. Author manuscript; available in PMC: 2013 Apr 16.

Published in final edited form as: Soc Ment Health. 2012 Jun 6;2(2):99–119. doi: 10.1177/2156869312445211

Table 1.

Description of the main model parameters for the network selection model

Parameter	$Formula = s_{k i}^{net}$	Description
Selection Parameters & Covariate Effects
Alter (potential friend)	$\sum_{j} x_{i j} v_{j}$	Main effect of potential friend’s CES-D or varname on the selection of friends (−β=exclusion)
Ego (adolescent)	$v \sum_{j} x_{i j}$	Main effect of adolescent’s CES-D or varname on the selection of friends (−β=withdrawal)
Similarity potential friend & adolescent^a	$\sum_{j} x_{i j} ({sim}_{i j} - \bar{sim})$	Tendency to choose a friend based upon CES-D or varname similarity (+β=homophilous selection)
Same potential friend & adolescent^b	$\sum_{j} x_{i j} I (v_{i} = v_{j})$	Tendency to choose friends with exactly the same varname
Structural Network Effects
Outdegree	$\sum_{j} x_{i j}$	General tendency to choose a friend
Reciprocity	$\sum_{j} x_{i j} x_{j i}$	Tendency to have reciprocal friendships
Transitive triplets	$\sum_{j, h} x_{i h} x_{i j} x_{j h}$	Tendency to become the friend of a friend’s friend
3-Cycles^*	$\sum_{j, h} x_{i j} x_{j h} x_{h i}$	Tendency for a friend’s friend to chose the focal adolescent as a friend
Number distance=2^**,^c	#(j\|x_ij = 0, G = 2)	Tendency to be indirectly connected through one intermediary
Rate Parameters
Basic rate parameter	---	Determines the average number of change opportunities in each period
varname	---	Differences in the rate of change by varname

Notes for structural network effects: A positive effect implies generalized reciprocity while a negative effect with a positive transitive triplet effect suggests local hierarchies (Ripley and Snijders 2011).

^**

This effect is an inverse effect of network closure so effects tend to be negative, suggesting that indirect connections tend to close through, e.g., the formation of transitive triplets, or else the indirect connections are lost.

Notes for equations and notation: All covariates are centered at the grand mean and v generically refers to CES-D and additional covariates (varname).

sim_ij = 1 – |v_i – v_j|/max_ij |v_i – v_j| and $\bar{sim}$ is the average similarity.

I(v_i = v_j) is a function indicating whether v_i = v_j (=1) or v_i ≠ v_j (=0).

This function is the number (#) of actors at geodesic distance=2 (G=2) to which the actor is not directly tied (x_ij = 0).