Declare a latent construct (MIMIC, reflective, or formative)

Declares a latent construct within the piecewise SEM framework. Supports MIMIC (Multiple Indicators, Multiple Causes), reflective (latent factor with multiple indicators), and formative (composite) constructs.

Usage

drm_latent(
  name,
  indicators,
  causes = NULL,
  type = c("mimic", "reflective", "formative"),
  identification = c("marker", "unit_variance"),
  marker = NULL,
  method = c("pca", "fa", "fixed"),
  weights = NULL,
  data = NULL,
  standardize = FALSE
)

Arguments

name: Name of the latent construct column to create.
indicators: Character vector of indicator column names (length >= 2), or a list of drm_indicator() declarations.
causes: Optional character vector of structural cause variables for MIMIC constructs.
type: Type of construct: "mimic" (default; causes -> latent -> indicators), "reflective" (latent -> indicators), or "formative" (indicators -> construct).
identification: Identification constraint: "marker" (unit loading on marker indicator, \(\lambda_{\text{marker}} = 1\)) or "unit_variance" (\(\text{Var}(\eta) = 1\)). Defaults to "marker".
marker: Optional name of the marker indicator for "marker" identification (defaults to the indicator with marker = TRUE or the first indicator).
method: Measurement estimation method: "pca" (first principal component / factor score), "fa" (1-factor analysis), or "fixed" (user weights).
weights: Optional numeric weights for method = "fixed".
data: Optional data frame containing indicator and cause columns. If provided, measurement structure and loadings are estimated immediately.
standardize: Logical. If TRUE, materialized latent score is standardized (mean 0, sd 1). Default FALSE.

Value

A drm_latent declaration object (inheriting from drm_composite).

Details

In piecewise SEM, measurement equations and structural causes are estimated piece-by-piece with sign-alignment and marker/unit-variance identification. Latent scores are materialized into data before fitting, allowing structural nodes to use the latent construct as an ordinary predictor or response in any drm_node() formula. Indicator loadings are reported by loadings() and kept strictly separate from structural paths().

References

Jöreskog KG, Goldberger AS (1975). “Estimation of a Model with Multiple Causes and Multiple Indicators of a Single Latent Variable.” Journal of the American Statistical Association, 70(351), 631–639. doi:10.1080/01621459.1975.10482485 .

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

Raykov T (1997). “Estimation of Composite Reliability for Congeneric Measures.” Applied Psychological Measurement, 21(2), 173–184. doi:10.1177/01466216970212006 .

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 .

Examples

dat <- data.frame(
  x1 = rnorm(50), x2 = rnorm(50),
  y1 = rnorm(50), y2 = rnorm(50), y3 = rnorm(50)
)
# MIMIC construct with marker identification:
lat <- drm_latent("size", indicators = c("y1", "y2", "y3"), causes = c("x1", "x2"), data = dat)
print(lat)
#> <latent construct: mimic> size (identification: marker) = y1, y2, y3
#> structural causes: x1, x2
#> composite reliability (Raykov's rho): 0.001
#> Cronbach's alpha: -0.24