Cognitive Modelling Assignment

Create Model

Examining the data for single classification

• Step 1: Examine the training data and establish the patterns within.– I took notes on two patterns: 1.How often a symptom occurred in one disease as a

percentage of how often that symptom occurred overall.

2.What proportion one symptom was of all the examples of one disease.

Patterns of Dimensions

• A clear pattern emerged throughout, for each of the 3 disease categories it could be said that one dimension was more reliable than the others.

• However, I noticed that this differed for each disease – unlike in the exemplar model

How the question was asked

• The importance of how the question was asked:Had it been presented differently it would have favoured the method applied by the exemplar model

Part 1 of my model

• I built this theory into my model by applying a “reliability parameter” βi.

• Each dimension has a different reliability parameter β1 β2 β3

• These reliability parameters vary from disease to disease- the model has to be applied independently for each category

Reliability parameters

• Disease A: D1 (.9) most reliable to the point of outweighing D2(.1) or D3(.5) (especially if D1=A)

• Disease B: D3(.7) seems most reliable, followed by D2(.5), then D1(.3)

• Disease C: Again D1 (.9) most reliable, followed closely by D3(.8), D2 inconsistent (.3)

• (These were worked out from combining the two patterns mentioned earlier)

Part 2 of my model

• The second part of my model was to define a membership score for each symptom for each disease.

• To do this I took how often the symptom occurred in the disease as a proportion of how often it occurred overall and I then subtracted how often it occurred elsewhere

• M= S-S’

M=S-S’

• M=S-S’, S’=1-S

• WHY?

M=S-S’

• This formula provides a negative value if a symptoms membership in a different disease outweighs its membership in the tested disease

• If it has even distribution between two then a value of zero is given

• IF it is most common in this disease then it has a positive value

Model

• The model is created by combining part 1 and part two in a product.

• The reliability parameter for a dimension is multiplied by the membership score for the given symptom

• The products are then summed to give the overall similarity score for the test item

Model for single classification

Example: Model Applied to Disease A

M M M

1 1 -1 0.333332 -0.6 -0.5 -13 0 0.2 -0.64 -1 -1 -0.65 -1 -0.5 -1

βiMi

β 0.9 0.1 0.5

1 0.9 -0.1 0.166665

2 -0.54 -0.05 -0.5

3 0 0.02 -0.3

4 -0.9 -0.1 -0.3

5 -0.9 -0.05 -0.5

Similarity ScoresTEST ITEM SIMILARITY SCORE1 0.9666652 -1.093 -0.284 -1.35 -1.45

Rescaled Data/People ScoresModel A

People A

Model B

People B

Model C

People C

3.22222 6.78 -1.66667 -2.00 -4.88897 -9.06

-3.63333 -9.33 -0.27787 -3.22 1.22224 6.11

-0.93333 -3.11 -4 -5.28 -1.6 -3.78

-4.33333 -3.06 -0.33334 -0.56 -0.399 0.22

-4.83333 -1.39 1.05544 7.00 -2.77767 -7.00

Correlation to data

Disease Correlation

A 0.74399B 0.798195C 0.967607Average 0.836597

Disease A

1 2 3 4 5

-12

-10

-8

-6

-4

-2

0

2

4

6

8

MODELACTUAL

Disease B

1 2 3 4 5

-6

-4

-2

0

2

4

6

8

MODELACTUAL

Disease C

1 2 3 4 5

-10

-8

-6

-4

-2

0

2

4

6

8

MODELACTUAL

Conjunction Classification

• I took an integrative approach to my conjunctive classification.

• The reason for this is that I don’t think people would combine their answers from earlier questions to answer a new question.

• Instead I think people would recall the examples they had seen and combine these in some way

Conjunction Classification

• As such, I combined the data at the symptom membership score stage (i.e. When determining M)

• I believe people would use A&B given as a sample of how to create conjunctions.

• These examples include prominent members of both categories and I feel this would be a rule to go by.

