Consider a dataset consisting of 610 males involved in a study of coronary heart disease. The outcome variable is CHD status (1 = case, 0 = noncase), the exposure variable of interest is CAT which is a dichotomous variable that indicates high (coded 1) or normal (coded 0) catecholamine level. The only other variables recorded in the data set are AGE (1 = age > 55, 0 = age ≤ 55) and ECG (1 = abnormal, 0 = normal). The dataset involving the above variables is given as follows: a) Is data listing described above in events/trials format or in subject-specific format? Explain briefly. (b) Show that the saturated model yields the same probability of having CHD for those with covariate profile AGE = 1, CAT = 0, and ECG = 1 as that computed directly from the data. (c) Conduct an appropriate goodness-of-fit test to determine if the model adequately fits the data. As given in the SAS code above, the model is a full model with all main effects and interactions (both two way and three way interactions). A main effect model can be obtained from SAS by this model statement – model cases/total = AGE CAT ECG / cl;Perform a hypothesis test to see if the interactions (including all of the two-way and the three-wayInteractions) help with the model using a likelihood ratio test (LRT) to compare the full model and the main effect model using alpha of 0.05.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 3TU

See similar textbooks

Related questions

Question

100%

Consider a dataset consisting of 610 males involved in a study of coronary heart disease. The outcome variable is CHD status (1 = case, 0 = noncase), the exposure variable of interest is CAT which is a dichotomous variable that indicates high (coded 1) or normal (coded 0) catecholamine level. The only other variables recorded in the data set are AGE (1 = age > 55, 0 = age ≤ 55) and ECG (1 = abnormal, 0 = normal). The dataset involving the above variables is given as follows: a) Is data listing described above in events/trials format or in subject-specific format? Explain briefly. (b) Show that the saturated model yields the same probability of having CHD for those with covariate profile AGE = 1, CAT = 0, and ECG = 1 as that computed directly from the data. (c) Conduct an appropriate goodness-of-fit test to determine if the model adequately fits the data. As given in the SAS code above, the model is a full model with all main effects and interactions (both two way and three way interactions). A main effect model can be obtained from SAS by this model statement – model cases/total = AGE CAT ECG / cl; Perform a hypothesis test to see if the interactions (including all of the two-way and the three-way Interactions) help with the model using a likelihood ratio test (LRT) to compare the full model and the main effect model using alpha of 0.05.

Output from SAS - full model (including interactions)
Criterion Intercept Only
AIC 448.851
SC 453.264
-2 Log L 446.851
Model Fit Statistics
Output from SAS - reduced model (without interaction)
AIC 448.851
SC 453.264
-2 Log L 446.851
Intercept and Covariates
Log Likelihood Full Log Likelihood
438.648
44.990
473.955
80.297
422.648
28.990
Criterion Intercept Only
Model Fit Statistics
Intercept
Covariates
Log Likelihood Full Log Likelihood
432.352
38.694
450.006
56.348
424.352
30.694

data datal;
input cases total CAT AGE ECG;
cards;
17 275 000
15 121 0 1 0
7 59 0 0 1
5 32 0 1 1
1 8 1 0 0
10 40 1 1 0
4 17 1 0 1
14 58 1 1 1
;
run;
We are interested in the following logistic model:
The saturated model is obtained in SAS by:
proc logistic data = datal;
class CAT (ref = '0') / param =
'0') / param
class ECG (ref = '0') / param =
model cases/total = AGE CAT ECG
CAT AGE ECG AGE CAT ECG CAT AGE*ECG
/ cl;
ref;
class AGE (ref =
ref;
π = P(CHD, 1| AGE,, CAT, ECG,)
logit(x) = B₁ + B, AGE, + ß₂CAT, + ß₂ECG,
ref;
run;
Parameter Estimates and Wald Confidence Intervals
Parameter
Estimate 95% Confidence Limits
Intercept
-2.7197 -3.2104 -2.2289
AGE
0.7643 0.0341
1.4945
CAT
11
0.7738 -1.3782
2.9258
CAT AGE
11 0.0831 -2.2483
2.4146
1 0.7143 -0.2149
1.6436
ECG
AGE ECG 11-0.4454 -1.8829 0.9921
CAT*ECG 11 0.0530 -2.4984 2.6044
CAT AGE ECG111-0.3685 -3.2988
2.5617

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 6 steps with 22 images

SEE SOLUTION Check out a sample Q&A here