### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# 694 Class Note for PHYS 597A with Professor Albert at PSU

### View Full Document

## 21

## 0

## Popular in Course

## Popular in Department

This 33 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 21 views.

## Similar to Course at Penn State

## Reviews for 694 Class Note for PHYS 597A with Professor Albert at PSU

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

Ruth M Hummel Phys 597A Department of Statistics 7 Penn State University April 24 2007 Umug Review of some useful ways to generate random networks For SIR Susceptible Infected Removed models of disease spread we could consider the following 39philosophies39 of network generation F inli M Hi Review of some useful ways to generate random networks For SIR Susceptible Infected Removed models of disease spread we could consider the following 39philosophies39 of network generation a Poisson Mean Field F inli M Hi Review of some useful ways to generate random networks For SIR Susceptible Infected Removed models of disease spread we could consider the following 39philosophies39 of network generation a Poisson Mean Field 9 Small world F inli M Hi Review of some useful ways to generate random networks For SIR Susceptible Infected Removed models of disease spread we could consider the following 39philosophies39 of network generation 0 Poisson Mean Field 9 Small world o Scale free F inli M Hi Field random networks 0 closed to birth non disease death immigration 0 susceptibility to disease is homogenous across the network 0 degree of each node is randomly generated from a Poisson distibution edges assigned to correspond to specified degrees 0 rate of exposure is directly proportional to the density of infections Wm M Hm liking ma ll wng Wat r teem Mime amid 0 closed to birth non disease death immigration 0 susceptibility to disease is homogenous across the network 0 degree distribution is roughly symmetric 0 much custering 0 short average path length F mh M Hui 1 lt 39 Wm jgai emi39wkwamn a closed to birth non disease death immigration a susceptibility to disease is homogenous across the network 0 highly skewed distribution of contacts follows a discretized Weibull distribution 0 most nodes have few connections a a few nodes are highly connected called quothubsquot or su perconnectors Wm M Hui liking ma ll wng must t teem WWW amid Another option model based random networks 0 For many situations these frameworks are reasonable but often the resulting networks look dramatically different than the real life networks F mli lHl Hi idel based random networks 0 For many situations these frameworks are reasonable but often the resulting networks look dramatically different than the real life networks 0 Model based random networks allow us to specify characteristics about the network shape and structure and about nodal attributes that we want to have some control over in our simulated networks mm M Hm Lima model based random networks o For many situations these frameworks are reasonable but often the resulting networks look dramatically different than the real life networks 0 Model based random networks allow us to specify characteristics about the network shape and structure and about nodal attributes that we want to have some control over in our simulated networks 0 Goodness of fit tests can be employed to help us choose models that include highly predictive covariate and network characteristic effects mm M Hi wig an W ERGM I o The Exponential family Random Graph Model ERGM uses the exponential family form which allows us to include a variety of properties as inputs in a statement that assigns probabilities to the outcomes which are networks mm M Hi Limin ma W l ERGM in o The Exponential family Random Graph Model ERGM uses the exponential family form which allows us to include a variety of properties as inputs in a statement that assigns probabilities to the outcomes which are networks 0 Just as in regression we specify the characteristics of interest like Gender or Degree Distribution use an observed network to estimate the strength of each effect the parameter and standard error associated with each specified characteristic and then we can use these estimated parameters to produce new networks that will be related to our original network in the properties that we specified mm M Hi wig an W y EXpt91X1 02X2 93X3 Y is any random network y is the network we have observed X is a nodal or network attribute that we think is important in describing when edges will exist between certain dyads and 0 is the parameter measuring the strength of the effect of X F mh M Hi mmg magi mint we W iz 3 kiwi aws mth 0 I want to start with a data set on which I have some information 0 I want to start with a data set on which I have some information 0 My next step is to find a model that fits reasonably well more on this later l The Plan 0 I want to start with a data set on which