 0:
lavTestLRT(t6.1, t6.0, test = "satorra.bentler", method = "satorra.bentler.2010")

## Likewise, other scaled statistics can be selected:
lavTestLRT(t6.1, t6.0, test = "yuan.bentler")
## == lavTestLRT(update(t6.1, test = "yuan.bentler"),
##               update(t6.0, test = "yuan.bentler"))
lavTestLRT(t6.1, t6.0, test = "yuan.bentler.mplus")
## == lavTestLRT(update(t6.1, test = "yuan.bentler.mplus"),
##               update(t6.0, test = "yuan.bentler.mplus"))

## To request the difference between Browne's (1984) residual-based statistics,
## rather than statistics based on the fitted model's discrepancy function,
## use the type= argument:
lavTestLRT(t6.1, t6.0, type = "browne.residual.adf")

## Despite requesting multiple robust tests, it is still possible to obtain
## the standard chi-squared difference test (i.e., without a robust correction)
lavTestLRT(t6.1, t6.0, method = "standard")
## == lavTestLRT(update(t6.1, test = "standard"), update(t6.0, test = "standard"))