Tracy Morrison Sweet

After my meeting, I’m going to work on two things.  Getting my tech report into a paper form to submit to either Psychometrika, JEBS, etc.  If we can get a great data set, maybe even JASA.  I guess it’ll depend on what the paper looks like.

In coding news, I’m going to start coding a new MMSBM for Jim and Megan.  We’ll see how it goes.  Remember log normal.

***Other stuff****

(1)  A paper comparing the HLSM with the multilevel p2 model.

*I’ve started it.  I need to keep working on it.

(2) Bullying data

*Running one last set of models and then I think I’m ready to hang this one up for a bit.

(3)  Spillane new model for across teacher ties

(4)  Madill data

*Need to do 3 and 4*

(5)  Simulation study investigating the correlation among ties

*So I wasn’t thinking about this correctly.  The way that I’ve set up the simulation, I’d expect the correlation to be constant with network size.  With LS positions coming from the same distribution, I’ve basically constrained the distances to be of a certain scale and with that the correlations.  I need to revisit this paper and see how I can make sense of the Cramer stuff and the GEE stuff.

(6)  SREE talk

*First draft done.  Did a practice talk at SERG last Monday and received a lot of really useful feedback.  Still need to do the edits, but I have plenty of time.

(7) Edits to MM Chapter

*Done!  Sent off to Andrew to edit.

(8)  Working with Megan on fitting a p2 model

*Stochnet downloaded, now I’m not sure which data set I’m supposed to be using!

I need to return to my blog because I need a place to organize my progress on the many different projects I’m working on.

(1)  A paper comparing the HLSM with the multilevel p2 model.

(2) Bullying data (see below)

(3)  Spillane new model for across teacher ties

(4)  Madill data

(5)  Simulation study investigating the correlation among ties

(6)  SREE talk

(7) Edits to MM Chapter

(8)  Working with Megan on fitting a p2 model

(9)  New ideas (a spatial HNM, spatial component to an IRT model, network as mediator)

(10)  Other odds and ends (emails, job decisions!, potential collaborations with psychologists)

*Bully Data*

I’ve fit separate fits and it’s not clear that there’s an effect.  One last thing before I give up.  I’m going to fit a Control group only and Treatment group only and estimate an overall mean of each group.  We’ll see what happens.

BP-SeparateFits

*Correlation Sim Study*

It’s not at all clear that the LSM produces more or less correlated ties as network size increases.  But the GEE results suggest that to be the case.  What is going on?  To answer this question (in part), I’ll look into correlation among valued networks (simulated).

To simulate a valued network: I’ll simulate some type of sparsity.  So there’s a probability of a non-zero.  And then I’ll simulate some count (poisson).  Overdispersed poisson.  And see what happens.

Oh right, I keep forgetting about these zeros.  If one tie is always 0, it’s not possible to calculate correlation.  So ties that are consistently 0 (which could be a good number) have undefined correlation.  And that’s problem – there might be some kind of dependence that “causes” these ties to consistently zero.  Tie-12 might be always 0 but that would affect Tie-13 if 2 and 3 are close together.  Ugh.

I can’t seem to get my head oriented in the right direction.  The LS positions (for this simulation) are fixed.  So it’s really the distance that contributes to probability of a tie and that’s the same for each round.   So maybe what I need to do is jitter/alter the intercept in the model and that will change the overall probabilities and I should compute the correlation among those.  Let’s see…

I’m still not measuring what I want to measure.  I want to somehow measure how a tie between 1-2 affects a tie between 1-3 or 2-4.  The last attempt really just brought me back to correlating the linear functions of the two distances, which is not what I want.

Power Analysis – the plan is to continue in the literature search to find tools that can help.  So far, very little is out there to help.

A few things to note: Cross-classified models what I’ve found so far use simulations to estimate power.  That’s not a great sign.  And the more I delve into GEE (which isn’t all that deep, but still), the more I realize it requires having some idea of the covariance structure- which is problematic since we have no idea what each network will actually look like.  We could make some assumptions if we were in an ERGM framework (like Markov dependence possibly), but it seems pretty complicated.

The plan for today is to continue reading about the biostats literature, but I’m not optimisitic.  Another plan is to scrap the power analysis stuff altogether – try to publish what results we do have, do a more formal simulation study, and call it a day.

