lavaan.mi-class: Class for a lavaan Model Fitted to Multiple Imputations

Description

This class extends the lavaan::lavaanList class, created by fitting a lavaan model to a list of data sets. In this case, the list of data sets are multiple imputations of missing data.

Usage

# S4 method for lavaan.mi
show(object)
# S4 method for lavaan.mi
summary(
  object,
  header = TRUE,
  fit.measures = FALSE,
  fm.args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level =
    0.9, rmsea.h0.closefit = 0.05, rmsea.h0.notclosefit = 0.08, robust = TRUE,
    cat.check.pd = TRUE),
  estimates = TRUE,
  ci = FALSE,
  standardized = FALSE,
  std = standardized,
  cov.std = TRUE,
  rsquare = FALSE,
  fmi = FALSE,
  asymptotic = FALSE,
  scale.W = !asymptotic,
  omit.imps = c("no.conv", "no.se"),
  remove.unused = TRUE,
  modindices = FALSE,
  nd = 3L,
  ...
)
# S4 method for lavaan.mi
nobs(object, total = TRUE)
# S4 method for lavaan.mi
coef(object, type = "free", labels = TRUE, omit.imps = c("no.conv", "no.se"))
# S4 method for lavaan.mi
vcov(
  object,
  type = c("pooled", "between", "within", "ariv"),
  scale.W = TRUE,
  omit.imps = c("no.conv", "no.se")
)
# S4 method for lavaan.mi
fitted(object, omit.imps = c("no.conv", "no.se"))
# S4 method for lavaan.mi
fitted.values(object, omit.imps = c("no.conv", "no.se"))
# S4 method for lavaan.mi
fitMeasures(
  object,
  fit.measures = "all",
  baseline.model = NULL,
  h1.model = NULL,
  fm.args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level =
    0.9, rmsea.h0.closefit = 0.05, rmsea.h0.notclosefit = 0.08, robust = 0.08,
    cat.check.pd = TRUE),
  output = "vector",
  omit.imps = c("no.conv", "no.se"),
  ...
)
# S4 method for lavaan.mi
fitmeasures(
  object,
  fit.measures = "all",
  baseline.model = NULL,
  h1.model = NULL,
  fm.args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level =
    0.9, rmsea.h0.closefit = 0.05, rmsea.h0.notclosefit = 0.08, robust = 0.08,
    cat.check.pd = TRUE),
  output = "vector",
  omit.imps = c("no.conv", "no.se"),
  ...
)

Value

coef: signature(object = "lavaan.mi", type = "free", labels = TRUE, omit.imps = c("no.conv","no.se")): See argument description on the help page for lavaan::lavaan class. Returns the pooled point estimates (i.e., averaged across imputed data sets; see Rubin, 1987).
vcov: signature(object = "lavaan.mi", scale.W = TRUE, omit.imps = c("no.conv","no.se"), type = c("pooled","between","within","ariv")): By default, returns the pooled covariance matrix of parameter estimates (type = "pooled"), the within-imputations covariance matrix (type = "within"), the between-imputations covariance matrix (type = "between"), or the average relative increase in variance (type = "ariv") due to missing data.
fitted.values: signature(object = "lavaan.mi", omit.imps = c("no.conv","no.se")): See corresponding lavaan::lavaan method. Returns model-implied moments, evaluated at the pooled point estimates.
fitted: alias for fitted.values
nobs: signature(object = "lavaan.mi", total = TRUE): either the total (default) sample size or a vector of group sample sizes (total = FALSE).
fitMeasures: signature(object = "lavaan.mi", fit.measures = "all", baseline.model = NULL, h1.model = NULL, fm.args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level = 0.90, rmsea.h0.closefit = 0.05, rmsea.h0.notclosefit = 0.08, robust = TRUE, cat.check.pd = TRUE), output = "vector", omit.imps = c("no.conv","no.se"), ...): See lavaan::fitMeasures() for details. Pass additional arguments to lavTestLRT.mi() via ....
fitmeasures: alias for fitMeasures.
show: signature(object = "lavaan.mi"): returns a message about convergence rates and estimation problems (if applicable) across imputed data sets.
summary: signature(object = "lavaan.mi", header = TRUE, fit.measures = FALSE,fm.args = list(standard.test = "default", scaled.test = "default", rmsea.ci.level = 0.90, rmsea.h0.closefit = 0.05, rmsea.h0.notclosefit = 0.08, robust = TRUE, cat.check.pd = TRUE), estimates = TRUE, ci = FALSE, standardized = FALSE, std = standardized, cov.std = TRUE, rsquare = FALSE, fmi = FALSE, asymptotic = FALSE, scale.W = !asymptotic, omit.imps = c("no.conv","no.se"), remove.unused = TRUE, modindices = FALSE, nd = 3L, ...): Analogous to summary() for lavaan-class objects. By default, summary returns output from parameterEstimates.mi(), with some cursory information in the header. Setting fit.measures=TRUE will additionally run fitMeasures(), and setting modindices=TRUE will additionally run modindices.mi().

