Wald test for testing a linear hypothesis about the parameters of lavaan models fitted to multiple imputed data sets. Statistics for constraining one or more free parameters in a model can be calculated from the pooled point estimates and asymptotic covariance matrix of model parameters using Rubin's (1987) rules, or by pooling the Wald test statistics across imputed data sets (Li, Meng, Raghunathan, & Rubin, 1991).
lavTestWald.mi(object, constraints = NULL, test = c("D1","D2"),
asymptotic = FALSE, scale.W = !asymptotic,
omit.imps = c("no.conv","no.se"),
verbose = FALSE, warn = TRUE)A vector containing the Wald test statistic (either an F or
\(\chi^2\) statistic, depending on the asymptotic argument),
the degrees of freedom (numerator and denominator, if
asymptotic = FALSE), and a p value. If
asymptotic = FALSE, the relative invrease in variance (RIV, or
average for multiparameter tests: ARIV) used to calculate the denominator
df is also returned as a missing-data diagnostic, along with the
fraction missing information (FMI = ARIV / (1 + ARIV)).
An object of class OLDlavaan.mi.
A character string (typically between single
quotes) containing one or more equality constraints.
See examples for more details
character indicating which pooling method to use.
"D1" or "Rubin" (default) indicates Rubin's (1987) rules
will be applied to the point estimates and the asymptotic covariance
matrix of model parameters, and those pooled values will be used to
calculate the Wald test in the usual manner. "D2", "LMRR",
or "Li.et.al" indicate that the complete-data Wald test statistic
should be calculated using each imputed data set, which will then be
pooled across imputations, as described in Li, Meng, Raghunathan, & Rubin
(1991) and Enders (2010, chapter 8).
logical. If FALSE (default), the pooled test
will be returned as an F-distributed statistic with numerator
(df1) and denominator (df2) degrees of freedom.
If TRUE, the pooled F statistic will be multiplied by its
df1 on the assumption that its df2 is sufficiently large
enough that the statistic will be asymptotically \(\chi^2\) distributed
with df1.
logical. If FALSE, the pooled
asymptotic covariance matrix of model parameters is calculated as the
weighted sum of the within-imputation and between-imputation components.
Otherwise, the pooled asymptotic covariance matrix of model parameters is
calculated by scaling the within-imputation component by the
average relative increase in variance (ARIV; see Enders, 2010, p. 235),
which is only consistent when requesting the F test (i.e.,
asymptotic = FALSE. Ignored (irrelevant) if test = "D2".
character vector specifying criteria for omitting
imputations from pooled results. Can include any of
c("no.conv", "no.se", "no.npd"), the first 2 of which are the
default setting, which excludes any imputations that did not
converge or for which standard errors could not be computed. The
last option ("no.npd") would exclude any imputations which
yielded a nonpositive definite covariance matrix for observed or
latent variables, which would include any "improper solutions" such
as Heywood cases. Specific imputation numbers can also be included in this
argument, in case users want to apply their own custom omission criteria
(or simulations can use different numbers of imputations without
redundantly refitting the model).
logical. If TRUE, print the restriction
matrix and the estimated restricted values.
logical. If TRUE, print warnings if they occur.
Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)
Adapted from lavaan source code, written by Yves Rosseel (Ghent University; Yves.Rosseel@UGent.be)
The constraints are specified using the "==" operator.
Both the left-hand side and the right-hand side of the equality can contain
a linear combination of model parameters, or a constant (like zero).
The model parameters must be specified by their user-specified labels from
the link[lavaan]{model.syntax}. Names of defined parameters
(using the ":=" operator) can be included too.
Enders, C. K. (2010). Applied missing data analysis. New York, NY: Guilford.
Li, K.-H., Meng, X.-L., Raghunathan, T. E., & Rubin, D. B. (1991). Significance levels from repeated p-values with multiply-imputed data. Statistica Sinica, 1(1), 65--92. Retrieved from https://www.jstor.org/stable/24303994
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York, NY: Wiley.
lavaan::lavTestWald()
semTools-deprecated()
## See the new lavaan.mi package
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