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Many thanks for the good feedback. Here are last few thoughts from my end.

"When it there is a correlation, you can't just drop the nodefactor
terms and interpret the nodematch terms naively.  The interpretation
of nodematch terms will be unclear if, for example, there is a
difference in the level of homophily for groups that are more (or
less) active."

If nodefactor is not included, the coefficient for nodematch is the
log-odds of the presence of ties between actors with same attribute as
compared to the presence of ties between actors with differential
attributes. We can also allow for differential homophiliy. In either
case, the reference category is the presence of ties between actors
with differential attributes.

The ambiguity regarding the interpretation of nodematch comes when
nodefactor is included. When nodefactor is included, it adds one
statistics which is equal to the number of ties that have the active
factor attribute, including both 0-1 and 1-1 ties, while nodematch
adds a statistics which is equal to the number of ties that both
actors share the same attributes including 0-0 and 1-1 ties. The
sharing of 1-1 ties in the statistics leads nodefactor and nodematch
to be correlated. The coefficients for the two models (with or without
nodefactor) will certainly be different because of the correlation.

The question is whether the correlation makes it illegitimate to
specify a model that includes only the nodematch terms and whether we
can still properly interpret that model. I think we can, as the
reference category is clear. In contrast, in the model with nodefactor
included, the reference category seems not to be that clear (ties
from/to actors with the passive state of the attribute?). In general,
the latter is a more interesting model, as the nodefacor term captures
the inequality effect while the nodematch term captures the
segregation effect. But this does not imply that an ERGM cannot just
have the segregation effect.

In our case, almost all nodefactor terms are not significant, because
of the spatial constrain in the friending process. My co-authors and I
want to include only just nodematch terms.But we want to hear some
good counter-arguments before really deciding to do so. Thanks!


best,

Weihua

P.s. Even if you look at the literature on main effect and interaction
effect in regression analysis, there seems not be a good consensus on
whether the main effect should always be included. In general, yes,
but it also depends. I think in network case, it may not be necessary
to always include nodefactor, as the nodematch term is not exactly
like the interaction term between two variables. If nodefactor is one
variable, what is the other main variable? How should  we include the
main effect for that variable?


