1. Step 5: Analysis of Causal Diary
Farrokh Alemi Ph.D.
I am professor Alemi and this lecture discusses how you can analyze causal diaries.
This research was funded by Grant RO1 HL from the National Heart Blood and Lung Institute.

2. Step 5: Analysis of Causal Diaries
Continues from a previous section
This lecture continues from a previous section on maintaining a causal diary.

3. Clean Data Day … 1 2 3 4 5 6 14 Exercise Cause A Constraint on A
Cause B
Constraint on B … 1 2 3 4 5 6 14
The analysis of diary starts with a few house keeping tasks.  Sometimes, you may list causes that are so rare that they never occur during the 2-weeks diary period.  These causes are not included in the analysis. 

4. Clean Data Day … 1 2 3 4 5 6 14 Exercise Cause A Constraint on A
Cause B
Constraint on B … 1 2 3 4 5 6 14
Here we see that cause B is never present in the two weeks of keeping diary. This cause must be dropped from the analysis. The same occurs if a cause or a constraint is always present, that too should be dropped from the analysis.

5. Get More Data Day … 1 2 3 4 5 6 14 Exercise Cause A Constraint on A
Cause B
Constraint on B … 1 2 3 4 5 6 14
If two causes always co-occur with each other in every data entry, then the analysis cannot tell us which one is effective. Here for example we see that Constraint A and Cause B always co-occur. It is not possible to decide the influence of each of them separately.  The constraint A and cause B cannot be distinguished through data analysis. Either more data is needed or a better definition of the constraint or the cause is needed.

6. Maximum Impact of a Cause
One way to estimate the conditional probability of success given the various causes is to limit the data to the cases in which the cause has occurred and is not limited by any constraints. We refer to these occasions as unconstrained causes. Then the conditional probability of success given the cause is calculated as the frequency of success among occasions of unconstrained causes. For example, to calculate probability of success given cause X, we first restrict the cases to all situations where unconstraint causes are present and then calculate probability of success in this reduced sample space. This produces a maximum estimate for the impact of the cause on success as it assumes all successes reported in the reduced sample space did not have an alternative cause.

7. Making a Cause Unconstrained
Day
Exercise
Cause A
Constraint on A 1 2 3 4 5 6 … 14
Day 3
Lets demonstrate what do we mean by unconstraint causes. We need to limit the data to days in which the cause has occurred and is not limited by any constraints. In day 3 cause A has occurred but so has its constraint.

8. Making a Cause Unconstrained
Day
Exercise
Cause A
Constraint on A 1 2 3 4 5 6 … 14
So we can think of this day as if the cause has not occurred.

9. Making a Cause Unconstrained
Day
Exercise
Cause A
Constraint on A 1 2 3 4 5 6 … 14
The same applies on day Here again cause A is not going to have its desired effect because of its constraint.
Day 14

10. Making a Cause Unconstrained
Day
Exercise
Cause A
Constraint on A 1 2 3 4 5 6 … 14
So we assume that on day 14 the cause has not happened.
Day 14

11. Reducing Universe of Possibilities
Day
Exercise
Unconstrained Cause A 1 2 3 4 5 6 … 14
Now that we have eliminated all occasions that cause A is constrained, we can refer to it as the unconstrained cause. Now we need to look at all days in which the unconstrained cause A has occurred and report the conditional probability of success. We restrict the analysis to days in which unconstrained cause A has occurred by eliminating data for days in which cause A has not occurred.

12. Maximum Impact of a Cause
Day
Exercise
Unconstrained Cause A 1 2 3 4 5 6 … 14
Here we are looking at all occasions in which cause A has occurred. We can see that the probability of exercise in this reduced universe of possibilities is 2 out of three times. Therefore the maximum for the conditional probability of cause A is 2 divided by 3.

13. Minimum Impact of a Cause
The minimum impact of a cause is calculated in the same fashion with a minor difference. As before, the constrains are removed. But now, all days in which the effect has an alternative cause is also removed from the analysis. The universe of possibilities is reduced to all occasions in which the unconstrained cause occurs and no other alternative cause occurs. The probability of success in this reduced universe of possibilities is the minimum impact of the cause.

14. Plan to commute with bike
Example
Day
Rain
Plan to commute with bike
Plan to shower at gym
Sleep early
Exercise pattern kept 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1=Yes, 0=No
Suppose you have collected the diary data in this Table  You had hypothesized three causes of exercise.  First cause was that planning to bike to work leads to exercise.  The second cause was that planning to take morning showers in the gym would increase visits to the gym.  The last possible cause was to sleep early and thus be able to wake up earlier and have more time in the morning.  The diary also marks rainy days, which are expected to reduce the possibility of biking to work. 

15. Plan to commute with bike
Unconstrained Causes
Day
Plan to commute with bike
Plan to shower at gym
Sleep early
Exercise pattern kept 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1=Yes, 0=No
This table shows unconstrained causes, where days in which it rained we set the plan to commute to work to zero.

16. Maximum Impact of Planning to Bike to Work
Day
Plan to commute with bike
Plan to shower at gym
Sleep early
Exercise pattern kept 4 1 14
Using the unconstrained causes, you can calculate the maximum and minimum conditional probability of success for various causes. This table shows the reduction of diary entries if you look at days in which you were planning to bike to work and it was not raining. In these days we exercised every day and therefore the maximum conditional probability of exercise given we have plans to bike to work is 1 or 100%. The minimum probability of success is obtained by eliminating days in which alterative explanations are possible. This includes day 4 as on this day the plan to shower at the gym might have led to exercise. Therefore the minimum probability of success is calculated solely based on the data in day 14, which is still 1 or 100%.

17. Minimum Impact of Planning to Bike to Work
Day
Plan to commute with bike
Plan to shower at gym
Sleep early
Exercise pattern kept 4 14 1
The minimum probability of success is obtained by eliminating days in which alterative explanations are possible. This includes day 4 as on this day the plan to shower at the gym might have led to exercise. Therefore the minimum probability of success is calculated solely based on the data in day 14, which is still 1 or 100%.

18. Impact of Various Causes
Probability of Success Given the Cause
Minimum
Maximum
Plan to commute with bike 1
Plan to shower at gym
0.80
0.86
Sleep early
0.50
0.67
Following the same procedure, the probability of success of various causes can be estimated. From this table we see that the cause more likely to lead to exercise is planning to bike to work. Sleeping early does not seem to consistently lead to exercise.

19. Lecture Continues Step 6: Taking Action
This lecture continues to the next section titled taking action.