Max

• One way I thought about incorporating the “most prominent members of both categories” idea into my model way by using the MAX of the two M values, however this results in obvious problems. (High values of A will be high values of AB and AC ignoring the other disease)

Reliability parameter

When choosing my reliability parameters for the conjunction categories I chose the max of the two included categories as I feel that this would be prioritised in the conjunction also

Conjunction model

• After trying Max I looked at the other functions and “SUM” and “ NORMALISED SUM” made the most intuitive sense as I think people would probably say “it could be in A or B then it might be in A&B” (The SUM models were rescaled from -6to6)

β=MAX, M=SUMMODEL AB ACTUAL

MODEL AC ACTUAL

MODEL BC ACTUAL

-0.77778 1.17 -1 -5.39 -4.77781 -7.83

-3.62265 -8.56 -1.87213 -4.06 -0.41667 4.33

-2.53333 -3.72 -1.5 -1.06 -3.03333 -4.72

-2.86672 -2.72 -2.9995 -5.06 -0.53333 -1.67

-2.22235 -3.33 -4.47163 -7.28 -0.41667 -0.89

CORRELATIONCATEGORY CORRELATION

A&B0.926166

A&C0.646386

B&C0.868461

AVERAGE0.813671

A&B

1 2 3 4 5

-10

-8

-6

-4

-2

0

2

MODEL ABACTUAL

A&C

1 2 3 4 5

-8

-7

-6

-5

-4

-3

-2

-1

0

MODEL ACACTUAL

B&C

1 2 3 4 5

-10

-8

-6

-4

-2

0

2

4

6

MODEL BCACTUAL

Varying the Model

• Using the Sum model didn’t always provide high values for the most prominent characteristics. As such, I retested the model inputting a value of 1 where any symptom had a value of 1 for either category

Varied ModelMODEL AB ACTUAL

MODEL AC ACTUAL

MODEL BC ACTUAL

1.55552 1.17 0.5 -5.39 -3.94448 -7.83

-3.62265 -8.56 -1.87213 -4.06 1.08333 4.33

-2.53333 -3.72 -1.5 -1.06 -3.03333 -4.72

-2.86672 -2.72 -2.9995 -5.06 0.3 -1.67

-2.22235 -3.33 -4.47163 -7.28 -0.41667 -0.89

CorrelationsCATEGORY CORRELATION

A&B0.863503

B&C0.929426

A&C0.412961

AVERAGE0.735297

A&B

1 2 3 4 5

-10

-8

-6

-4

-2

0

2

4

MODEL ABACTUAL

B&C

1 2 3 4 5

-8

-7

-6

-5

-4

-3

-2

-1

0

1

MODEL ACACTUAL

A&C

1 2 3 4 5

-10

-8

-6

-4

-2

0

2

4

6

MODEL BCACTUAL

NORMALISED SUM

• Finally, I decided that using Normalised sum might be a better measure of the parameters I want to include. As such I applied the model with NORMALISED SUM and MAX reliability parameter

• This data had to be rescaled from -9to9 to -10to10

Β=MAX, M=NSUMMODEL AB ACTUAL

MODEL AC ACTUAL

MODEL BC ACTUAL

1.29603 1.17 0.09875 -5.39 -3.92597 -7.83

-2.63524 -8.56 -1.24062 -4.06 1.11723 4.33

-2.04444 -3.72 -0.66667 -1.06 -1.6 -4.72

-1.48896 -2.72 -2.3463 -5.06 0.84462 -1.67

-0.76859 -3.33 -3.90728 -7.28 0.22832 -0.89

CORRELATIONCATEGORY CORRELATION

A&B0.897844

B&C0.895839

A&C0.608521

AVERAGE0.800735

A&B

1 2 3 4 5

-10

-8

-6

-4

-2

0

2

MODEL ABACTUAL

A&C

1 2 3 4 5

-8

-7

-6

-5

-4

-3

-2

-1

0

1

MODEL ACACTUAL

B&C

1 2 3 4 5

-10

-8

-6

-4

-2

0

2

4

6

MODEL BCACTUAL