Question 2 - complete in jupyter

There are various threshold values for the MMSE score that classify the severity of cognitive impairment. Suppose there is interest in the threshold between 'normal' cognitive function and 'impaired' cognitive function, and the value 27 has been selected as a threshold. All scores of 27 or above will count as normal, while scores of 26 or below mean the the participant should be tested further for dementia.

(a) Make new object called mmseIndex that takes the value 0 when mmse is 26 or less and takes the value 1 when mmse is 27 or above.

(Hint: the ifelse() function may be useful to create the object mmseIndex.) [1]

(b) (i) Fit a generalised linear model (GLM) where mmseIndex is the response variable. Explain:

which distribution you are choosing for your GLM (with

justification) which explanatory variables and interactions between them you consider putting in the model your model selection approach the form of the linear predictor of your final model. [5]

(ii) Give an interpretation of your final model. [2]

(iii) Discuss how well your final model fits. [4]

(c)

(i) For your final model from part (b), create a new object called modIndex2 that takes two possible values:

0: if the predicted probability for a participant to achieve a

score of 27 or more in the MMSE test is less than 0.5

1: if the predicted probability for a participant to achieve a score of 27 or more in the MMSE test is greater than or equal

to 0.5.

Explain, in the context of the simulation study, what the two values in modIndex2 mean. Then find the difference

mmseIndex modIndex2 (which should be an object containing values 1, 0, 1). Interpret what each of these three possible values for this difference means. Find how many 1s, 0s and 1s there are. [4]

(ii) Now make new object called modIndex1 for your model from Question 1(b), that takes two possible values:

0: if the fitted value is less than 26.5

1: otherwise.

Explain, in the context of the studies from which the data were simulated, what the two values in modIndex1 mean. Also explain why 26.5 is used as a threshold value here instead of 27. Then find the difference

mmseIndex modIndex1 and find how many 1s, 0s and 1s there are. [3]

(iii) Give one reason why the final model you obtained in part (b)(ii) is better for predicting mmseIndex than the final model you obtained in Question 1(b)(i). Also give one reason why it is worse.