Regression Models for Nominal, Ordinal and Count Data

Question 1

What is an example of binary data and what type of analysis is used to study it?

Answer 1

Example: Improved/Not improved

Type of analysis: Logistic regression

Question 2

What is an example of Categorical (multinomial) and what type of analysis can be used to study it?

Answer 2

Example:Diagnosis (schizophrenia, affective, other)

Type of analysis: Multiple logistic regression

Question 3

What is an example of Ordered categorical (ordinal) data and what type of analysis can be used to study it?

Answer 3

Example: Likert scale (agree strongly, disagree strongly)

Type of analysis: Ordered logistic regression

Question 4

What is an example of count data and what type of analysis can be used to study it?

Answer 4

Example: Number of lesions in the brain

Type of analysis: Poisson or negative binomial regression

Question 5

What regression test is used for multiple unordered categories?

Answer 5

multinomial multiple logistic regression

It may be easier to convert data to a simple binary so that standard logistic regression can be used, if this
is clinically valid

As in chi-squared test or standard logistic regression, may need to combine small categories

Important: unless you specify using the base option, Stata will choose the most frequent category for the dependent variable as the reference category.

Question 6

What stata command is used to run a multinomial multiple logistic regression?

Answer 6

mlogit

Question 7

For regression modelling we may need to assume what?

Answer 7

That the scale is interval ie 0-1 is the same distance as 1-2, etc

This may be controversial but in practice this is often assumed (check this is not ridiculous though!)

Question 8

What does the stata command ologit do?

Answer 8

Makes the proportional odds assumption (that the odds of category 2 compared to 1 is the same as
for category 1 compared to 0, etc)

Question 9

If the number of categories is large, we could just use what?

Answer 9

linear regression as an approximation

Question 10

What is individual data?

Answer 10

One record per case with the dependent variable coded as 0/1

Question 11

What is grouped data?

Answer 11

Cases aggregated over subgroups; data are counts in each subgroup

Question 12

What is poisson regression often used for?

Answer 12

Modeling count data.

Question 13

What does a rate ratio of less than 1 imply?

Answer 13

There is a decreasing association between the predictor and the outcome

Question 14

What does a rate ratio of greater than 1 imply?

Answer 14

An increasing association between predictor and outcome

Question 15

What does a rate ratio of 0.91 mean?

Answer 15

That an increase in the independent variable of 1 point would decrease the
rate ratio by a factor of 0.91

Question 16

In standard Poisson distribution which describes the probabilities of independent events, the variance equals what?

Answer 16

Mean

Often however the observed variance is greater than the mean.

Example: a child missing school one day is assumed to be independent from missing school another day- but is this reasonable? Perhaps certain children tend to miss more days than others.
The consequence is that the observed variance is higher than expected = overdispersion or extra Poisson variation

(The variance might also be lower = underdispersion but this is rare).

Question 17

If a dependent variable is continuous what test should be used?

Answer 17

Linear regression

Question 18

What is a rate ratio?

Answer 18

In epidemiology, a rate ratio, sometimes called an incidence density ratio or incidence rate ratio, is a relative difference measure used to compare the incidence rates of events occurring at any given point in time.

Question 19

What test should be carried out if we run a goodness of fit model for our poisson regression model and find that the observed variance is higher than expected = overdispersion or extra Poisson variation?

Answer 19

We run a Negative Binomial regression- Here the dependent variable, Y, follows the negative binomial. As a result, the variables can be positive or negative integers.

Question 20

Negative Binomial regression can be used for under dispersion.

True or false

Answer 20

FALSE

Can only be used for over dispersion

Question 21

In a negative binomial regression output what is the likelihood ratio test comparing?

Answer 21

negative binomial regression to poisson model

Question 22

Linear regression, ANOVA, logistic and Poisson regression can be considered to be what?

Answer 22

Special cases of a class of models called generalized linear model (GLMs).

Question 23

What are generalised linear models characterised by?

Answer 23

“The distribution of the dependent variable y (the ‘family’) and a link function, g(), that connects the expected value of the dependent variable E(y) with the linear predictor, n derived from the explanatory variables”

Question 24

Why should we use a generalised linear model?

Answer 24

More general way of modelling continuous, binary and count outcomes
Logistic, Poisson regression can all be performed using glms (along with regressions based on some other models such as gamma)
Advantages:
* more detailed output;
* easier to compare one model with another because all under one ‘umbrella’, and they use common
measures of fit (deviance)
* More control over specific form of model fitted
Stata command is glm

Question 25

What are the advantages of using a generalised linear model?

Answer 25

Advantages:
* more detailed output;
* easier to compare one model with another because all under one ‘umbrella’, and they use common
measures of fit (deviance)
* More control over specific form of model fitted

Question 26

What is the stata command for a generalised linear model?

Answer 26

glm

Question 27

The glm stata command is: glm depvar indepvars,family(familyname)link(linkname)

What do the options for the link name include?

Answer 27

• identity – identity function
• log – natural logarithm
• logit – logit function
• probit – probit function (inverse cumulative distribution function of a standard normal)
• cloglog – complemtary log-log function
• opower # - odds power of order #k
• power # - power of order #k ….

For example, a Poisson regression model is a special GLM where the dependent variable is assumed to arise from a Poisson distribution (distribution for counts) and the link function is the log function

Question 28

Adding eform to the glm command is equivalent to asking for what?

Answer 28

The or or irr

Question 29

1. Why might non-independent observations occur?
2. What might these suggest?
3. What format does the data usually have to be in and what stata command can be used to ensure this?

Answer 29

1. • Cluster randomisation
     - Clustered sampling (Not ‘cluster analysis’ this is something different!)
     - Repeated measures
     - Longitudinaldata
     - Random effects model
     - Multilevelmodel
2. The use of the cluster option with the usual command eg logistic, logit or poisson, or a specific random effects model such as xtlogit or xtpoisson
3. The data usually has to be in ‘long’ format in Stata: use reshape

Question 30

What are types of non-independent data?

Answer 30

Cluster randomised trial
* Clinics are randomised to deliver intervention or not
* Outcome is for patients (binary: “improved” or “not improved”)

Longitudinal data
* Survey of patients at 3 time points
* Dependent variable is binary: agree with statement Y/N

Multilevel study
* Children observed in classrooms in school
* Dependent variable is “days off sick”

Question 31

In stata when computing a nbreg or passion model what does the option irr report?

Answer 31

Rate ratios (exponentiated coefficients)