Supplement to Chapter on Association Networks
Presentations
 Association networks Read►
 Introduction to chisquare test Read►
 Statistical test of independence in 2 variables Slides►
 Statistical test of independence in 3 variables Slides►
 Independence test through Poisson regression Slides►
 Jee Vang's lecture on independence test through Mutual Information Slides►
Assignment
Question 1: For
this assignment you can use any statistical package including SQL or
Excel. Work can be done in group's of two students but you cannot
work with a student that you have previously teamed up with.
A. For the following data:
MD 
RN 
Complaint 
Observed 
George 
Jim 
Yes 
53 
George 
Jim 
No 
424 
George 
Jill 
Yes 
11 
George 
Jill 
No 
37 
Smith 
Jim 
Yes 
0 
Smith 
Jim 
No 
16 
Smith 
Jill 
Yes 
4 
Smith 
Jill 
No 
139 

Estimate chisquare for complete independence, 3 joint independence
models, and 3 homogenous models

Which model best fits the data and why? Shruti's
response► Aryan
& Saeed's SQL►
Question 2: In the following data, test which pair of
variables are independent and which pairs are associated. First
calculate the goodness of fit of a homogenous model (all main effects
and all pair wise associations). Then progressively remove one of
the pairs from the model until you can find a set of associations that
fit the data. R
code► Slides►
Center for Medicare Services reimburses hip fracture treatment based on
one price for the hospital, physician or post acute care. Each
group continues to bill for their service as usual but at end of the
year the hospitals that have above average bundled costs are penalized
and hospitals that have below average bundled costs receive a financial
incentive. The hospital manager is interested to understand which
component of the operations contributes most to above average cost. The
data shows the number of hip fracture patients with above and below
average cost when cared for by various teams of clinicians. There
are five dimensions in the contingency table: orthopedic surgeon
(O), use of rehabilitation services (R), use of one of two skilled
nursing facilities (N), severity of patients' illness (S), and whether
the cost of the patient exceeded average bundled cost (A). You are
asked to fit a model that includes all pairwise interactions, including
OR, ON, OS, OA, RN, RS, RA, NS, NA, and SA. Calculate the fit of
the model to the data using chisquare. Then remove one of the
pairwise terms to see if it affects model performance significantly.
Continue to do so until you obtain a parsimonious model that describes
the relationships in the data and whose fit to the data cannot be
rejected. Verify that the associations shown in the following Figure
fits the result of your analysis. For every associated pair in the
model (significant or not significant), there should be a link in the
Figure. Identify which arc should not be there and which arc
should be there but is not there.

N: Skilled Nursing Facility A 
Skilled Nursing Facility B 
S: High Severity 
Low Severity 
High Severity 
Low Severity 
O: Orthopedic Surgeon 
R: Rehab Services 
A: > Bundle Cost 
< Bundle Cost 
> Bundle Cost 
< Bundle Cost 
> Bundle Cost 
< Bundle Cost 
> Bundle Cost 
< Bundle Cost 
Joe 
Yes 
405 
268 
453 
228 
23 
23 
30 
19 
Joe 
No 
13 
218 
28 
201 
2 
19 
1 
18 
Jim 
Yes 
1 
17 
1 
17 
0 
1 
1 
8 
Jim 
No 
1 
117 
1 
133 
0 
12 
0 
17 
Data
adapted from Agresti A. Categorical Data Analysis, 3rd Edition,
Wiley InterScience, 2013, page 381 
Question 3. Select
3 variables from the STAR*D data and analyze the independence
relationship among the variables.

Read about the STAR*D study protocol. Protocol►

Download data. Use instructor's last name as password. Must enter
password twice. Data
2010► Data
2003►

Select 3 variables

Test 1 complete independence, 3 joint independence, and 3 homogenous
associations.

Identify the most parsimonious model whose fit to the data cannot be
rejected

Describe the meaning of your insight.
Arpitha and Shruti's Response► Sheri
Moinamin's Teach One Video► R
Code► Data►
More
For additional information (not part of the required reading), please
see the following links:

Independence and Bayesian networks Video►

Introduction to probability models Read► Slide►

Event time stratification Read►

Bayes rule & independence Video►

Estimating effects of nursing in clinical teams
Read►

Breaking nominal variables into binary variables Read►
 The
relationship between chisquare statistics from matched and
unmatched analyses Read►

Jeff Lin's analysis of independence of 3 variables Read►

Decomposable (independent) subgraphs in 5 variable models Read►

Visualizing conditional probability See►
