Herbert Is Studying the Risk Factors Associated with Heart Diseases

Multiple Choice

Herbert is studying the risk factors associated with heart diseases. He identified three risk factors (age, sex, and cholesterol level) , and built two different models.
Model 1: Logit(Y_i) = -7 + 2.5X₁ - X₂. -2LL = 3
Model 2: Logit(Y_i) = -8.5 + 1.5X₃ -2LL = 8
Y: 1= diagnosed with major heart disease; 0 = no major heart disease;
X₁: age in years (above 40) ;
X₂: sex, where 0 is male and 1 is female;
X₃: cholesterol level (in mmol/L)
Herbert conducted a log likelihood difference test (p = .025) and concluded that Model 1 fit the data significantly better than Model 2. Evaluate his analysis.

A) The analysis is not valid. The two models cannot be compared using the log likelihood difference test because they are not nested models.
B) The interpretation of the test results is erroneous. The fact that the null hypothesis is rejected indicates that Model 2 fit the data better than Model 1.
C) The interpretation of the test results is erroneous. The fact that null hypothesis is rejected indicates that Model 1 and Model 2 do not differ substantially in fit.
D) There is nothing wrong with the analysis.