# IID vs IIA; mixed vs conditional vs multinomial logit models

#### t.wang21@yahoo.com.au

##### Member
I am reading books on categorical data analysis. are the assumption of indepently and identically distributed (errors terms) and independence of irrelevant alternatives one assumption or two distinct assumptions?

what are differences amongthe multinomial logit model, conditional logit model, and mixed logit model? My understanding is that independent variables in the multinomial logit model are individual specific, independent variables in the conditional logit model alternative specific, independent variables in the mixed model are individual specific and choice specific. Not sure whether this is correct or not. Many thanks.

Tim

#### d21e7x11

##### New Member
Assumption of "independence of irrelevant alternatives"? Tha's an interesting one - can you please provide more text about it from the books that you're reading?

Logit model and multinomial logit model --> modelling dichotomus oucome and modelling oucome that has more than two categories.

Conditional logit model? Hmmmm... Not sure since "conditional" can refer to different things depending on context.

Logit model and mixed logit model --> observations are independent and not all observations are independent.

#### t.wang21@yahoo.com.au

##### Member
Thanks.
page 245 of statistical methods for categorical data analysis by Powers and Xie: the aforemention logit models (eg conditional model,mixed model) possess the remarkable property that the relative odds between two alternative outcomes depend exclusively on characteristics pertaining to the two outcomes and are therefore independent of the number and the nature of all other outcomes that are simultaneously considered. this property is known as independence of irrelevant alternatives.
Tim

Assumption of "independence of irrelevant alternatives"? Tha's an interesting one - can you please provide more text about it from the books that you're reading?

Logit model and multinomial logit model --> modelling dichotomus oucome and modelling oucome that has more than two categories.

Conditional logit model? Hmmmm... Not sure since "conditional" can refer to different things depending on context.

Logit model and mixed logit model --> observations are independent and not all observations are independent.

##### Ninja say what!?!
Assumption of "independence of irrelevant alternatives"? Tha's an interesting one - can you please provide more text about it from the books that you're reading?

Logit model and multinomial logit model --> modelling dichotomus oucome and modelling oucome that has more than two categories.

Conditional logit model? Hmmmm... Not sure since "conditional" can refer to different things depending on context.

Logit model and mixed logit model --> observations are independent and not all observations are independent.
Welcome to the club d21e7x11! I'm always happy to see more knowledgeable members here willing to help!

For conditional logit, there is plenty of info online that you can look up. The way I like to think of it is that it's a method that allows you to deal with non-independent observations (i.e. clustered observations) by taking a weighted average over the clusters.

For mixed logistic, you can think of this as an extension to conditional logit in that there is an estimate that is attributed to each cluster. These models tend to assume a distribution in the random effects that it attributes though.

#### d21e7x11

##### New Member
Thank you for the warm welcome. "weighted average over the clusters." - with weights depending on the cluster size?

#### d21e7x11

##### New Member
Yes, thank you, I am a "SAS person" too. Hope to learn R sometime.