Module 7: Count Data

Question 1

What is count data?

Answer 1

• Dependent variable is nonnegative integer
• Often, few small discrete values
• zeros present
• right skew
• heteroskedastic

Ex. Fertility, airline safety, visits to docor, days in hospital

Question 2

List the types of count data models.

Answer 2

• Poisson
• Negative binomial
• Zero inflated (both poisson and negative binomial)

Question 3

Define equidispersion.

Answer 3

When the mean of a distribution is equal to the variance.

Question 4

Given the following poisson output, interpret age.

y | coeff. | std. err.
age | 0.0676 | 0.001
educ | -0.0509 | 0.002
1.urban | -0.099 | 0.0217
1.usemeth | 0.517 | 0.026

Where the dependent variable is number of children.

Answer 4

Each year increase in age is associated with 6.8% more children.

Question 5

Given the following poisson output, interpret usemeth.

y | coeff. | std. err.
age | 0.0676 | 0.001
educ | -0.0509 | 0.002
1.urban | -0.099 | 0.0217
1.usemeth | 0.517 | 0.026

Where y is number of children and usemeth is a dummy for birth control.

Answer 5

Using birth control is associated with 68% more children.

(e^0.5171)-1 = .68

Question 6

How do you choose between the Poisson model and the negative binomial model?

Answer 6

H0: poisson, equal disposition
H1: negataive binomial, overdisposition
Use chi^2 value and < 0.05, reject the null and poisson preferred

Question 7

When do you use zero-inflated models?

Answer 7

• Have excess zeros in y
• Poisson and NB under-predicted nonuse (zeros)

Question 8

How do you interpret a coefficient for zero-inflated poisson model, inflated on the constant?

Answer 8

Each 1 unit increase in x leads to a ___% more y.

Question 9

Given the following zero-inflated poisson, interpret age.

y | coef. | std. err.
age | 0.0561 | 0.0013
educ | -0.043 | 0.002
inflated
age | -0.8027 | 0.067
educ | 0.209 | 0.0518

(Inflated on the x-variables)

Answer 9

Each year of increase in age is associated with 5.6% more children.
Each year increase in age is associated with an 55% decrease in the probability of having no children. (exact formula)

Question 10

How do you choose between each of the count data models?

Answer 10

• Look at histograms
• alpha significance levels
• correlation between y and predicted y
• probabilities of various y outcomes
• AIC/BIC

Question 11

T/F: Linear models have probabilities and AIC/BIC

Answer 11

False: They do not have these.