CAS Exam MAS-II Fall 2018, Question 2
Study guide: Exam MAS-II
In the supplemental material, you have been given a case study, "Systolic Blood Pressure Case Study", showing the results of different treatment options and the description of how that study was set up. There are different ways of setting up models to examine the benefits of the different treatment options. You have been asked which of two models structures will give a better fit to the experience.
The relevant output from the case study is reproduced below. Change in systolic blood pressure is modelled for 1,680 observations, with random intercepts for 21 hospitals and for 210 doctors nested within them; Mean_F_G_1 is Mean Group #1, which pools the eight treatments into three mean groups, and Var_F_G_1 is Variance Group #1.
Model 4 — all eight treatments as fixed effects, doctors nested within hospitals, variance grouped under Variance Group #1, fitted by maximum likelihood:
## Linear mixed-effects model fit by maximum likelihood
## Data: systolic_g
## AIC BIC logLik
## 9238.455 9303.573 -4607.227
##
## Random effects:
## Formula: ~1 | Hospital_F
## (Intercept)
## StdDev: 0.2597347
##
## Formula: ~1 | Doctor_F %in% Hospital_F
## (Intercept) Residual
## StdDev: 0.321243 3.882077
##
## Variance function:
## Structure: Different standard deviations per stratum
## Formula: ~1 | Var_F_G_1
## Parameter estimates:
## 0 1
## 1.000000 0.925956
## Fixed effects: change_systolic ~ Treatment_F
## Value Std.Error DF t-value p-value
## (Intercept) -6.792998 0.2753713 1463 -24.668501 0.0000
## Treatment_F2 7.504027 0.3797572 1463 19.760066 0.0000
## Treatment_F3 6.781470 0.3797572 1463 17.857385 0.0000
## Treatment_F4 4.521330 0.3797572 1463 11.905844 0.0000
## Treatment_F5 2.399954 0.3659680 1463 6.557824 0.0000
## Treatment_F6 3.360502 0.3659680 1463 9.182503 0.0000
## Treatment_F7 0.822955 0.3659680 1463 2.248707 0.0247
## Treatment_F8 -1.316800 0.3659680 1463 -3.598129 0.0003
Model 12 — the treatments grouped using Mean Group #1 as fixed effects, doctors nested within hospitals, variance grouped under Variance Group #1, fitted by maximum likelihood:
## Linear mixed-effects model fit by maximum likelihood
## Data: systolic_g
## AIC BIC logLik
## 9301.501 9339.486 -4643.75
##
## Random effects:
## Formula: ~1 | Hospital_F
## (Intercept)
## StdDev: 0.2552653
##
## Formula: ~1 | Doctor_F %in% Hospital_F
## (Intercept) Residual
## StdDev: 0.09628534 3.942655
##
## Variance function:
## Structure: Different standard deviations per stratum
## Formula: ~1 | Var_F_G_1
## Parameter estimates:
## 0 1
## 1.000000 0.943903
## Fixed effects: change_systolic ~ Mean_F_G_1
## Value Std.Error DF t-value p-value
## (Intercept) 0.349750 0.2005733 1468 1.743753 0.0814
## Mean_F_G_12 -3.756755 0.2448066 1468 -15.345811 0.0000
## Mean_F_G_13 -7.313573 0.2448066 1468 -29.874906 0.0000
Model Structure XYZ has:
- Treatment options should be grouped using Mean Group #1 in the fixed effects section of the model
- A random effect of doctors nested within hospitals
- An assumption that the variance by treatment can be grouped under Variance Group #1
Model Structure STW has:
- All eight treatment options in the fixed effects section of the model
- A random effect of doctors nested within hospitals
- An assumption that the variance by treatment can be grouped under Variance Group #1
The null hypothesis is that the Mean Group #1 should be retained to evaluate the effectiveness of treatment options.
Determine the level of significance at which one would reject the null hypothesis using a likelihood ratio test.
- A) Less than .005
- B) At least .005, but less than .01
- C) At least .01, but less than .025
- D) At least .025, but less than .05
- E) Greater than .05
Answer this question and see the worked solution
Concepts tested
- Likelihood Ratio Test
- Restricted Maximum Likelihood
- Fixed Effects
- Linear Mixed Model
- Maximum Likelihood Estimation
- Model Output