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Build confirmatory factor-analysis syntax

Source: R/nomo_model.R
nomo_model.Rd

nomo_model() is a small convenience helper for reflective CFA models. It converts a named list of factor-to-indicator assignments into lavaan measurement-model syntax. It deliberately does not add residual covariances, cross-loadings, equality constraints, or other post-hoc changes.

Usage

nomo_model(
  factors,
  structure = c("correlated", "higher_order", "bifactor"),
  general = "G"
)

Arguments

factors

A named list. Each element name is a latent-factor name and each element value is a character vector of observed indicators. For hierarchical structures these are the first-order or group factors.

structure

One of "correlated", "higher_order", or "bifactor".

general

Name of the second-order or general factor. Used only when structure is "higher_order" or "bifactor".

Value

A character scalar of class nomo_model that can be passed directly to nomo_cfa() or to lavaan::cfa(). Attributes record the factors, structure, general factor, and any identification notes.

Details

Three structures are available, and the researcher chooses among them. The helper never derives a structure from exploratory results.

  • "correlated" (default): one factor per element of factors, with factors free to correlate.

  • "higher_order": the elements of factors become first-order factors, and a second-order factor named by general explains their correlations. At least three first-order factors are required, because with two the second-order loadings are not identified without further constraints. With exactly three, the second-order part is just identified: the model fits exactly as well as the correlated-factors model, so fit cannot distinguish the two.

  • "bifactor": a general factor named by general is measured by every indicator, and each element of factors becomes a group factor. All factors are orthogonal. Identification is written into the syntax (each factor's first loading is freed and its variance fixed to 1), so the model is identified the same way whatever std.lv is used to fit it. At least two group factors with at least two indicators each are required; configurations known to be fragile are noted.

Any identification notes are attached as the "notes" attribute and printed with the syntax. Use nomo_hierarchical() to evaluate a fitted higher-order or bifactor model.

References

Holzinger, K. J., & Swineford, F. (1937). The bi-factor method. Psychometrika, 2(1), 41-54. doi:10.1007/BF02287965

Reise, S. P. (2012). The rediscovery of bifactor measurement models. Multivariate Behavioral Research, 47(5), 667-696. doi:10.1080/00273171.2012.715555

Yung, Y.-F., Thissen, D., & McLeod, L. D. (1999). On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika, 64(2), 113-128. doi:10.1007/BF02294531

Examples

factors <- list(
  engagement = c("e1", "e2", "e3"),
  belonging = c("b1", "b2", "b3"),
  efficacy = c("f1", "f2", "f3")
)

nomo_model(factors)
#> engagement =~ e1 + e2 + e3
#> belonging =~ b1 + b2 + b3
#> efficacy =~ f1 + f2 + f3
nomo_model(factors, structure = "higher_order", general = "Wellbeing")
#> engagement =~ e1 + e2 + e3
#> belonging =~ b1 + b2 + b3
#> efficacy =~ f1 + f2 + f3
#> Wellbeing =~ NA*engagement + belonging + efficacy
#> Wellbeing ~~ 1*Wellbeing
#> 
#> Identification notes:
#> - With three first-order factors the second-order part is just identified: this model fits exactly as well as the correlated-factors model, so model fit cannot distinguish the two.
nomo_model(factors, structure = "bifactor", general = "Wellbeing")
#> Wellbeing =~ NA*e1 + e2 + e3 + b1 + b2 + b3 + f1 + f2 + f3
#> engagement =~ NA*e1 + e2 + e3
#> belonging =~ NA*b1 + b2 + b3
#> efficacy =~ NA*f1 + f2 + f3
#> Wellbeing ~~ 1*Wellbeing
#> engagement ~~ 1*engagement
#> belonging ~~ 1*belonging
#> efficacy ~~ 1*efficacy
#> Wellbeing ~~ 0*engagement + 0*belonging + 0*efficacy
#> engagement ~~ 0*belonging + 0*efficacy
#> belonging ~~ 0*efficacy