R: Likelihood Ratio Test for Multiple Imputations

lavTestLRT.mi {semTools} | R Documentation

## Likelihood Ratio Test for Multiple Imputations

### Description

Likelihood ratio test (LRT) for lavaan models fitted to multiple imputed data sets. Statistics for comparing nested models can be calculated by pooling the likelihood ratios across imputed data sets, as described by Meng & Rubin (1992), or by pooling the LRT statistics from each imputation, as described by Li, Meng, Raghunathan, & Rubin (1991).

### Usage

    lavTestLRT.mi(object, h1 = NULL, test = c("D3", "D2"),
      asymptotic = FALSE, pool.robust = FALSE, ...)

### Arguments

`object, h1` | An object of class `lavaan.mi`. `object` should be nested within (more constrained than) `h1`.
`test` | `character` indicating which pooling method to use. `"D3"`, `"mr"`, or `"meng.rubin"` (default) requests the method described by Meng & Rubin (1992). `"D2"`, `"LMRR"`, or `"Li.et.al"` requests the complete-data LRT statistic should be calculated using each imputed data set, which will then be pooled across imputations, as described in Li, Meng, Raghunathan, & Rubin (1991). Find additional details in Enders (2010, chapter 8).
`asymptotic` | `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 χ^2 distributed with `df1`.
`pool.robust` | `logical`. Ignored unless `test = "D2"` and a robust test was requested. If `pool.robust = TRUE`, the robust test statistic is pooled, whereas `pool.robust = FALSE` will pool the naive test statistic (or difference statistic) and apply the average scale/shift parameter to it (unavailable for mean- and variance-adjusted difference statistics, so `pool.robust` will be set `TRUE`).
`...` | Additional arguments passed to `lavTestLRT`, only if `test = "D2"` and `pool.robust = TRUE`

### Details

The Meng & Rubin (1992) method, also referred to as the `"D3"` statistic, is only applicable when using a likelihood-based estimator. Otherwise (e.g., DWLS for categorical outcomes), users are notified that `test` was set to `"D2"`.

`test = "Mplus"` implies `"D3"` and `asymptotic = TRUE` (see Asparouhov & Muthen, 2010).

Note that unlike `lavTestLRT`, `lavTestLRT` can only be used to compare a single pair of models, not a longer list of models. To compare several nested models fitted to multiple imputations, see examples on the `compareFit` help page.

### Value

A vector containing the LRT statistic (either an `F` or χ^2 statistic, depending on the `asymptotic` argument), the degrees of freedom (numerator and denominator, if `asymptotic = FALSE`), and a p value. Robust statistics will also include the average (across) imputations) scaling factor and (if relevant) shift parameter(s), unless `pool.robust = TRUE`.

### Author(s)

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

### References

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

Meng, X.-L., & Rubin, D. B. (1992). Performing likelihood ratio tests with multiply-imputed data sets. Biometrika, 79(1), 103–111. Retrieved from https://www.jstor.org/stable/2337151

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

### See Also

`lavTestLRT`, `compareFit`

### 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 <- '
      visual  =~ x1 + b1*x2 + x3
      textual =~ x4 + b2*x5 + x6
      speed   =~ x7 + b3*x8 + x9
    '

    fit1 <- cfa.mi(HS.model, data = imps, estimator = "mlm")
    fit0 <- cfa.mi(HS.model, data = imps, estimator = "mlm", orthogonal = TRUE)

    ## By default, use D3.
    ## Must request a chi-squared statistic to be robustified.
    lavTestLRT.mi(fit1, h1 = fit0, asymptotic = TRUE)

    ## Using D2, you can either robustify the pooled naive statistic ...
    lavTestLRT.mi(fit1, h1 = fit0, asymptotic = TRUE, test = "D2")
    ## ... or pool the robust chi-squared statistic
    lavTestLRT.mi(fit1, h1 = fit0, asymptotic = TRUE, test = "D2",
                  pool.robust = TRUE)

    ## End(Not run)

[Package semTools version 0.5-1 Index]