Arguments

object: An object of class lavaan.mi
header, fit.measures, fm.args, estimates, ci, standardized, std, cov.std, rsquare, remove.unused, modindices, nd, output: See descriptions of summary() arguments in the help page for lavaan::lavaan class. Also see lavaan::fitMeasures() for arguments fit.measures and fm.args.
fmi: logical indicating whether to add the Fraction Missing Information (FMI) and (average) relative increase in variance (ARIV) to the output.
asymptotic: logical. If FALSE (typically a default, but see Value section for details using various methods), pooled tests (of fit or pooled estimates) will be F or t statistics with associated degrees of freedom (df). If TRUE, the (denominator) df are assumed to be sufficiently large for a t statistic to follow a normal distribution, so it is printed as a z statistic; likewise, F times its numerator df is printed, assumed to follow a $\chi^2$ distribution.
scale.W: logical. If TRUE (default), the vcov method will calculate the pooled covariance matrix by scaling the within-imputation component by the ARIV (see Enders, 2010, p. 235, for definition and formula). Otherwise, the pooled matrix is calculated as the weighted sum of the within-imputation and between-imputation components (see Enders, 2010, ch. 8, for details). This in turn affects how the summary method calculates its pooled standard errors, as well as the Wald test (lavTestWald.mi()).
omit.imps: 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. NPD solutions are not excluded by default because they are likely to occur due to sampling error, especially in small samples. However, gross model misspecification could also cause NPD solutions, users can compare pooled results with and without this setting as a sensitivity analysis to see whether some imputations warrant further investigation. 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).
...: Additional arguments passed to lavTestLRT.mi(), or subsequently to lavaan::lavTestLRT(). This is how users can specify a pool.method= for the model's $\chi^2$ statistic (optionally used in any fit.measures=), or set pool.method="D1" when summary(modindices=TRUE).
total: logical (default: TRUE) indicating whether the nobs() method should return the total sample size or (if FALSE) a vector of group sample sizes.
type: The meaning of this argument varies depending on which method it it used for. Find detailed descriptions in the Value section under coef() and vcov().
labels: logical indicating whether the coef() output should include parameter labels. Default is TRUE.
baseline.model, h1.model: See lavaan::fitMeasures().

Slots

coefList: list of estimated coefficients in matrix format (one per imputation) as output by lavInspect(fit, "est")

phiList

list of model-implied latent-variable covariance matrices (one per imputation) as output by lavInspect(fit, "cov.lv")

miList

list of modification indices output by lavaan::modindices()

lavListCall

call to lavaan::lavaanList() used to fit the model to the list of imputed data sets in @DataList, stored as a list of arguments

convergence

list of logical vectors indicating whether, for each imputed data set, (1) the model converged on a solution, (2) SEs could be calculated, (3) the (residual) covariance matrix of latent variables ($\Psi$) is non-positive-definite, and (4) the residual covariance matrix of observed variables ($\Theta$) is non-positive-definite.

version

Named character vector indicating the lavaan and lavaan.mi version numbers.

DataList

The list of imputed data sets

SampleStatsList

List of output from lavInspect(fit, "sampstat") applied to each fitted model.

ParTableList,vcovList,testList,baselineList

See lavaan::lavaanList

h1List

See lavaan::lavaanList. An additional element is added to the list: $PT is the "saturated" model's parameter table, returned by lavaan::lav_partable_unrestricted().

call,Options,ParTable,pta,Data,Model,meta,timingList,CacheList,optimList,impliedList,loglikList,internalList,funList,external

By default, lavaan.mi() does not populate the remaining @*List slots from the lavaan::lavaanList class. But they can be added to the call using the store.slots= argument (passed to lavaan::lavaanList() via ...).

Objects from the Class

See the lavaan.mi() function for details. Wrapper functions include cfa.mi(), sem.mi(), and growth.mi().

Author

Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)

References

Enders, C. K. (2010). Applied missing data analysis. New York, NY: Guilford.

Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York, NY: Wiley. tools:::Rd_expr_doi("10.1002/9780470316696")

Examples

Run this code


data(HS20imps) # import a list of 20 imputed data sets

## specify CFA model from lavaan's ?cfa help page
HS.model <- '
  visual  =~ x1 + x2 + x3
  textual =~ x4 + x5 + x6
  speed   =~ x7 + x8 + x9
'

## fit model to imputed data sets
fit <- cfa.mi(HS.model, data = HS20imps)

## vector of pooled coefficients
coef(fit)
## their pooled asymptotic covariance matrix
vcov(fit)
## which is the weighted sum of within- and between-imputation components
vcov(fit, type = "within")
vcov(fit, type = "between")

## covariance matrix of observed variables,
## as implied by pooled estimates
fitted(fit)

## custom null model for CFI
HS.parallel <- '
  visual  =~ x1 + 1*x2 + 1*x3
  textual =~ x4 + 1*x5 + 1*x6
  speed   =~ x7 + 1*x8 + 1*x9
'
fit0 <- cfa.mi(HS.parallel, data = HS20imps, orthogonal = TRUE)
fitMeasures(fit, baseline.model = fit0, fit.measures = "default",
            output = "text")

## See ?lavaan.mi help page for more examples

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