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Count Data Models

2. Count Data Models. Used for modelling the count of things as a function of covariates. Counts are non-negative integers.. 3. Examples:. Count of vehicles in a queue Number of defective entities Number of failures Number of computers/cars/telephones/etc. in a household. 4. Why special' method

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Count Data Models

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    1. 1 Count Data Models Simon Washington

    2. 2 Count Data Models Used for modelling the count of things as a function of covariates. Counts are non-negative integers.

    3. 3 Examples: Count of vehicles in a queue Number of defective entities Number of failures Number of computers/cars/telephones/etc. in a household

    4. 4 Why ‘special’ methodology? OLS regression can/will predict values that are negative and will also predict non-integer values There are a number of ways to model counts, but Poisson and negative binomial are ‘popular’. Also, zero-inflated model can work under certain circumstances

    5. 5 Poisson Models

    6. 6 Expressions b/w Response and Predictors The expression shown is the log-linear form—there are others as well, but log-linear is most common. It is the exp portion of the expression that constrains the model forecasts to be positive.

    7. 7 Poisson Models

    8. 8 Poisson Model Elasticities

    9. 9 Why are elasticities useful? i.e., why not just use coefficient estimates?

    10. 10 Pseudo Elasticity

    11. 11

    12. 12 Poisson Models, GOF Measures

    13. 13 Poisson Models, GOF Measures

    14. 14 Poisson Models, GOF Measures

    15. 15

    16. 16 Resultant Model

    17. 17

    18. 18

    19. 19 Poisson Model Restriction

    20. 20 Over-dispersion

    21. 21 Over-dispersion (cntd.)

    22. 22 Poisson & Negative Binomial Models: Mathematical Development:

    23. 23 Negative Binomial Models:

    24. 24 Negative Binomial Model:

    25. 25 Test for Overdispersion

    26. 26 Test for Overdispersion

    27. 27

    28. 28

    29. 29

    30. 30 Censoring & Truncation:

    31. 31 Examples

    32. 32 Fixed and random effects:

    33. 33 fixed and random effects: examples

    34. 34 Unobserved Heterogeneity

    35. 35 Zero inflated probability (ZIP)

    36. 36 Zero inflated probability (ZIP)

    37. 37 Poisson and Negative Binomial ZIP Models

    38. 38 Vuong’s Statistic

    39. 39 Vuong’s Statistic (cntd.)

    40. 40 Vuong’s Statistic

    41. 41

    42. 42

    43. 43 Sample Selection Models

    44. 44 Count Model: Example 2

    45. 45 Count Model Example:

    46. 46 Count Model Example:

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    48. 48

    49. 49 Count Model Example:

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    55. 55 Count Model Example

    56. 56

    57. 57 Count Model Example:

    58. 58 Count Model Example:

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    65. 65

    66. 66 Count Model Example:

    67. 67

    68. 68 Count Model Example:

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