On Wed, Aug 7, 2013 at 1:44 PM, martina morris <[log in to unmask]> wrote:
> On Wed, 7 Aug 2013, Weihua An wrote:
>
>> *****  To join INSNA, visit http://www.insna.org  *****
>>
>> Hi,
>>
>> I have a similar problem. In my networks, by design each person has a
>> fixed (or very close) number of connections. That means no main
>
>
> Nice.  This is a perfect example:  if, by design, your nodes have a fixed
> number of edges, you don't need nodefactor terms.
>
>
>> effects of any covariate will be significant. So our interested is in
>> segregation in friendship networks. Indeed, we find almost no
>> covariates has significant predictive effect, but a lot of the
>> nodematch terms are significant, when both of the terms are included.
>> We are thinking about dropping the nodefactor terms as well, for
>> simpler and clearer interpretation.
>
>
> If the variation in edges by group is insignificant, then this is
> justifiable.
>
>
>> If we keep only the nodematch terms, the base ties will be the
>> asymmetric ties (i.e., the ties that are between people with different
>> binary attributes, assuming the factors are binary).
>
>
> You can make the reference category (base) be either level.
>
>
>> If we keep both nodefactor and nodematch, the base ties seem to be the
>> ties from/to those with the passive attribute (zero in the binary case). So
>> if our understanding is correct, whether to include nodefactor in a model
>> depends on what base ties you want to have and what theoretical questions
>> you want to ask.
>
>
> Not really -- in your case, there is no correlation btwn nodefactor and
> nodematch (b/c there is essentially no variation in nodefactor).  So
> dropping the nodefactor term will have no impact on the estimate of
> nodematch (try it and see if this is true).  But this absence of correlation
> will not be true in general.  When it there is a correlation, you can't just
> drop the nodefactor terms and interpret the nodematch terms naively.  The
> interpretation of nodematch terms will be unclear if, for example, there is
> a difference in the level of homophily for groups that are more (or less)
> active.
>
> The kind of interpretability you're pointing to here -- the reference
> category for factor level comparisons -- can be handled by directly setting
> which factor level to use as a reference category.
>
> You haven't mentioned looking at differential homophily, but that's another
> possible option.
>
> best,
> mm
>
>>
>> best,
>>
>> Weihua
>>
>> On Tue, Aug 6, 2013 at 1:16 PM, martina morris <[log in to unmask]>
>> wrote:
>>>
>>> *****  To join INSNA, visit http://www.insna.org  *****
>>>
>>> Hi Jeff,
>>>
>>> In general, you probably wouldn't want to fit a model with nodematch but
>>> not
>>> nodefactor.  It's a bit like fitting an interaction without the main
>>> effects
>>> -- to the extent that the two are correlated, the interpretation of the
>>> terms changes when one is excluded.  If the nodematch becomes
>>> insignificant
>>> when nodefactor is added, it could mean a couple of different things.
>>>
>>> I'd suggest taking a look at the actual mixing pattern (using the
>>> "mixingmatrix" function), and getting some sense of what is going on in
>>> your
>>> data.
>>>
>>> best,
>>> Martina
>>>
>>>
>>> On Tue, 6 Aug 2013, Jeff Webb wrote:
>>>
>>>> ***** To join INSNA, visit http://www.insna.org ***** Dear list members,
>>>>
>>>> I'm fitting an ergm model to a small network with 20 actors.  The
>>>> feature
>>>> of the
>>>> network in which I'm most interested is homophily among members of a
>>>> subgroup,
>>>> designated "ea."  I test this with nodematch("ea"), which is included in
>>>> the model
>>>> along with structural terms, edges and GWESP ; the effect is positive
>>>> and
>>>> significant.  However, Goodreau et al. (2008) note: "if one is including
>>>> nodematch
>>>> terms in a model, one would typically also include nodefactor terms for
>>>> the same
>>>> attributes."   When I add nodefactor("ea") to the model, the effect of
>>>> nodematch("ea") is no longer significant. Any thoughts on when—if
>>>> ever—one
>>>> would
>>>> fit a model using nodematch() without nodefactor()?
>>>>
>>>> A related question.  I would also like to fit a tergm model to two waves
>>>> of the
>>>> above network.  In this case, unfortunately, the formation part of the
>>>> model will
>>>> not converge when I include the interaction term (node match()) along
>>>> with
>>>> the
>>>> main effect, but it will converge if I include only the the interaction
>>>> term.
>>>>  Would it be reasonable to leave out the main effect in order to get a
>>>> coefficient
>>>> for the interaction?   Thanks in advance for your replies.
>>>> Jeff
>>>> _____________________________________________________________________
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>>>
>>> ****************************************************************
>>>  Professor of Sociology and Statistics
>>>  Director, UWCFAR Sociobehavioral and Prevention Research Core
>>>  Box 354322
>>>  University of Washington
>>>  Seattle, WA 98195-4322
>>>
>>>  Office:        (206) 685-3402
>>>  Dept Office:   (206) 543-5882, 543-7237
>>>  Fax:           (206) 685-7419
>>>
>>> [log in to unmask]
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>>>
>>> _____________________________________________________________________
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>>
>>
>>
>>
>> --
>> Weihua (Edward) An
>>
>> Assistant Professor of Sociology and Statistics
>> Indiana University Bloomington
>> 752 Ballantine Hall
>> 1020 East Kirkwood Avenue
>> Bloomington, IN 47405-7103
>> http://mypage.iu.edu/~weihuaan/
>>
>> _____________________________________________________________________
>> SOCNET is a service of INSNA, the professional association for social
>> network researchers (http://www.insna.org). To unsubscribe, send
>> an email message to [log in to unmask] containing the line
>> UNSUBSCRIBE SOCNET in the body of the message.
>>
>
> ****************************************************************
>  Professor of Sociology and Statistics
>  Director, UWCFAR Sociobehavioral and Prevention Research Core
>  Box 354322
>  University of Washington
>  Seattle, WA 98195-4322
>
>  Office:        (206) 685-3402
>  Dept Office:   (206) 543-5882, 543-7237
>  Fax:           (206) 685-7419
>
> [log in to unmask]
> http://faculty.washington.edu/morrism/



-- 
Weihua (Edward) An

Assistant Professor of Sociology and Statistics
Indiana University Bloomington
752 Ballantine Hall
1020 East Kirkwood Avenue
Bloomington, IN 47405-7103
http://mypage.iu.edu/~weihuaan/

_____________________________________________________________________
SOCNET is a service of INSNA, the professional association for social
network researchers (http://www.insna.org). To unsubscribe, send
an email message to [log in to unmask] containing the line
UNSUBSCRIBE SOCNET in the body of the message.