Indistinguishable dyads

MLM and SEM for dyads whose members are interchangeable

When the two members of each dyad are not marked by a distinguishing variable — siblings, strangers paired in an experiment, friends — the APIM treats the actor and partner slopes as equal. The two tutorials in this section show how to fit and interpret the model in long format with lme4 and in wide format with lavaan.

When to use these tutorials

You have dyadic data with no distinguishing variable, or you are fitting a baseline model whose constraints you will later relax (distinguishable dyads). The distinguishable tutorials in the next section build on these.

Tutorial 02 — Indistinguishable dyads: MLM

Long format, lme4::lmer. Random intercept per dyad. ICC. Full APIM with all actor and partner effects. Likelihood ratio test for the partner block. Profile-likelihood confidence intervals.

MLM Beginner

Open tutorial →

Tutorial 03 — Indistinguishable dyads: SEM wide

Wide format, lavaan::sem. Equality-constrained actor and partner slopes. Fit indices. The Olsen & Kenny (2006) specification. Likelihood ratio test against the unconstrained model.

SEM Intermediate

Open tutorial →

How the two tutorials relate

Both tutorials fit the same APIM, but they go about it differently.

The MLM tutorial uses long-format data. The random intercept for dyad_id accounts for the non-independence. The slope labels are the same for actor and partner predictors — by construction, in the long format, the same variable name is used for both partners’ scores.
The SEM tutorial uses wide-format data. The equality of actor and partner slopes is imposed explicitly in the lavaan model syntax, by labelling the two paths with the same label.

In the simulated dyad_data dataset, the actor and partner slopes are equal in the data-generating process. The two approaches should give you identical point estimates, but the SEM is more flexible (it can test the equality of slopes via an LRT against the unconstrained model — see the distinguishable SEM wide tutorial for that).

--- title: "Indistinguishable dyads" subtitle: "MLM and SEM for dyads whose members are interchangeable" --- When the two members of each dyad are not marked by a distinguishing variable — siblings, strangers paired in an experiment, friends — the APIM treats the actor and partner slopes as equal. The two tutorials in this section show how to fit and interpret the model in long format with `lme4` and in wide format with `lavaan`. ::: {.callout-note} ## When to use these tutorials You have dyadic data with no distinguishing variable, **or** you are fitting a baseline model whose constraints you will later relax (distinguishable dyads). The distinguishable tutorials in the next section build on these. ::: ::: {.card-grid} ::: {.card} ### [Tutorial 02 — Indistinguishable dyads: MLM]{.card-title-link} Long format, `lme4::lmer`. Random intercept per dyad. ICC. Full APIM with all actor and partner effects. Likelihood ratio test for the partner block. Profile-likelihood confidence intervals. MLM Beginner [Open tutorial →](mlm.html) ::: ::: {.card} ### [Tutorial 03 — Indistinguishable dyads: SEM wide]{.card-title-link} Wide format, `lavaan::sem`. Equality-constrained actor and partner slopes. Fit indices. The Olsen & Kenny (2006) specification. Likelihood ratio test against the unconstrained model. SEM Intermediate [Open tutorial →](sem.html) ::: ::: ## How the two tutorials relate Both tutorials fit the same APIM, but they go about it differently. - The **MLM** tutorial uses long-format data. The random intercept for `dyad_id` accounts for the non-independence. The slope labels are the same for actor and partner predictors — by construction, in the long format, the same variable name is used for both partners' scores. - The **SEM** tutorial uses wide-format data. The equality of actor and partner slopes is imposed *explicitly* in the `lavaan` model syntax, by labelling the two paths with the same label. In the simulated `dyad_data` dataset, the actor and partner slopes are equal in the data-generating process. The two approaches should give you identical point estimates, but the SEM is more flexible (it can test the equality of slopes via an LRT against the unconstrained model — see the [distinguishable SEM wide tutorial](../distinguishable/sem-wide.html) for that).