# How to interpret this multinomial logistic regression result?

#### Annvdb

##### New Member
I done a multinomial logistic regressie for influence of income on voting right or left.

Right-left is coded as a continuous as =0 extreme right and 10 extreme left

And income = 1.hard to very hard to cope with income
2. can cope with it and
3. can cope very well with income (which is the dummy)

My results show that those who have a hard time coping with their income are significantly different than those doing very well with their income regards voting right-left. The results is B -.161

How exactly do i interpret this -.161 with Right being coded as 0 and left as 10. Does this mean that those who have a hard time coping with their income are more likely to vote right wing than left wing than those who do well with their income?

#### Injektilo

##### New Member
You are using the wrong type of regression. MNL requires the dependent variable to be categorical - that is, there is no direction from 0 to 1 to 2 up to 10. There is however a direction in your DV.

You should be using an OLS regression or something similar to OLS.

#### Annvdb

##### New Member
You are using the wrong type of regression. MNL requires the dependent variable to be categorical - that is, there is no direction from 0 to 1 to 2 up to 10. There is however a direction in your DV.

You should be using an OLS regression or something similar to OLS.
OOPs I know sorry I wrote it wrong.
I recoded the left right scale to make it into a categorical one ranging 1-5
So 1 is extreme right, 2 is right, 3 is middle 4 is left and 5 extreme left

#### Injektilo

##### New Member
Before I go any further, I'd say that I'm a little bit concerned about the question chosen to capture people's voting intention. You would have been better off providing actual parties (or something generic like "extreme right wing party", "moderate right wing", etc.) rather than providing a 10 point scale question. The reasoning is that people who vote for extremist parties tend to have more in common than those who vote for moderate/centrist parties, whether it is on the right or on the left. But by using a scaled variable, you are assuming that their decisions are linear in nature down the left/right political spectrum.

Moreover, since people can interpret scale points differently from each other and from you, you end up categorizing people in ways that may not be reflective of their actual voting intentions. For example, if you choose between 3 and 4 as the line drawn between extremist and moderate right wing, it's possible that a respondent considers 3 to still be moderate right wing. You'd thus mis-categorize that respondent.

I'm not familiar with running MNL on SPSS (I use R when I do this), but you should end up with 4 different models (# of categories in the DV - 1). The 1st category is typically the one omitted (so in your case, "extreme right").

The easiest way to interpret the output is to apply the logit rule to get the probability of voting for one party over another, given the specific IVs you included in the model.

First, you need to calculate a certain situation - so pick a certain value to give to each IV. Then for each of the 4 models, multiply the IV's values you chose with their B coefficients, and their constant. You will end up with a score for each of the 4 categories. The omitted category is always given a score of 1.

Second, apply the following equation to each result to turn it into probabilities:
For the first omitted category: 1/(1+exp(scorecat2)+exp(scorecat3)+exp(scorecat4)+exp(scorecat5))
For each of the other 4 categories:
Exp(scorecat2)/(1+exp(scorecat2)+exp(scorecat3)+exp(scorecat4)+exp(scorecat5))
Exp(scorecat3)/(1+exp(scorecat2)+exp(scorecat3)+exp(scorecat4)+exp(scorecat5))
Exp(scorecat4)/(1+exp(scorecat2)+exp(scorecat3)+exp(scorecat4)+exp(scorecat5))
Exp(scorecat5)/(1+exp(scorecat2)+exp(scorecat3)+exp(scorecat4)+exp(scorecat5))

You should end up with a percentage for each of the 5 that adds up to 100%. Those are the probabilities of someone's voting intentions given the IVs you specified.

Try it again using a different value for their income, and observe the change in probabilities. This should provide you with an indication of what kind of impact that particular variable has on their voting intentions.

#### Annvdb

##### New Member
It's not my questionary. I am basing this on the European Social Survey. Altho actual parties are also included so I will use that measure instead! Thanks
Im not familiar tho with what you wrote , it seems abit complicated since I have never seen that before.
You sayd 'so pick a certain value to give to each IV.' . Just a random number? For all the same? Or different for each?

#### Injektilo

##### New Member
Turning the scores to probabilities is pretty easy. If you use Excel, you can use the formula exactly as I wrote it to make it work. Exp(x) is the exponent of x, that is 2.7181... to the power of x.

Yes, you apply any number to the attributes (as long as it is within the range observed in the data set), and set the income variable to 1, or whatever the lowest value is. Observe the resulting probabilities of voting for each of the parties. Then change the income variable's level to the next category, and see what those resulting probabilities are. This will give you an indication of the impact and the direction that this variable has on their voting intention.

#### Annvdb

##### New Member
I just checked and Party choice has way too many missings = 96%
Left/right scale only has 14% missings .

#### rogojel

##### TS Contributor
hi,
actually you have an ordinal logistic regression if you code the outcome from 0 to 4. The interpretation is slightly tricky, you can look at the odds ratio. Assuming that your outcome random variable is Y the odds ratio will give you the ratio of the odds of Y>D if you change the DV by one unit. D is a level of your Y (in your case one of 0,...4 . The odds ratio is independent of the concrete value of D - this is one of the assumptions of the ordinal logistic regression.

Some programs -like Minitab for instance, calculate the odds ratio of Y<D - sonyou would need to check yours for the direction of the inequality.

regards
rogojel

#### Annvdb

##### New Member
hi,
actually you have an ordinal logistic regression if you code the outcome from 0 to 4. The interpretation is slightly tricky, you can look at the odds ratio. Assuming that your outcome random variable is Y the odds ratio will give you the ratio of the odds of Y>D if you change the DV by one unit. D is a level of your Y (in your case one of 0,...4 . The odds ratio is independent of the concrete value of D - this is one of the assumptions of the ordinal logistic regression.

Some programs -like Minitab for instance, calculate the odds ratio of Y<D - sonyou would need to check yours for the direction of the inequality.

regards
rogojel
We havent seen ordinal regression tho at uni. So I have no clue how this works. Also I dont quite understand what you say, it sounds abit like chinese to me. I also dont know what D and DV is? You seem way more advanced in statistics than I.

#### Annvdb

##### New Member
Ok so I am looking in SPSS.
I have managed to use parties voted for anyway, I did something wrong.

So what I have now is I arranged the parties from left to right going from 1 extreme left to 5 extreme right. Altho 1 is left out since no one voted extreme left, so its not even in the analysis.

Then for example if I want to link this to wether they can do well with their income, cope with it, or do badly with it (1-3 from bad to doing well).

I then insert this in spss under 'ordinal regression'. Put income as a covariat, and dependent voting choice

Right?

#### rogojel

##### TS Contributor
hi Annvddb,
DV is simply dependent variable in your case how people vote. D is a placeholder for one of the values 1,2,3,4,5 .

I am not sure about the covariant, but I do not know SPSS - is this where you put your independent variable? But if yes then it should be the right setup.

regards
rogojel

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