Fit a model to multiply imputed data and pool it with Rubin's rules
Source:R/pool-imputations.R
pool_imputations.RdFits multilpa() to every completed data set, aligns each fit's profile and
group-class labels to the first one, and pools the estimates with Rubin's
rules. This is the route for missing covariates, which
missing = "fiml" cannot integrate out: the model conditions on
covariates, so it has no distribution for them to integrate over. Impute
them first (for example with the mice package, including the indicators and
the group identifier in the imputation model), then pass the completed data
here.
Usage
pool_imputations(
imputed,
vars,
id,
n_profiles,
...,
level = 0.95,
vcov_type = c("observed", "robust", "opg"),
adjust = .multilpa_p_adjust_methods
)Arguments
- imputed
The completed data sets: a list of at least two data frames with the same columns and rows in the same order, or a
midsobject from the mice package (which is then completed here).- vars, id, n_profiles
As in
multilpa().- ...
Further arguments for
multilpa(), such asn_group_classes,profile_covariates,group_covariates,categorical,n_startsandseed. The same arguments fit every imputation.- level
Confidence level of the pooled intervals.
- vcov_type, adjust
As in
parameter_inference(), applied to every imputation's fit.
Value
An object of class latents_pooled. as.data.frame() and
get_results(x, "estimates") give one row per parameter, with the columns
of parameter_inference() (level, outcome, term, parameter,
estimate, standard_error, statistic, p_value, p_adjusted,
conf_low, conf_high) plus df (Rubin's degrees of freedom),
within and between (the two variance components), riv (the
relative increase in variance due to missingness) and fmi (the fraction
of missing information). statistic and p_value are NA where
parameter_inference() reports no test (variances and probabilities).
get_results(x, "imputations") gives each imputation's aligned estimates,
one row per imputation and parameter, and get_results(x, "fits") one row
per imputation with its log likelihood, convergence and the label
permutation that aligned it.
Details
Pooling is on the reported (natural) scale: for each parameter the pooled
estimate is the mean over imputations, and its variance is the mean
within-imputation variance plus (1 + 1/m) times the between-imputation
variance. Degrees of freedom follow Rubin (1987) with a large complete-data
sample, which is what maximum-likelihood inference assumes.
Pooled intervals are symmetric t intervals on this scale; unlike the
transformed Wald intervals of parameter_inference(), they can extend
outside the parameter space for probabilities or variances.
Choosing the imputation model
Rubin's rules are only as good as the imputations. The covariate and the
indicators are related through the latent classes, so an imputation model
that is linear in the indicators (mice's defaults) misses that structure:
in validation/pool-imputations-coverage.R (a membership slope with 30%
of its covariate missing at random given the indicators, 200 replications,
ten imputations) 95% intervals covered 0.925 under predictive mean
matching and 0.935 under Bayesian linear regression, against 0.995 when the
covariate was approximately drawn from its conditional distribution using
known generating parameters. That oracle arm omits uncertainty in the
imputation parameters and is not a validation of proper multiple
imputation or nominal interval coverage. The study is one design, not a
general guarantee for any method. Use an imputation model that accounts for
the latent structure and clustering, includes the indicators and relevant
nonlinearities, and propagates parameter uncertainty. Imputing separately
within assigned classes alone ignores classification uncertainty.
Complete-case coverage was 0.955 in that design, but selecting on the
indicators changes their within-class distributions; the usual logistic
case-control slope argument does not guarantee unbiased slopes when the
outcome is latent and its measurement model is estimated.
Conditions
latents_bad_data when imputed is not a list of at least two data frames
with identical columns and row counts; latents_pooling_failed when an
imputation's fit or inference fails (its message names the imputation and
carries the original reason), since Rubin's rules need every imputation;
latents_missing_package for a mids object without mice installed.
Warnings from the individual fits are passed on as they are raised.
References
Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys. Wiley.
Meng, X.-L. (1994). Multiple-imputation inferences with uncongenial sources of input. Statistical Science, 9(4), 538–558.
van Buuren, S. (2018). Flexible Imputation of Missing Data (2nd ed.), section 5.2. Chapman & Hall/CRC.
Examples
set.seed(1)
# Two stand-in completed data sets. With real missing covariates, pass the
# `mids` object mice::mice() returns instead.
completed <- lapply(1:2, function(i) {
within(subset(course_engagement, student <= 40),
previous_grade <- previous_grade + rnorm(length(previous_grade), sd = 0.1))
})
pooled <- pool_imputations(completed, c("browse", "lectures", "forum_read"),
"student", n_profiles = 2, n_group_classes = 1,
profile_covariates = "previous_grade",
n_starts = 2, seed = 1)
pooled
#> Pooled over 2 imputations (Rubin's rules): multilpa_covariates, 2 profiles, 1 group classes
#> Largest fraction of missing information: 0.002
#> level outcome term parameter estimate standard_error
#> measurement profile_1 browse mean 0.5673 0.04202
#> measurement profile_1 lectures mean 0.4578 0.05095
#> measurement profile_1 forum_read mean 0.6314 0.04056
#> measurement profile_2 browse mean -0.8397 0.05746
#> measurement profile_2 lectures mean -0.6244 0.05838
#> measurement profile_2 forum_read mean -0.9156 0.04881
#> measurement profile_1 browse variance 0.5414 0.04379
#> measurement profile_1 lectures variance 0.8138 0.06410
#> measurement profile_1 forum_read variance 0.4739 0.03935
#> measurement profile_2 browse variance 0.4890 0.05734
#> measurement profile_2 lectures variance 0.5656 0.06255
#> measurement profile_2 forum_read variance 0.3392 0.04177
#> profile profile_1 (Intercept) coefficient 0.6142 0.10890
#> profile profile_1 previous_grade coefficient 0.6516 0.10996
#> conf_low conf_high fmi
#> 0.4850 0.6497 8.932e-04
#> 0.3580 0.5577 3.942e-04
#> 0.5519 0.7109 1.837e-03
#> -0.9523 -0.7271 1.458e-03
#> -0.7388 -0.5100 7.534e-04
#> -1.0113 -0.8200 1.307e-03
#> 0.4556 0.6272 5.457e-05
#> 0.6881 0.9394 8.143e-05
#> 0.3968 0.5511 8.404e-04
#> 0.3766 0.6014 1.212e-04
#> 0.4430 0.6882 6.422e-04
#> 0.2573 0.4211 6.997e-05
#> 0.4008 0.8276 3.305e-04
#> 0.4361 0.8671 1.322e-03
get_results(pooled, "fits")
#> imputation log_likelihood n_parameters converged profile_order group_order
#> 1 1 -2099.880 14 TRUE 1,2 1
#> 2 2 -2099.696 14 TRUE 1,2 1