Declare a composite construct from observed indicators

A composite construct is a deterministic index built from two or more observed indicator columns and materialized as a single column before fitting, so it can be used as an ordinary predictor or response in a node formula. With method = "fixed" the construct is a weighted sum of the (raw) indicators; with method = "pca" it is the first principal-component score of the scaled indicators. The indicator loadings are recorded and reported by loadings().

Usage

drm_composite(
  name,
  indicators,
  weights = NULL,
  method = c("fixed", "pca"),
  data,
  standardize = FALSE
)

Arguments

name

Name of the construct column to create. Must not collide with an existing data column or node name.

indicators

Character vector (length >= 2) of numeric indicator columns present in data.

weights

Optional numeric weights for method = "fixed" (defaults to equal weights 1/k). Ignored for method = "pca".

method

"fixed" (weighted sum of raw indicators) or "pca" (first principal-component score of the scaled indicators).

data

A data frame containing the indicators (used to validate them and, for "pca", to derive the loadings).

standardize

If TRUE, the materialized construct column is standardized (mean 0, sd 1). Default FALSE.

Value

A drm_composite declaration object. It records the indicator loadings and the construct's reliability (Cronbach's alpha, an internal-consistency measure for reflective indicator sets), shown by print() / summary().

Details

This is the formative / composite construct (indicators define the construct), which stays fully within drmSEM's piecewise, likelihood-based core. Reflective latent variables (a latent common cause estimated through a measurement model) require a joint likelihood drmTMB does not fit piecewise and are out of scope here; see docs/design/09-latent-variables.md.

References

Bollen KA, Lennox R (1991). “Conventional Wisdom on Measurement: A Structural Equation Perspective.” Psychological Bulletin, 110(2), 305–314. doi:10.1037/0033-2909.110.2.305 .

Grace JB, Bollen KA (2008). “Representing General Theoretical Concepts in Structural Equation Models: The Role of Composite Variables.” Environmental and Ecological Statistics, 15(2), 191–213. doi:10.1007/s10651-007-0047-7 .

Bollen KA (1989). Structural Equations with Latent Variables. Wiley, New York.

See also

loadings(), drm_sem().

Examples

dat <- data.frame(len = rnorm(50), mass = rnorm(50), wing = rnorm(50))
# equal-weighted index of three indicators:
drm_composite("body_size", c("len", "mass", "wing"), data = dat)
#> <composite construct> body_size = fixed(len, mass, wing)
#> reliability (Cronbach's alpha): 0.284
# first principal-component index instead:
drm_composite("body_size", c("len", "mass", "wing"), method = "pca", data = dat)
#> <composite construct> body_size = pca(len, mass, wing)
#> first-PC proportion of variance: 0.468
#> reliability (Cronbach's alpha): 0.284