Table 2 Effects included in SIENA models for modeling the co-evolution of friendship ties and smoking/vaping outcomes.

Constant friendship rate (period 1)

Rate effect.

A constant term representing the dependence of friendship nominations on the period (i.e., the rate of changing friendship ties in period 1).

Smoking/vaping outcome alter^a

Peer selection effects

The sum of the smoking/vaping outcome over all actors to whom ego is tied. Represents the association between the smoking/vaping outcome level and the tendency to be nominated as a friend.

Smoking/vaping outcome squared alter^a,b

The sum of the squared (centered) smoking/vaping outcome over all actors to whom ego is tied. Represents the marginal association between the smoking/vaping outcome level and the tendency to be nominated, controlling for the previous effect.

Smoking/vaping outcome ego^a

Ego’s outdegree (number of friendship nominations) weighted by his/her value of the smoking/vaping outcome. Represents the association between the smoking/vaping outcome level and the tendency to nominate friends.

Smoking/vaping outcome similarity (peer selection homophily)^a

The sum of centered similarity scores on the smoking/vaping outcome between ego and the other actors to whom ego is tied (higher similarity scores indicate greater similarity between ego and the actors to whom ego is tied). Represents the tendency to select a friend based on similarity on the smoking/vaping outcome.

Outdegree (density)

Control effects

Ego’s out-degree (number of friendship nominations). Represents the general tendency to nominate friends (i.e., the density of the network).

Reciprocity

The number of ego’s reciprocated ties. Represents the tendency to return friendship nominations.

Transitive ties

The number of actors to whom ego is directly as well as indirectly tied. Represents the tendency to select a friend who is already friends with one of an adolescent’s other friends.

Transitive triplets

The number of transitive patterns in ego’s relations (i.e., ordered pairs of actors, both of whom are tied to ego, and also tied to each other). Represents the tendency to select further friends of friends in addition to the first such friend, which is represented by the previous “transitive ties” effect.

Number of actors at distance 2

The number of actors to whom ego is indirectly tied, through at least one intermediary. Represents the tendency to be indirectly (through one of your friends) instead of directly connected to others.

Three-cycles

Ego’s number of three cycles. Represents a generalized form of reciprocity, or the tendency to stay indirectly tied to other actors within a closed triad (actor ‘a’ nominates actor ‘b’, actor ‘b’ nominates actor ‘c’, actor ‘c’ nominates actor ‘a’). A significant negative “Three-cycles” effect, in addition to positive “Transitive ties” or “Transitive triplets” effects, may be interpreted as a tendency towards local hierarchy within the network.

Gender alter

Tendency for girls/PNTS to be selected as friends more often compared to boys.

Gender ego

Tendency for girls/PNTS to select more friends compared to boys.

Gender similarity

Tendency to select a friend based on similar gender.

Age alter

Tendency for older pupils to be selected as friends more often compared to younger pupils.

Age ego

Tendency for older pupils to select more friends compared to younger pupils.

Age similarity

Tendency to select a friend based on similar age.

SES alter^c

Tendency for pupils with higher SES to be selected as friends more often compared to pupils with lower SES.

SES ego^c

Tendency for pupils with higher SES to select more friends compared to pupils with lower SES.

SES similarity^c

Tendency to select a friend based on similar SES.

School class similarity

The number of ties ego has to all other actors in the same school class. Represents the tendency to nominate a friend based on being in the same school class.

Rate smoking/vaping outcome (period 1)

Rate effect.

A constant term representing the dependence of the level of smoking/vaping outcome on the period (i.e., the tendency for individuals to change their values of the smoking/vaping outcome in period 1).

Smoking/vaping outcome friends (peer influence)^a

Peer influence effects.

Average similarity effect. The average of centered similarity scores on the smoking/vaping outcome between ego and the other actors to whom ego is tied (higher similarity scores indicate greater similarity between ego and the actors to whom ego is tied). Represents the tendency for ego to change his/her value of the smoking/vaping outcome to become similar to current friends.

Linear shape

Control effects.

Ego’s value of the smoking/vaping outcome. Represents the general trend of the smoking/vaping outcome variable.

Quadratic shape^b

Ego’s squared value of the smoking/vaping outcome. Represents the effect of the smoking/vaping outcome on itself, controlling for the previous effect (where the attractiveness of further increases/decreases in the smoking/vaping outcome depends on the actor’s current value of the outcome).

Effect from ego’s gender

Effect of ego’s gender on ego’s own value of the smoking/vaping outcome (higher values indicate girls/PNTS tend to have higher values of the smoking/vaping outcome compared to boys).

Effect from ego’s age

Effect of ego’s age on ego’s own value of the smoking/vaping outcome (higher values indicate older pupils tend to have higher values of the smoking/vaping outcome compared to younger pupils).

Effect from ego’s SES^c

Effect of ego’s SES on ego’s own value of the smoking/vaping outcome (higher values indicate pupils with higher SES tend to have higher values of the smoking/vaping outcome compared to pupils with lower SES).