Model Parameters for Multiply Imputed Repeated Analyses

Model Parameters from mira objects

model_parameters() can be used in combination with the mice package to deal with missing data, in particular to summaries regression models used with multiple imputed datasets. It computes pooled summaries of multiple imputed repeated regression analyses, i.e. of objects of class mira. Thus, model_parameters() for mira-objects is comparable to the pool()-function from mice, but only focuses on the final summary of parameters and does not include the diagnostic statistic per estimate.

library(mice)
library(parameters)

data("nhanes2")
imp <- mice(nhanes2, printFlag = FALSE)
fit <- with(data = imp, exp = lm(bmi ~ age + hyp + chl))

model_parameters(fit)

#> # Fixed Effects
#> 
#> Parameter   | Coefficient |   SE |          95% CI | Statistic |    df |      p
#> -------------------------------------------------------------------------------
#> (Intercept) |       18.93 | 2.89 | [ 12.82, 25.03] |      6.54 | 16.91 | < .001
#> age40-59    |       -6.16 | 1.65 | [ -9.74, -2.58] |     -3.73 | 12.59 | 0.003 
#> age60-99    |       -7.87 | 2.17 | [-12.99, -2.76] |     -3.63 |  7.05 | 0.008 
#> hypyes      |        2.23 | 1.68 | [ -1.40,  5.86] |      1.33 | 12.84 | 0.208 
#> chl         |        0.06 | 0.02 | [  0.02,  0.09] |      3.51 | 17.27 | 0.003

Not all packages work with with.mids() from package mice. Thus, for some modeling packages, it’s not possible to perform multiply imputed repeated analyses, i.e. you cannot work with imputed data for such models. We give an example for the GLMMadaptive package here.

First, we generate a dataset with missing values. We take the data cbpp from lme4 and randomly assign some missing values into one of the predictors. Then we impute the data, using mice() from package mice.

library(lme4)
library(GLMMadaptive)

data(cbpp)
cbpp$period[sample(seq_len(nrow(cbpp)), size = 10)] <- NA

imputed_data <- mice(cbpp, printFlag = FALSE)

Using with to compute multiple regression analyses for each imputed dataset fails.

fit <- with(data = imputed_data, expr = GLMMadaptive::mixed_model(
  cbind(incidence, size - incidence) ~ period,
  random = ~ 1 | herd,
  family = binomial
))
# > Error in as.data.frame(data) :
# >   argument "data" is missing, with no default

However, we can use a workaround by using pool_parameters(), which works on a list of model objects. So whenever a model-object is not yet supported by mice::with(), you can instead fit multiple models to the imputed datasets and pool all parameters with pool_parameters():

The steps would be:

1. Calculate the regression models for each imputed dataset manually (either by using complete() from package mice to get the imputed datasets, or by accessing the datasets directly from the mids object)

2. Save all model objects in a list.

3. Pass the list to pool_parameters().

models <- lapply(1:imputed_data$m, function(i) {
  mixed_model(
    cbind(incidence, size - incidence) ~ period,
    random = ~ 1 | herd,
    data = complete(imputed_data, action = i),
    family = binomial
  )
})
pool_parameters(models)

#> # Fixed Effects
#> 
#> Parameter   | Log-Odds |   SE |         95% CI | Statistic |      p
#> -------------------------------------------------------------------
#> (Intercept) |    -1.45 | 0.24 | [-1.93, -0.97] |     -5.93 | < .001
#> period [2]  |    -0.88 | 0.34 | [-1.55, -0.20] |     -2.55 | 0.011 
#> period [3]  |    -1.41 | 0.38 | [-2.16, -0.66] |     -3.70 | < .001
#> period [4]  |    -1.65 | 0.62 | [-2.87, -0.43] |     -2.66 | 0.008

For comparison and to show that the results from mice:pool() and pool_parameters() are identical, we take an example that also works with the mice package:

library(mice)
library(parameters)

data("nhanes2")
imp <- mice(nhanes2, printFlag = FALSE)

# approach when model is supported by "mice"
fit <- with(data = imp, exp = lm(bmi ~ age + hyp + chl))
summary(pool(fit))

#>          term estimate std.error statistic df p.value
#> 1 (Intercept)   19.667     3.373       5.8 11 0.00013
#> 2    age40-59   -5.705     1.711      -3.3 14 0.00475
#> 3    age60-99   -7.007     1.783      -3.9 18 0.00099
#> 4      hypyes    2.713     1.829       1.5 11 0.16544
#> 5         chl    0.051     0.017       2.9 12 0.01290

# approach when model is *not* supported by "mice"
models <- lapply(1:5, function(i) {
  lm(bmi ~ age + hyp + chl, data = complete(imp, action = i))
})
pool_parameters(models)

#> # Fixed Effects
#> 
#> Parameter   | Coefficient |   SE |          95% CI | Statistic |    df |      p
#> -------------------------------------------------------------------------------
#> (Intercept) |       19.67 | 3.37 | [ 12.21, 27.13] |      5.83 | 10.62 | < .001
#> age [40-59] |       -5.71 | 1.71 | [ -9.37, -2.04] |     -3.33 | 14.41 | 0.005 
#> age [60-99] |       -7.01 | 1.78 | [-10.76, -3.26] |     -3.93 | 17.88 | < .001
#> hyp [yes]   |        2.71 | 1.83 | [ -1.30,  6.73] |      1.48 | 11.24 | 0.165 
#> chl         |        0.05 | 0.02 | [  0.01,  0.09] |      2.90 | 12.34 | 0.013

Model Parameters from mipo objects

It is also possible to compute summaries of pooled objects of class mipo.

data("nhanes2")
imp <- mice(nhanes2, printFlag = FALSE)
fit <- with(data = imp, exp = lm(bmi ~ age + hyp + chl))
pooled <- pool(fit)

model_parameters(pooled)

#> # Fixed Effects
#> 
#> Parameter   | Coefficient |   SE |          95% CI |     t |    df |      p
#> ---------------------------------------------------------------------------
#> (Intercept) |       17.10 | 3.87 | [  8.63, 25.58] |  4.42 | 11.51 | < .001
#> age [40-59] |       -5.03 | 2.55 | [-11.44,  1.38] | -1.97 |  5.42 | 0.101 
#> age [60-99] |       -7.39 | 2.70 | [-13.87, -0.92] | -2.73 |  6.59 | 0.031 
#> hyp [yes]   |        1.36 | 2.44 | [ -4.27,  6.99] |  0.56 |  8.03 | 0.593 
#> chl         |        0.06 | 0.02 | [  0.01,  0.12] |  2.68 |  8.34 | 0.027