Other things I can work on is a continuous tie version of the HLSM.  That might be fun to think about – and use Peter Hoff’s work as a spring board.  OR, I can think about something else entirely.

Does this mean, I shouldn’t continue doing research when I’m in a funk right now?  Should I be thinking about teaching positions instead?  I don’t know.

It’s official, the post-doc has begun.

Plans for the next few months:

1. Continue power work
2. Fit multilevel p2 models
3. Spillane data
4. Bullying Prevention data
5. Spend 1 morning a week thinking about incorporating social networks as a covariate.

Very productive meeting = I have a busy week of work!

Literature Review

1 – Look into power analysis work for cross-classified models.  Since these are similar to p1 models, maybe there’s something there about adapting them.

2 – Look into papers on consistency of MLEs (in particular when the data are not identically distributed).

Regarding the Single Network stuff:  We can look at the OLS estimate as a function of beta + a linear combination of gammas (see notes).  We’re essentially estimating a lower bound on the treatmenteffect.  Can we push it further?

Multiple Networks: Brian also had the idea to focus on the multiple networks.  We have independent networks (that are not distributed identically).  Perhaps there are some assumptions (either ones that can be relaxed or not) that will allow us to say the mle (i.e. treatment effect estimator) is in fact consistent.  I need to look at some papers.

1- I  need to look at the Lehmann book examples (6.4 and 6.8).

2 – I need to read the paper Brian sent (thm 4.1 which is an example of this method of proving consistency from Serfling’s book).

3 – Read the pdf on this too.

So the blog has taken a backseat for the past month since I’ve been focusing on my “theoretical chapter”.

My quest in putting together power analyses for HLSMs has taken me in a few areas.

(1) Looking at the biostats literature on RCTs with binary outcomes.  It seems people focus on the test and don’t pay too much attention to the binary outcome (?).  If the data is clustered, then people do GEE/sandwich estimators and/or do some form of linearization of the logit model.

(2) If I assume Euclidean squared distance, the latent space pairwise distances have a Gamma distribution (assuming a mean 0, diagonal covariance on the LS positions).  We still have this issue of dependence of these “residuals” and so the GEE stuff comes up again.

In other news:

I can think about the random effect/treatment effect identifiability and actually start putting together my thesis when I have free time.

I need to start scheduling my time a little bit better since I only have a few months to finish this and put together a draft.

Plots for our meeting:

(1) Fitting each of the models separately.

PittsBetas

SepPittsBetas

PittsMuSigmas

(2) Plots of the Pitts Neworks

PittsNetworksLSpositions

(3)  Heat Map Showing LS distance recovery

LS-truedistance

SimAis0.5LSdistances

SimAis1LSdistances

SimAis2LSdistances

SimAis3LSdistances

Mid-February already!

Topics to discuss at our meeting:

(1) Reviews from the JEBS paper.

(2) Comments on the MM paper.

(3) Copyright form that I need to complete.

(4)  Chugging away at power.

A heat map comparison of a strong and less strong prior.  Still waiting on the weak prior results.

ColorSchools1-4

ColorSchools5-8

ColorSchools9-12

ColorSchools13-16

ColorSchools17-20

A now (finally) preliminary results from my covariate sampler.  Note: theB matrix has been entirely reparameterized into logitB.

AlphaTrace

BTraceplot1

BTraceplot2

Things to do following my meeting:

(1) Observation Simulations lead us to some questions/ideas: We see that the parameters are high prior driven.  And in actually we see an interaction between sample size and block structure in that a larger sample size would make things more data driven, but networks with strong block structure appear to be more data driven.

• This is something to think about.  What would we need to do to make the model fit more data driven?
• Are the traceplots of the gammas really different (weak vs strong)?  Look at the trace plots of the log(gamma) to see.
• It’s interesting that the point estimates don’t appear to be affected by the difference in prior.  But we don’t know that for sure unless we look at variability.  Do a heat map type plot (roygbiv color) of the point estimates and another one for variance.

(2)  What is going on with my Covariate MM stuff?

• Evaluate the log likelihood at a sequence from 0 to 1 at the new value of B proposed.  And look at what it looks like.  It should look normal.
• Fix B at the truth and see what’s going on with alpha.
• Propose new values for logit(B) instead of B and do a normal random walk instead.  An alternative would be a uniform centered at B_0 (see notes).