R: Score Test for Multiple Imputations

lavTestScore.mi {semTools}

R Documentation

Score Test for Multiple Imputations

Description

Score test (or Lagrange multiplier test) for lavaan models fitted to multiple imputed data sets. Statistics for releasing one or more fixed or constrained parameters in model can be calculated by pooling the gradient and information matrices pooled across imputed data sets using Rubin's (1987) rules, or by pooling the score test statistics across imputed data sets (Li, Meng, Raghunathan, & Rubin, 1991).

Usage

lavTestScore.mi(object, add = NULL, release = NULL, type = c("D2",
  "Rubin"), scale.W = FALSE, asymptotic = !is.null(add),
  univariate = TRUE, cumulative = FALSE, epc = FALSE, verbose = FALSE,
  warn = TRUE)

Arguments

`object`	An object of class `lavaan`.
`add`	Either a `character` string (typically between single quotes) or a parameter table containing additional (currently fixed-to-zero) parameters for which the score test must be computed.
`release`	Vector of `integer`s. The indices of the equality constraints that should be released. The indices correspond to the order of the equality constraints as they appear in the parameter table.
`type`	`character` indicating which pooling method to use. `"Rubin"` indicates Rubin's (1987) rules will be applied to the gradient and information, and those pooled values will be used to calculate modification indices in the usual manner. `"D2"` (default), `"LMRR"`, or `"Li.et.al"` indicate that modification indices calculated from each imputed data set will be pooled across imputations, as described in Li, Meng, Raghunathan, & Rubin (1991) and Enders (2010).
`scale.W`	`logical`. If `FALSE` (default), the pooled information matrix is calculated as the weighted sum of the within-imputation and between-imputation components. Otherwise, the pooled information is calculated by scaling the within-imputation component by the average relative increase in variance (ARIV; see Enders, 2010, p. 235). Not recommended, and ignored (irrelevant) if `type = "D2"`.
`asymptotic`	`logical`. If `FALSE` (default when using `add` to test adding fixed parameters to the model), the pooled test will be returned as an F-distributed variable 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 χ^2 distributed with `df1`. When using the `release` argument, `asymptotic` will be set to `TRUE` because (A)RIV can only be calculated for `add`ed parameters.
`univariate`	`logical`. If `TRUE`, compute the univariate score statistics, one for each constraint.
`cumulative`	`logical`. If `TRUE`, order the univariate score statistics from large to small, and compute a series of multivariate score statistics, each time including an additional constraint in the test.
`epc`	`logical`. If `TRUE`, and we are releasing existing constraints, compute the expected parameter changes for the existing (free) parameters (and any specified with `add`), if all constraints were released. For EPCs associated with a particular (1-df) constraint, only specify one parameter in `add` or one constraint in `release`.
`verbose`	`logical`. Not used for now.
`warn`	`logical`. If `TRUE`, print out warnings if they occur.

Value

A list containing at least one data.frame:

$test: The total score test, with columns for the score test statistic (X2), the degrees of freedom (df), and a p value under the χ^2 distribution (p.value).
$uni: Optional (if univariate=TRUE). Each 1-df score test, equivalent to modification indices.
$cumulative: Optional (if cumulative=TRUE). Cumulative score tests.
$epc: Optional (if epc=TRUE). Parameter estimates, expected parameter changes, and expected parameter values if all the tested constraints were freed.

See lavTestScore for details.

Author(s)

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

Adapted from lavaan source code, written by Yves Rosseel (Ghent University; Yves.Rosseel@UGent.be)

type = "Rubin" method proposed by Maxwell Mansolf (University of California, Los Angeles; mamansolf@gmail.com)

References

Bentler, P. M., & Chou, C.-P. (1992). Some new covariance structure model improvement statistics. Sociological Methods & Research, 21(2), 259–282. doi:10.1177/0049124192021002006

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 http://www.jstor.org/stable/24303994

Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York, NY: Wiley.

Examples

 ## Not run: 
## impose missing data for example
HSMiss <- HolzingerSwineford1939[ , c(paste("x", 1:9, sep = ""),
                                      "ageyr","agemo","school")]
set.seed(12345)
HSMiss$x5 <- ifelse(HSMiss$x5 <= quantile(HSMiss$x5, .3), NA, HSMiss$x5)
age <- HSMiss$ageyr + HSMiss$agemo/12
HSMiss$x9 <- ifelse(age <= quantile(age, .3), NA, HSMiss$x9)

## impute missing data
library(Amelia)
set.seed(12345)
HS.amelia <- amelia(HSMiss, m = 20, noms = "school", p2s = FALSE)
imps <- HS.amelia$imputations

## specify CFA model from lavaan's ?cfa help page
HS.model <- '
  speed =~ c(L1, L1)*x7 + c(L1, L1)*x8 + c(L1, L1)*x9
'

out <- cfa.mi(HS.model, data = imps, group = "school", std.lv = TRUE)

## Mode 1: Score test for releasing equality constraints

## default type: Li et al.'s (1991) "D2" method
lavTestScore.mi(out, cumulative = TRUE)
## Rubin's rules
lavTestScore.mi(out, type = "Rubin")

## Mode 2: Score test for adding currently fixed-to-zero parameters
lavTestScore.mi(out, add = 'x7 ~~ x8 + x9')


## End(Not run)

[Package semTools version 0.5-0 Index]