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Standardized component-labelled path coefficients

Source: R/standardize.R
standardize.Rd

Rescales fitted path coefficients so they are comparable across predictors. Two scalings are offered, both reported on the component's link scale:

Usage

standardize(object, method = c("sd_x", "latent"), ...)

# S3 method for class 'drm_sem'
standardize(object, method = c("sd_x", "latent"), ...)

Arguments

object

A drm_sem object.

method

"sd_x" or "latent".

...

Unused.

Value

The paths() table with an added std.estimate column (link scale).

Details

  • "sd_x" multiplies each coefficient by the standard deviation of its predictor, giving the link-scale change in the component per one-SD change in the predictor.

  • "latent" additionally divides by the standard deviation of the fitted linear predictor of that component, the latent-scale standardization used for generalized responses (after Grace & Bollen 2005).

Conventions (0.2)

These are the finalized standardization conventions; see docs/design/08-standardization.md for the full rationale and citations.

  • Link scale only. Standardized coefficients are reported on each component's link scale (the link column of paths()), where the linear-predictor algebra is valid. They are not back-transformed: under a nonlinear link a standardized coefficient has no constant response-scale counterpart. For response-scale, functional interpretations use the effect engine (direct_effects(), total_effects()) instead.

  • Factor predictors use SD = 1 (no rescaling), so a factor / dummy coefficient is reported as its raw per-contrast effect (lavaan's std.nox convention; piecewiseSEM likewise does not SD-rescale categorical predictors). Multiplying a 0/1 dummy by its column SD would produce a data-dependent value that is not "one SD of a construct"; a Gelman (2008) 2-SD rescaling of the continuous predictors for continuous-vs-binary comparability is planned as an opt-in (OQ-4).

  • Per-component latent. The latent divisor is the SD of that component's own linear predictor, so a sigma or zi path is standardized on its own (log / logit) link scale — there is no marginal outcome SD for a non-mu component. This per-component latent standardization is drmSEM's distributional generalization of Grace & Bollen.

GLM mean paths (OQ-4 sigma_E)

For a mu path on a link with a constant theoretical error variance, the latent divisor is sqrt(Var(eta) + sigma_E^2), adding the link's distribution-specific latent-scale error variance (logit pi^2/3, probit 1, cloglog pi^2/6; after Grace et al. 2018 / piecewiseSEM's latent.linear). This corrects the earlier mild over-standardization of GLM mean paths. The log-link families (Poisson, negative binomial, Gamma, lognormal) carry a mean-dependent (observation-level) latent variance rather than a constant, so no sigma_E term is added there yet — that case is still deferred. Identity links and non-mu components are unchanged (the divisor is sd(eta) on the component's own link scale).

References

Grace JB, Bollen KA (2005). “Interpreting the Results from Multiple Regression and Structural Equation Models.” Bulletin of the Ecological Society of America, 86(4), 283–295. doi:10.1890/0012-9623(2005)86[283:ITRFMR]2.0.CO;2 .

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 .

Grace JB, Johnson DJ, Lefcheck JS, Byrnes JEK (2018). “Quantifying Relative Importance: Computing Standardized Effects in Models with Binary Outcomes.” Ecosphere, 9(6), e02283. doi:10.1002/ecs2.2283 .

Gelman A (2008). “Scaling Regression Inputs by Dividing by Two Standard Deviations.” Statistics in Medicine, 27(15), 2865–2873. doi:10.1002/sim.3107 .

Examples

if (FALSE) { # \dontrun{
sem <- drm_sem(
  size = drm_node(drmTMB::bf(size ~ temp + habitat, sigma ~ temp),
                  family = stats::gaussian()),
  abundance = drm_node(drmTMB::bf(abundance ~ size + temp, zi ~ habitat),
                       family = drmTMB::nbinom2()),
  data = dat)
standardize(sem, method = "latent")
} # }