Staged imputation

Impute missing data at different utterance lengths using successive linear models.

Usage

impute_values_by_length(
  data,
  var_y,
  var_length,
  id_cols = NULL,
  include_max_length = FALSE,
  data_train = NULL
)

Arguments

data

dataframe in which to impute missing value

var_y

bare name of the response variable for imputation

var_length

bare name of the length variable

id_cols

a selection of variable names that uniquely identify each group of related observations. For example, c(child_id, age_months).

include_max_length

whether to use the maximum length value as a predictor in the imputation models. Defaults to FALSE.

data_train

(optional) dataframe used to train the imputation models. For example, we might have data from a reference group of children in data_train but a clinical population in data. If omitted, the dataframe in data is used to train the models. data_train can also be a function. In this case, it is applied to the data argument in order to derive (filter) a subset of the data for training.

Value

a dataframe with the additional columns {var_y}_imputed (the imputed value), .max_{var_length} with the highest value of var_length

with observed data, and {var_y}_imputation for labeling whether observations were "imputed" or "observed".

Background

In Hustad and colleagues (2020), we modeled intelligibility data in young children's speech. Children would hear an utterance and then they would repeat it. The utterances started at 2 words in length, then increased to 3 words in length, and so on in batches of 10 sentences, all the way to 7 words in length. There was a problem, however: Not all of the children could produce utterances at every length. Specifically, if a child could not reliably produced 5 utterances of a given length length, the task was halted. So given the nature of the task, if a child had produced 5-word utterances, they also produced 2--4-word utterances as well.

The length of the utterance probably influenced the outcome variable: Longer utterances have more words that might help a listener understand the sentence, for example. Therefore, it did not seem appropriate to ignore the missing values. We used the following two-step procedure (see the Supplemental Materials for more detail):

Other notes

Remark about data and data_train: One might ask, why shouldn't some children help train the data imputation models? Let's consider a norm-referenced standardized testing scenario: We have a new participant (observations in data), and we want to know how they compare to their age peers (participants in data_train). By separating out data_train and fixing it to a reference group, we can apply the same adjustment/imputation procedure to all new participants.

References

Hustad, K. C., Mahr, T., Natzke, P. E. M., & Rathouz, P. J. (2020). Development of Speech Intelligibility Between 30 and 47 Months in Typically Developing Children: A Cross-Sectional Study of Growth. Journal of Speech, Language, and Hearing Research, 63(6), 1675–1687. https://doi.org/10.1044/2020_JSLHR-20-00008

Hustad, K. C., Mahr, T., Natzke, P. E. M., & J. Rathouz, P. (2020). Supplemental Material S1 (Hustad et al., 2020). ASHA journals. https://doi.org/10.23641/asha.12330956.v1

Examples

set.seed(1)
fake_data <- tibble::tibble(
  child = c(
    "a", "a", "a", "a", "a",
    "b", "b", "b", "b", "b",
    "c", "c", "c", "c", "c",
    "e", "e", "e", "e", "e",
    "f", "f", "f", "f", "f",
    "g", "g", "g", "g", "g",
    "h", "h", "h", "h", "h",
    "i", "i", "i", "i", "i"
  ),
  level = c(1:5, 1:5, 1:5, 1:5, 1:5, 1:5, 1:5, 1:5),
  x = c(
    c(100, 110, 120, 130, 150) + c(-8, -5, 0, NA, NA),
    c(100, 110, 120, 130, 150) + c(6, 6, 4, NA, NA),
    c(100, 110, 120, 130, 150) + c(-5, -5, -2, 2, NA),
    c(100, 110, 120, 130, 150) + rbinom(5, 12, .5) - 6,
    c(100, 110, 120, 130, 150) + rbinom(5, 12, .5) - 6,
    c(100, 110, 120, 130, 150) + rbinom(5, 12, .5) - 6,
    c(100, 110, 120, 130, 150) + rbinom(5, 12, .5) - 6,
    c(100, 110, 120, 130, 150) + rbinom(5, 12, .5) - 6
  )
)
data_imputed <- impute_values_by_length(
  fake_data,
  x,
  level,
  id_cols = c(child),
  include_max_length = FALSE
)

if (requireNamespace("ggplot2")) {
  library(ggplot2)
  ggplot(data_imputed) +
    aes(x = level, y = x_imputed) +
    geom_line(aes(group = child)) +
    geom_point(aes(color = x_imputation))
}