Evaluate Structural Equation Model Identification Rules

Evaluates selected necessary and sufficient identification conditions in structural equation models (SEMs), including latent-variable scaling constraints. Output reports rule status and applicability and provides diagnostic messages to support model specification and respecification. The package is intended as a diagnostic aid and does not implement a universal identification algorithm. For more details, see Bollen (2026, ISBN:978-1009312820).

semrulesid

semrulesid allows the user to check a structural equation model (SEM) written in lavaan (Rosseel, 2012) syntax, or supplied as a lavaan parameter table or fit object, against a number of identification rules from the literature. Rules are specified as being necessary and/or sufficient and specific reasons are given when a rule is not satisfied or not applicable.

Users should not treat the package output as the sole determinant of model identification. Instead, semrulesid should be used as a “quick check” for potential identification issues and outstanding model specification concerns.

Installation

You can install semrulesid from CRAN:

install.packages("semrulesid")

You can install the development version from GitHub with:

install.packages("pak")
pak::pak("zacharyvig/semrulesid")

Functions

• id() takes a lavaan model string, parameter table, or model fit and evaluates the identification rules with informative output.

  • The lav_fun argument is used to specify the lavaan function with which you intend to fit a model (e.g., "sem").
  • Output includes whether the rule passed, whether the rule is necessary and/or sufficient for identification, and, if print_msgs = TRUE, information about why a rule did or did not pass or whether a rule is relevant for the particular type or specification of the model.
  • Messages are grouped as Identification failure, Sufficient condition not satisfied, or Rule not applicable to this model specification. An identification failure indicates that a necessary condition was not met; a sufficient condition not satisfied means that the corresponding rule cannot establish identification; and a rule not applicable indicates that the rule does not apply to the current specification of the model.
  • Users can include additional arguments to the function that are passed to lavaan’s lavaanify function (e.g., meanstructure).

Example: id(my_model, print_msgs = TRUE, lav_fun = "sem")

• scaling() prints output about how, and if so why, latent variables in the model are scaled.

  • It relays which indicator is the scaling indicator (if applicable), whether the model has mean structure, and reasons why the latent variable is or is not scaled.

Example: scaling(my_model, print_msgs = TRUE, lav_fun = "cfa")

• id2() evaluates the two-step rule of identification for full SEMs only.

  • This rule first converts the model into a confirmatory factor analysis model by changing structural relationships to covariances; evaluates the identification of the CFA; then, if identified, converts the original model into a simultaneous equations model (treating latent variables as observed); evaluates the identification of the simultaneous equations model; and finally, if identified, confirms that the original model is identified. See Bollen’s Elements of Structural Equation Models (2026) for details.

Example: id2(my_model, print_msgs = TRUE, lav_fun = "sem")

• The package supports piping for comprehensive printing.

Example: id(my_model) |> scaling() or scaling(my_model) |> id()

Example

library(semrulesid)

my_model <- '
  L1 =~ x1 + x2 + x3
  L2 =~ x4 + x5 + x6
  L3 =~ x7 + x8 + x9
  L2 ~ L1
  L3 ~ L2
'

id(my_model, meanstructure = FALSE)      # Check identification rules
id2(my_model, meanstructure = FALSE)     # Check the two-step rule
scaling(my_model, meanstructure = FALSE) # Check latent-variable scaling