Models for Count data

Question 1

Count variable

Answer 1

An ordinal variable that takes non-negative and discrete values: 0, 1, 2, 3, etc.

Question 2

Types of models that can be used on count data:

Answer 2

1) Poisson regression
2) Negative binomial regression
3) Truncated poisson/negative binomial regression
4) Zero inflated poisson/negative binomial regression

Question 3

Examples of count variables:

Answer 3

• # of cars owned
• # of drinks consumed at festival
• # of products returned
• # of complaints
• # of stocks owned

Question 4

Why not standard regression OLS?

Answer 4

Cause it assumes a normal distribution, but also:

- often very low mean (> 10, it would be appropriate)

Question 5

Poisson distribution

Answer 5

• with parameter landa
• uses on parameter, since mean=variance
• if landa > 10, probably normal distribution so use OLS

Question 6

Poisson regression analysis

Answer 6

• DV = Count variable
• Goal to explain DV by set of Xi
• Each Yi is randomly drawn from a poisson distribution
• Mean = variance = landa
• Outcome metric is related to Xi via link function

Question 7

Link function

Answer 7

Yi = exp(XiB)

Question 8

Model estimation, via..

Answer 8

Maximum likelihood estimation, the parameters will be estimated by searching for those parameters values that give the highest likelihood to observe the data.

Question 9

Interpretation of the parameters

Answer 9

• If Xi changes with one unit (keeping all constant) the expect count (landa) is multiplied by exp(b1)
• Or.. if you use the LN of a Xi, parameter becomes elasticity. So increase in X leads to a % increase in landa (DV)

Question 10

Model fit and selection

Answer 10

1) Likelihood
2) Likelihood ratio test -> Only for nested models
3) AIC, BIC, CAIC -> models may differ, however data should be the same.

Question 11

Same violations or “cHaLLaNgEs”

Answer 11

1) Mean not equal to the variance
2) Zero events cannot be observed
3) More zeros then expected

Question 12

Under dispersion

Answer 12

Mean > variance

Almost never happens. If so still use poisson regression

Question 13

Over dispersion

Answer 13

Mean < variance

Use negative binomial regression.

Question 14

Dispersion test

Answer 14

If significant, assumption is violated. So the poisson distribution is not suitable.

Question 15

What to do if Zero events cannot be observed?

Answer 15

Use a truncated model. For the truncated negative binomial regression the second intercept represents the extra variable.

Question 16

When is observing Zeros not possible?

Answer 16

1) Basket size of online orders
2) Relationship length
3) Household size

Question 17

What to do if there are more Zeros then expected?

Answer 17

Investigate whether there is a peak at zero. If so? Two options:

1) Zero inflated models
2) Hurdle models or zero-altered models.