Estimate a CFA-based threshold for a multi-item questionnaire

mim_threshold() estimates an anchor-based interpretation threshold for a multi-item measure (MIM) using a one-factor CFA model with an anchor/transition rating item.

Usage

mim_threshold(
  mydata,
  var_formula,
  item_discretize = FALSE,
  item_levels = 10L,
  require_all_item_levels = FALSE,
  anchor_cut = 1,
  B = 0L,
  report_every = 50L,
  factor_name = "F1",
  item_suffix = "_ord",
  anchor_suffix = "_bin",
  std.lv = TRUE,
  parameterization = "theta",
  verbose = TRUE,
  ...
)

Arguments

mydata: Data frame.
var_formula: Formula of the form anchor ~ item1 + item2 + .... Use anchor ~ . to use all variables except the anchor as items.
item_discretize: Logical. If TRUE, discretize each item using var_discretize(). If FALSE, use the item values as observed ordinal categories.
item_levels: Number of levels to use when item_discretize = TRUE. Must be between 2 and 12.
require_all_item_levels: Logical. Passed to var_discretize().
anchor_cut: Cutpoint for binarizing the anchor if it has more than two unique non-missing values. Values >= anchor_cut are coded 1.
B: Number of bootstrap samples. Bootstrap CI is computed only if B >= 100.
report_every: During bootstrapping, print progress every report_every attempted fits.
factor_name: Name of the latent factor.
item_suffix: Suffix appended to item names when items are discretized or internally recoded.
anchor_suffix: Suffix appended to the anchor variable name if the anchor has more than two unique values and is dichotomized.
std.lv: Passed to lavaan::cfa().
parameterization: Passed to lavaan::cfa().
verbose: If TRUE, print item names and generated lavaan model.
...: Additional arguments passed to lavaan::cfa().

Value

A mim_threshold object. Additional details can be retrieved with mim_threshold_details().

Details

This technique is based on Terluin et al (2023) and Terluin et al (2024). Briefly, the mim_threshold() function:

fits a one-factor CFA model with the MIM items and an anchor item,
computes theta_star, the latent factor value where the anchor, threshold occurs,
maps theta_star to each item using CFA-implied category probabilities,
multiplies item category probabilities by item values or bin midpoints, and
sums the item-level expected values to obtain the MIM threshold.

References

Terluin, B., Koopman, J.E., Hoogendam, L. et al. Estimating meaningful thresholds for multi-item questionnaires using item response theory. Qual Life Res 32, 1819–1830 (2023)

Terluin, B., Trigg, A., Fromy, P. et al. Estimating anchor-based minimal important change using longitudinal confirmatory factor analysis. Qual Life Res 33, 963–973 (2024).

Examples

set.seed(123)
sim <- simdat(N = 500)
dat <- sim$datw
t1_items <- sim$item_names$t1_items

dat_t1 <- dat[, c(t1_items, "trat")]

out <- mim_threshold(
  mydata = dat_t1,
  var_formula = trat ~ .,
  B = 0
)
#> MIM items: item1, item2, item3, item4, item5, item6, item7, item8, item9, item10
#> Generated lavaan model:
#> F1 =~ item1_ord + item2_ord + item3_ord + item4_ord + item5_ord + item6_ord + item7_ord + item8_ord + item9_ord + item10_ord + lambda_anchor*trat
#> trat | tau_anchor*t1

out
#> CFA-based MIM threshold
#> ------------------------
#> Threshold: 13.7125 
#> Anchor variable: trat 
#> Number of items: 10 
#> Items: item1, item2, item3, item4, item5, item6, item7, item8, item9, item10 
#> 
#> Please use `mim_threshold_details(x)` to retrieve the lavaan fit, CFA data, probabilities, and bootstrap results.