Please read the instructions carefully for this test. You are expected to work on your own on this test and similarity across tests will be closely scrutinized. This test is due at the beginning of our class time (9:00AM) on Wednesday March 17th, 2021 and should be e-mailed to me with BST630 Midterm on the subject line. Please be sure to include your name in the file title. On calculation problems, it is always best to show your intermediate steps of calculations. If you do not show these steps, and only provide a final number, I cannot give partial credit for having the correct idea, but making a simple math error.
For the first 3 questions, we will use an example of predicting CD4 cell count over time. We use the square root of CD4 to make the dependent variable more closely to normally distributed. There are 4 time points and two treatment conditions in this data example:
1. When we use only Time as a predictor we get the following results:
Cov Parm Subject Estimate Standard
Error Z Value Pr Z
TOEP(2) ID 43.7894 5.5766 7.85 <.0001
TOEP(3) ID 40.1186 5.5601 7.22 <.0001
TOEP(4) ID 35.7987 5.6303 6.36 <.0001
Residual 49.8067 5.5909 8.91 <.0001
Effect stime Estimate Standard
Error DF t Value Pr > |t|
Intercept 21.2741 0.6754 124 31.50 <.0001
stime 0 0.01819 0.5338 274 0.03 0.9728
stime 1 0.2508 0.4619 274 0.54 0.5877
stime 2 -0.5901 0.3729 274 -1.58 0.1147
stime 3 0 . . . .
Row Effect stime Col1 Col2 Col3 Col4 Col5
1 Intercept 0.4561 -0.1700 -0.1248 -0.08026
2 stime 0 -0.1700 0.2850 0.1893 0.1146
Row Effect stime Col1 Col2 Col3 Col4 Col5
3 stime 1 -0.1248 0.1893 0.2134 0.1100
4 stime 2 -0.08026 0.1146 0.1100 0.1391
5 stime 3
Effect Num DF Den DF F Value Pr > F
stime 3 274 2.20 0.0882
1.) How is time being modeled here (5-pts)?
2.) Using the results above can you show me what the (residual) covariance matrix over time looks like (i.e. what are the values in the matrix) (5-pts)?
3.) What does this model tell you about change over time (use the appropriate statistical tests to back up what you say)(5-pts)?
4.) If I reran this model with the following contrast, what am I testing in this contrast (5 pts) (show null and alternative hypothesis)?
contrast "What is it?" stime 0 1 -1 0;
5.) Please test the hypothesis in 4 (10 pts)
The next several questions refer to the next set of output:
Fit Statistics
-2 Log Likelihood 2297.9
AIC (Smaller is Better) 2321.9
AICC (Smaller is Better) 2322.7
BIC (Smaller is Better) 2356.0
Effect RAN group assignment stime Estimate Standard
Error DF t Value Pr > |t|
Intercept 20.7115 0.9061 123 22.86 <.0001
stime 0 1.1121 0.6974 271 1.59 0.1120
Effect RAN group
assignment stime Estimate Standard
Error DF t Value Pr > |t|
stime 1 0.8944 0.6016 271 1.49 0.1383
stime 2 -0.3337 0.4906 271 -0.68 0.4970
stime 3 0 . . . .
TREAT 1 1.3488 1.3515 123 1.00 0.3203
TREAT 2 0 . . . .
TREAT *stime 1 0 -2.4829 1.0496 271 -2.37 0.0187
TREAT *stime 1 1 -1.4643 0.9176 271 -1.60 0.1117
TREAT *stime 1 2 -0.5127 0.7485 271 -0.68 0.4940
TREAT *stime 1 3 0 . . . .
TREAT *stime 2 0 0 . . . .
TREAT *stime 2 1 0 . . . .
TREAT *stime 2 2 0 . . . .
TREAT *stime 2 3 0 . . . .
6.) Calculate the means of the two treatment groups at each time (10-pts)
7.) Write out a contrast that will test if the difference between conditions at baseline is different from the difference between conditions at time=2 (5-pts).
8.) What is the difference in the difference between conditions at time=0 and time=2 (5-pts)?
The next set of questions are about the following model run on the data:
Fit Statistics
-2 Log Likelihood 2301.0
AIC (Smaller is Better) 2317.0
AICC (Smaller is Better) 2317.4
BIC (Smaller is Better) 2339.8
9.) How is time being treated in this model (5-pts)?
10.) What do the covariance parameter estimates in this model tell you (10-pts)?
11.) Please provide the empirical estimates of the residual variance covariance over time (in the Ys) (10-pts).
12.)What do the Fixed Effects estimates tell you about what happened in the study(10-pts)?
13.)Which of the two models (Model 2 or Model 3) are better fit to the data and why (5-pts)?
The final question does not refer to any of the prior models:
14.)I have a study where I have measured multiple family members (who all live in the same household) in a cross-sectional study. These family members are further nested within neighborhoods. My primary outcome is psychological distress (DIS). My predictors are Gender (F=1 if female), person income (PI) and Social Support (SS) at the individual level, at the family level we measure family cohesion (FC), and at the neighborhood level we measure amount of violent crime (VC) in the neighborhood. Please put together a statistical model which will account for the following things: 1) family members are not independent,
2) provide a test of whether the individual level variables of gender, person income and social support affect DIS, and 3) whether the Family level variable, family cohesion, and the neighborhood level variable of violent crime affect psychological distress, and 3 whether there is a contextual effect of family income on each individual’s psychological distress (DIS). Please write out a theoretical model that would allow me to accomplish all of these things. You may find using the multi-level approach to growth curves helpful in setting this up. Also please briefly explain each component of the model and any assumptions you are making and why. Be sure to tell me which statistical tests will tell me whether each of my conjectures are consistent with the data. Finally, please write out the SAS statements I would use to estimate the model and test these hypotheses. 20 Points
Extra Credit (If you do not need these points for the midterm they can/will be applied to your homework):
How would you modify your model in question 14 to test whether neighborhood violence moderates (interacts with) the effect of person-income on psychological distress?
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