How about generalized SEM? Does your software support it? If not, are you willing to try some other software that does?

I am not a useR, but this page suggests that it might be possible:

• https://lavaan.ugent.be/tutorial/cat.html

As far as I understand Baron and Kenny's approach, it doesn't require you use a common OLS linear regression model. Any type of model where you have a dependent variable and an independent variable would work.

Correct me if I'm wrong.

And I guess, say, if your moderator variable were categorical in nature, you'd have to use a different kind of model for the second step .

Given your ordinal outcome variable and continuous regressors and mediators, a direct application of the Baron and Kenny (1986) method would not be appropriate since that method assumes a linear regression framework. However, you can adapt mediation analysis to suit an ordinal outcome by following these steps:

1. Use Ordinal Logistic (or Probit) Regression for the Outcome

Since your dependent variable is ordinal, an ordinal logistic regression or ordinal probit regression is suitable to model the relationship between the independent variable and the outcome variable. In this model:

• You can regress the ordinal outcome (Y) on the independent variable (X).
• Then, you can regress the ordinal outcome (Y) on both the independent variable (X) and the mediator (M).

This will allow you to examine the effect of the independent variable on the outcome both with and without the mediator, which is central to mediation analysis.

2. Linear Regression for Continuous Mediators

For the continuous mediating variable, you can use standard linear regression:

• Regress the mediator (M) on the independent variable (X) using linear regression.

3. Test for Mediation Using the Product of Coefficients Approach

Mediation analysis in this case can be performed using the product of coefficients approach, which calculates the indirect effect as the product of:

• The coefficient of the effect of XXX on MMM (denoted as aaa),
• The coefficient of the effect of MMM on YYY, controlling for XXX (denoted as bbb).

The indirect effect is a×ba \times ba×b. If this product is significantly different from zero, there is evidence of mediation.

4. Bootstrap for Confidence Intervals

Since the distribution of the indirect effect might not be normal (especially when the outcome is ordinal), it's best to use bootstrapping to estimate the confidence intervals of the indirect effect. Bootstrapping is a non-parametric resampling method that provides more robust estimates of the mediation effect and its significance.

5. Alternative Methods for Nonlinear Mediation

You may also consider advanced mediation techniques designed for nonlinear models, such as structural equation modeling (SEM) or Bayesian mediation analysis. These methods can handle both ordinal outcomes and continuous mediators in a more flexible manner.

Steps for Mediation Analysis with Ordinal Outcome: