se = "bootstrap" and missing = "fiml"?

[Shu Fai Cheung]

I vaguely recall that se = "bootstrap" did not work when missing = "fiml" (not sure if I am right.) However, I tried the following today and there is no warning or error message (I used only 100 bootstrap samples but I think this is not an issue for this test):

library(lavaan)
#> This is lavaan 0.6-11
#> lavaan is FREE software! Please report any bugs.
data(HolzingerSwineford1939)
model <-
"
visual  =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed   =~ x7 + x8 + x9
"

HolzingerSwineford1939_miss <- HolzingerSwineford1939[, paste0("x", 1:9)]
set.seed(60841)
idx <- mapply(function(x, y) c(x, y),
              x = sample(seq_len(nrow(HolzingerSwineford1939_miss)), 50, replace = TRUE),
              y = sample(seq_len(ncol(HolzingerSwineford1939_miss)), 50, replace = TRUE),
              SIMPLIFY = FALSE)
for (i in idx) {
    HolzingerSwineford1939_miss[i[1], i[2]] <- NA
  }

fit <- cfa(model = model,
           data = HolzingerSwineford1939_miss,
           missing = "fiml",
           se = "bootstrap",
           bootstrap = 100)
summary(fit)
#> lavaan 0.6-11 ended normally after 51 iterations
#>
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        30
#>                                                      
#>   Number of observations                           301
#>   Number of missing patterns                        13
#>                                                      
#> Model Test User Model:
#>                                                      
#>   Test statistic                                86.784
#>   Degrees of freedom                                24
#>   P-value (Chi-square)                           0.000
#>
#> Parameter Estimates:
#>
#>   Standard errors                            Bootstrap
#>   Number of requested bootstrap draws              100
#>   Number of successful bootstrap draws             100
#>
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   visual =~                                          
#>     x1                1.000                          
#>     x2                0.533    0.142    3.764    0.000
#>     x3                0.713    0.162    4.400    0.000
#>   textual =~                                          
#>     x4                1.000                          
#>     x5                1.110    0.056   19.967    0.000
#>     x6                0.921    0.066   13.921    0.000
#>   speed =~                                            
#>     x7                1.000                          
#>     x8                1.194    0.165    7.232    0.000
#>     x9                0.973    0.482    2.019    0.043
#>
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   visual ~~                                          
#>     textual           0.413    0.105    3.929    0.000
#>     speed             0.251    0.056    4.511    0.000
#>   textual ~~                                          
#>     speed             0.169    0.059    2.869    0.004
#>
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .x1                4.935    0.066   74.374    0.000
#>    .x2                6.066    0.072   83.797    0.000
#>    .x3                2.254    0.065   34.685    0.000
#>    .x4                3.063    0.066   46.497    0.000
#>    .x5                4.345    0.075   58.088    0.000
#>    .x6                2.183    0.063   34.786    0.000
#>    .x7                4.184    0.073   57.673    0.000
#>    .x8                5.517    0.064   86.219    0.000
#>    .x9                5.367    0.060   89.928    0.000
#>     visual            0.000                          
#>     textual           0.000                          
#>     speed             0.000                          
#>
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .x1                0.534    0.195    2.746    0.006
#>    .x2                1.129    0.104   10.870    0.000
#>    .x3                0.858    0.116    7.428    0.000
#>    .x4                0.372    0.046    8.074    0.000
#>    .x5                0.453    0.059    7.723    0.000
#>    .x6                0.362    0.045    7.982    0.000
#>    .x7                0.777    0.104    7.492    0.000
#>    .x8                0.452    0.125    3.634    0.000
#>    .x9                0.586    0.138    4.232    0.000
#>     visual            0.835    0.204    4.101    0.000
#>     textual           0.987    0.120    8.224    0.000
#>     speed             0.408    0.113    3.605    0.000

Does this mean that lavaan now can do bootstrapping even with missing = "fiml"? Maybe it has been able to do this for a long time but I overlooked this feature?

If it can do bootstrapping with  missing = "fiml", does it do FIML in each bootstrap sample to get the bootstrap estimates?

-- Shu Fai

[Shu Fai Cheung]

I think I can answer this question myself (please correct me if I am wrong). While working on something else, I check the code and I believe lavaan just fits the model again in each bootstrap sample using whatever options set in the original call. Therefore, if missing = "fiml" in the call to lavaan/sem/cfa, then missing = "fiml" should be used again in each bootstrap sample.

This is indeed a good thing. As far as I recall, AMOS cannot combine nonparametric bootstrapping with FIML (It has the option to do parametric bootstrapping when missing data is present but this requires more assumptions than nonparametric bootstrapping does.) It's good to know that lavaan can combine both techniques.

-- Shu Fai

[Yves Rosseel]

On 4/19/22 18:55, Shu Fai Cheung wrote:
> I think I can answer this question myself (please correct me if I am
> wrong). While working on something else, I check the code and I believe
> lavaan just fits the model again in each bootstrap sample using whatever
> options set in the original call. Therefore, if missing = "fiml" in the
> call to lavaan/sem/cfa, then missing = "fiml" should be used again in
> each bootstrap sample.

I can confirm that this is correct.

Yves.