Multinomial logistic regression - testing assumptions

#1
Hello everyone,

I'm trying to perform an MLR with 4 continuous predictors for one ordinal dependent. I've tested my assumptions for the MLR except for whether there is a linear relationship between the continuous independent variables and the logit transformation of the dependent variable.

Firstly, I am getting a lot of conflicting information regarding logit transformations. I am working on SPSS, and from what i've seen some places suggest that the logit is binary or dichotomous, making the dependent variable also binary/dichotomous...but my dependent variable is an ordinal/categorical variable with 5 categories (effect of barrier from no barrier-complete barrier/1-5). How do I transform this data and what transformation code/equation do I apply to do it (in SPSS if possible)?

Secondly, what test do I perform to determine if there is a linear relationship or not? The only one i've found online is running a logistic regression but again, it demands a binary dependent variable which I do not have. And once I have run what I need to run, what statistic determines if there is linearity?

I appreciate that these are very basic questions but please be patient with me, I'm in a post-MSc research position after very poor stats teaching at university and I am trying very hard to teach myself. Thank you!
 

kiton

New Member
#2
Hello there!

For the MLR estimates to be unbiased (well, to some extent, of course :)), two assumptions must be in place -- (a) lack of multicollinearity, and (b) independence of irrelevant alternatives (IIA) (Starkweather, J., & Moske, A. K. (2011). Multinomial logistic regression). The first one is easy to test. The second one could be tested with -mlogtest- in Stata, guess there are similar ones for other software. This was the approach I used in a paper I recently published in a peer-reviewed journal. I wouldn't bother with linearity.
 

debadog

New Member
#3
Thanks for replying kiton! :) The issue that I'm having is that I cannot get a good model fit for the predictors when they should absolutely be related to the dependent variable - my R2 value is extremely low. I assumed that there must be a pretty huge issue to be causing this. I'm going by the assumptions specified by the SPSS manual, that include linearity. I'm happy to try and do an mlogtest (even if I have no idea what that is) but do you think that it will have a strong enough impact to fix this issue? I've tried many different combinations of predictors and i'm still getting terrible results!
 

debadog

New Member
#4
after some research, it appears that spss is not capable of performing an IIA test, and alas i'm not yet at the point of being able to bounce between different statistics programmes! any ideas how to check for linearity as an alternative?
 

kiton

New Member
#5
Note an important nuance -- r^2 is not very indicative of the model fit in case of MLR. I believe it's a so-called "pseudo-r^2", so you shouldn't be building your argument on it.
 

debadog

New Member
#6
Note an important nuance -- r^2 is not very indicative of the model fit in case of MLR. I believe it's a so-called "pseudo-r^2", so you shouldn't be building your argument on it.
After a week or two of faffing, I ultimately decided to drag my operation over to R studio. I've completed multicollinearity testing and its all dandy. I have really hit a wall with the Hausman-McFadden testing, though.

From what I can find out about it on the internet, it appears to be about "choices", but that's not what my data is about (excuse me if i'm misinterpreting this!).
My data is simply 8 factors, continuous, dichotomous and nominal, that contribute to the dependent - whether a barrier is passable by a fish or not (5 categories from "No Barrier" to "Complete Barrier" with varying stages of passability inbetween). This dependent is not affected by "choices" persay, but just physical attributes. I have to say that I'm getting very confused by every tutorial mentioning choices when I have none!

I'd really appreciate your help as you're clearly an expert on this, and I feel like i'm so close now! :)
 

debadog

New Member
#8
Thank you for the link, but I'm afraid that my concerns with the test are a bit more simple than just how its run. I'm quite confused with the fact that IIA testing appears to relate to decision theory and choices, and as I've explained my data is not related to social science, but rather geography. My dependent variable is a result of physical characteristics and not a choice. Here is the simplest definition of IIA I found:

"The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used with different meanings in different contexts; although they all attempt to provide an account of rational individual behavior or aggregation of individual preferences, the exact formulations differ from context to context."

I'd really appreciate it if you could please confirm that my data is in fact suitable for IIA testing/Hausman testing before I even attempt to do it? Thanks!