I have some information Q My next step is to find a model that fits reasonably well more on this later 9 I can then simulate new networks from the fitted model F mh M Hm Limin ma W Considerationi simulating from ERGMS 9 Just describing one or two features such as the degree distribution and the total number of edges can lead to a best fit model that will essentially never give us back a network that looks like the one from which we found the model parameters F mli M Hi l C I lldl sl ii quot imulating from ERGMS 0 Just describing one or two features such as the degree distribution and the total number of edges can lead to a best fit model that will essentially never give us back a network that looks like the one from which we found the model parameters 0 This is why Goodness of Fit tests are important they help us choose the best model mm M Hi Lima an W Fall 6th grade reciprocated friends shy n3 drum ax m mg 0 We use a simulated network called quotFaux High School published in the Statnet package thanks to Steve Goodreau for this 0 This network was simulated based on characteristics of one school in the first wave of the AddHealth study 0 The categorical nodel covariates in this network are sex race and grade mm M Hi Limin ma W Netwokepency 3 Because of the effect we believe network dependency will have on the rate of transmission of a contact disease in the network we are particularly interested in studying the network specific dependent statistics Wm M Hui Neitxwrl cl 0 Because of the effect we believe network dependency will have on the rate of transmission of a contact disease in the network we are particularly interested in studying the network specific dependent statistics 0 For this reason we need to include network specific terms mm M Hm Limin l Nemwrik 0 Because of the effect we believe network dependency will have on the rate of transmission of a contact disease in the network we are particularly interested in studying the network specific dependent statistics 0 For this reason we need to include network specific terms 0 Once we attempt to account for this dependence we can no longer estimate the model using simple logistic regression Instead we used Monte Carlo MLE to estimate the parameters in the model mm M Hm Lima Ell quote estats To capture the dyadic dependence we include o the geometrically weighted dyadic shared partner GWDSP statistic which is a function of the number of dyads which have k neighbors in common from k 1 to n 2 0 shared partners 3 54 5 1shared partner 1 31 42 51 54 22 3 2 shared partners 1 23 4 To capture the dyadic dependence we include o the geometrically weighted dyadic shared partner GWDSP statistic which is a function of the number of dyads which have k neighbors in common from k 1 to n 2 o a statistic for the geometrically weighted edgewise shared partner GWESP which is a geometrically weighted function of the number of edges which share 1 2 etc common nodes mm M Hu Lima an wmmuir To capture the dyadic dependence we include o the geometrically weighted dyadic shared partner GWDSP statistic which is a function of the number of dyads which have k neighbors in common from k 1 to n 2 o a statistic for the geometrically weighted edgewise shared partner GWESP which is a geometrically weighted function of the number of edges which share 1 2 etc common nodes 0 a statistic for the geometrically weighted degree distribution GWDEGREE which is a function of the number of nodes having each observed degree mm M H Lima an Wm Coefficient ModelO Modell Model2 Model3 Model4 edges x x x x x Nodefactorgrade x x x x Nodefactorrace x x x x Nodefactorsex x x x x GWDEGREE x x x GWESP x x GWDSP x AIC 22877 22398 21628 15585 BIC 22957 23273 22582 16698 mm M Hm Mama S lnmiur gt 39 g a Wm mummy 31g mgnw was a 0 Generate networks of different sizes to study how the parameters change when we re scale the network size 0 Generate networks of different sizes to study how the parameters change when we re scale the network size 9 Simulate disease spread across ERGM random networks and compare results to disease spread on Poisson Small world and Scale free networks Lia mg 0 Handcock M S Hunter D R Butts C T Goodreau S M and Morris M 2003 quotstatnet An R package for the Statistical Modeling of Social Networks URL iURL httpwwwcsdewashingtonedustatnet 9 Hunter D R and Handcock M S 2006 Inference in curved exponential family models for networks Journal of Computational and Graphical Statistics 9 Hunter DR Goodreau SM and Handcock MS 2005 Goodness of Fit of Social Network Models Working Paper 46 Center for Statistics and the Social Sciences University of Washington iURL wwwcssswashingtoneduPaperswp47pdf 9 Resnick MD Bearman PS Blum RW etal 1997 Protecting adolescents from harm Findings from the National Longitudinal Study on Adolescent Health Journal of the American Medical Association 278 82332 Thank You F ulh lHl Hui

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.