# What is the difference between Poisson Regression and Log-linear Models in terms of their usage and which should I use?

I'm currently analyzing a data set from an experiment, where participants could give one of three types of answers: 1) Correct, 2) incorrect-congruent, 3) incorrect-incongruent. The priming participants where exposed to beforehand also varied along these lines, being either a) congruent, b) incongruent or c) no priming.

My hypothesis is now, that congruent priming increases congruent answers, but that incongruent priming will not increase incongruent answers. This should show in an interaction between prime type (a and b) and answer type. Note that answers are not independent from each other (if the answer is type a, it cannot simultaneously be type b or c).

According to my research, the appropriate analysis would be a Poisson Regression, but my mentor suggested a Log-Linear Model. When looking this up on the internet, it seems that these analyses are sometimes used interchangeably.

My Question(s): Are they the same? If not, do they apply to the same data? And then, which one would be the correct analysis for my current data set?

• From description of your problem I don't see how Poisson regression relates to it... First, you do not to have count data, but rather categorical variables. Second, it seems to be rather hypothesis-testing than modelling problem. Could you describe your data and problem in greater detail?
– Tim
May 18, 2016 at 8:15
• It is count data, since I count the event of an answer belonging to category a, b or c. When I collapse the data, I will therefore have a contingency table with answer types as the row titles and prime types as column headers.
– AKN
May 18, 2016 at 8:34
• So you assume that counts of answers are independent of each other..? Such assumption is inconsistent with your data since each participant can give "one of three types of answers".
– Tim
May 18, 2016 at 9:39
• This is, what I stated in my description above: " Note that answers are not independent from each other (if the answer is type a, it cannot simultaneously be type b or c)."
– AKN
May 18, 2016 at 10:34
• Your data are really multinomial. The log linear model is a Poisson GLM adapted for analyzing multi-way contingency tables. I suspect (but can't tell for sure) that your data can be represented as a multi-way contingency table, so you could use the log linear model. There are examples on this site, if you search. May 18, 2016 at 12:38