Choosing mediator and outcome families

Do not choose a Gaussian likelihood merely because it is convenient. Match the family to the support and measurement process of the variable.

Variable	Candidate family	Requirements / cautions
approximately symmetric continuous dwell/score	Gaussian	inspect scale and residual behavior
strictly positive duration	lognormal or Gamma	zeros are invalid under these families
proportion strictly inside (0, 1)	beta	exact 0/1 values require another strategy
inspected vs not inspected	Bernoulli	values must be 0/1
fixation/visit count	Poisson	equidispersion may be unrealistic
overdispersed count	negative binomial	non-negative integer counts
ordered response	ordinal	contiguous ordered integer categories

Zero-heavy gaze variables

A dwell variable with many genuine zeros is not compatible with the current lognormal or Gamma mediator implementation. Do not add a tiny constant silently. Either model a scientifically defensible transformed/continuous representation, use a binary inspection mediator, or treat a hurdle/mixture extension as a separate model-development task.

Indirect-effect scale

For nonlinear likelihoods, the default path-product estimand is on the model's linear-predictor scale. a_W × b_W remains a useful coefficient-product summary, but it is not automatically a probability-scale natural indirect effect. Report the stored estimand scale explicitly.

Worked family-contract example

See Worked example: non-Gaussian mediator contracts for a deterministic support-validation workflow across lognormal, Gamma, beta, Bernoulli, Poisson, and negative-binomial mediators.