Standardized Effects
When a path model includes predictors on different scales — dollars, clicks, percentages — the raw (unstandardized) coefficients are not directly comparable. Stdyx standardization rescales each coefficient into a common unit: standard deviations of the outcome per standard deviation of the predictor.
The stdyx formula
For an unstandardized coefficient \beta on the edge X \to Y:
\beta_{\text{stdyx}} = \beta \times \frac{\text{SD}(X)}{\text{SD}(Y)}
The interpretation is: a one standard deviation increase in X is associated with a \beta_{\text{stdyx}} standard deviation change in Y.
In pathmc this is computed draw-by-draw from the posterior, so the result is a full distribution over the standardized coefficient — not a point estimate.
model.fit()
model.standardized()The returned DataFrame reports the posterior mean, standard deviation, and 94% highest density interval for each labeled coefficient.
Why “stdyx”?
The name comes from Mplus (Muthén and Muthén 2017), which distinguishes three standardization variants. lavaan (Rosseel 2012) adopted the same naming, and pathmc follows suit since it uses a lavaan-inspired DSL.
| Variant | Formula | When to use |
|---|---|---|
| STDYX | \beta \times \text{SD}(X) / \text{SD}(Y) | Continuous predictors and outcomes (default) |
| STDY | \beta / \text{SD}(Y) | Binary or categorical predictors, where standardizing X is not meaningful |
| STD | \beta \times \text{SD}_{\text{model}} | Standardize by model-implied (latent) SD only |
pathmc currently implements STDYX. For binary predictors, the coefficient is skipped rather than producing a misleading value (since \text{SD}(X) for a 0/1 variable depends on the base rate, not the scale of the effect).
What standardized coefficients are good for
Comparing relative importance. If ad_spend has \beta_{\text{stdyx}} = 0.35 and organic_search has \beta_{\text{stdyx}} = 0.12 in the same equation, then a one-SD change in ad spend moves the outcome roughly three times as much as a one-SD change in organic search — regardless of the original units.
Not for causal effect sizes. Standardized coefficients describe relative importance within a model, not the size of an intervention. For causal effect sizes in natural units, use do(), ate(), or cate(). For a discussion of the distinction, see Baguley (2009).
Interaction terms
Interaction terms (e.g., X:Z) are skipped during standardization. Standardizing an interaction is ambiguous — the product X \times Z does not have a single predictor SD — and the resulting value would be misleading. Report interaction effects on their original scale or use conditional predictions (cate()) to interpret them.
Latent variables
Variables that appear as latent mediators (defined by a := expression or absent from the data) are also skipped: there is no observed \text{SD}(X) or \text{SD}(Y) to standardize with.