Binary logistic regression results interpretation when one IV is ordinal

Question

I don't know how to interpret the ordinal variable 'Stress' in my binary logistic regression analysis.'Stress' was measured on a 10 point scale where 1 is 'Least stressed' and 10 is 'Most stressed'. The outcome variable is prosocial behaviour.

Edit: I now understand that the variable 'Stress' is not significant (p>.05) but I still would like to know how to interpret it in the case of an ordinal IV being significant. The coefficient is positive (+) which might mean that higher the stress, the higher the likelihood of prosocial behaviour? Could it be this non-specific? How to understand each 'stress' variable in comparison with the other stresses? There are supposed to be 10 (from least to most).

Another edit: The seven, eight, night, most (in the table) refer to numbers 7, 8, 9, and 10 (numbers on the scale). So all participant selected one of these numbers (7, 8, 9, 10) to indicate their level of stress. The other numbers on the stress scale weren't selected at all. So none of the numbers referring to lower levels of stress (1, 2, 3, 4, 5, 6) were picked. This is why only 4 levels are mentioned in the tables. None of the other levels of stress are present in cases of my data set.

If Stress is measured on an ordinal scale, maybe spline it in the model? That should help with interpretation! See https://stats.stackexchange.com/questions/195246/how-to-handle-ordinal-categorical-variable-as-independent-variable — kjetil b halvorsen, Nov 09 '23 at 12:24
Thank you for the response and the resource. Unfortunately, I don't understand any of what is being discussed in it. I don't know what 'spline' means. I can only use spss. Looking at my results, do you think I did something incorrectly? I did not create dummy variables, I read that those are only created for nominal variables. Looking at my tables, would this be a correct interpretation of 'Stress': The coefficient is positive (+) which means that higher the stress, the higher the likelihood of prosocial behaviour? (let's assume it was significant for the sake of interpreting it). — lisaarthur, Nov 10 '23 at 13:26
For a simple explanation of splines, see https://stats.stackexchange.com/questions/517375/splines-relationship-of-knots-degree-and-degrees-of-freedom I will try to write a short answer — kjetil b halvorsen, Nov 10 '23 at 14:34
I don't use spss --- your Stress variable is evidently not used as a continuous numerical variable, as there is some variables stress(1), stress(2), stress(3) You say it is a ten-point scale, but in the coding table is used seven, eighth , nine and most ? What is most ? seven, eight, nine seems to be coded as nominal, but I am not sure, so you need to clarify what is your coding. Tell us the exact commands used in spss? — kjetil b halvorsen, Nov 10 '23 at 16:07
Yes, Stress (one of the IVs) is not a continuous variable, it's an ordinal variable. It's measured on a 10 point scale where 1 is 'Least' (stressed) and 10 is 'Most' (stressed). So it's a scale of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. The seven, eight, night, most refer to numbers 7, 8, 9, and 10 (numbers on the scale). So all participant selected one of these numbers (7, 8, 9, 10) to indicate their level of stress. It makes sense because the other numbers on the stress scale weren't selected at all. So none of the numbers referring to lower levels of stress (1, 2, 3, 4, 5, 6) were picked. — lisaarthur, Nov 10 '23 at 16:59
There are no commands in spss. You just click here and there and the output appears. I did a binary logistic regression as my outcome variable is binary (yes, no). — lisaarthur, Nov 10 '23 at 17:00
I don't understand the 'Parameter coding' bit in that table at all. What is the (1), (2), (3) and how does it translate to my Stress variables? Thank you again. — lisaarthur, Nov 10 '23 at 17:02
How did you code the stress variable? Is it marked somehow as categorical? The way it seems to be coded indocates that. Is there a way to tell spss it is ordinal? — kjetil b halvorsen, Nov 10 '23 at 21:29
You are right! I went back and I can see that SPSS sees it as a categorical variable. It sees it the same as the gender and marital status variables. They all get a '(cat)' label there, meaning categorical. — lisaarthur, Nov 12 '23 at 01:33
'Gender(1)' = the number 1 refers to the 'male' category. So in this case, as the coefficient is positive males were more likely to engage in prosocial behaviour than females. In my data file, males are coded as '1' and females as '2'. 'Marital status(1)' = the number 1 refers to 'single' and number 2 refers to 'married'. So this means that those in the 'single' condition were more likely to be prosocial than those in the 'married' condition. — lisaarthur, Nov 12 '23 at 01:42
I would try to code the stress variable as numerical, and then model it as linear plus maybe a quadratic. The latest as a test of linearity ... — kjetil b halvorsen, Nov 12 '23 at 01:59
How do I do that? It already has numbers as codes. 1 - least stressed .... 10 - most stressed. — lisaarthur, Nov 12 '23 at 05:42
No, by linear i do not mean linear regression. Still logistic regression. As other generalized linear models, part of that model is a linear predictor ( which is then transformed in a non-linear way). Writing s for the stress variable, let that linear predictor contain the terms $ \beta_1 s +\beta_2 s^2$ — kjetil b halvorsen, Nov 12 '23 at 07:09
Oh no, this is like foreign language to me. I don't do formulas at all. How to code the stress variable as numerical? I'm in the social sciences field. We don't learn formulas in Research Methods, all we can do is click in spss. I wsh this site had people who do spss :( — lisaarthur, Nov 12 '23 at 14:41
I do not have access to spss soit is difficult for me to give concrete aadvice ... — kjetil b halvorsen, Nov 12 '23 at 15:21
How do I attract attention of those on this site who know spss and are in the social sciences? — lisaarthur, Nov 12 '23 at 17:24
This question appears to have nothing to do with SPSS and everything to do with understanding what SPSS is doing. Anybody who understands logistic regression will be able to help. At present, though, the information in the question appears self-contradictory, because it seems to be telling us different things about what kind of variable "stress" might be and how you have coded it. — whuber, Nov 12 '23 at 17:37
Part of the confusion is that you speak of having 10 levels of "stress" but your table of "Categorical Variable Codings" only shows 4 levels of Stress, and (correspondingly) your model results only show 3 coefficients reported for Stress. Are all 10 levels of Stress present in cases of your data set, or only levels 7 through 10? Please edit the question to clarify. — EdM, Nov 12 '23 at 17:49
@EdM I've explained this above. I'm attaching it here: 'The seven, eight, night, most refer to numbers 7, 8, 9, and 10 (numbers on the scale). So all participant selected one of these numbers (7, 8, 9, 10) to indicate their level of stress. It makes sense because the other numbers on the stress scale weren't selected at all. So none of the numbers referring to lower levels of stress (1, 2, 3, 4, 5, 6) were picked.' - This is why only 4 levels are mentioned in the tables. None of the other levels of stress are present in cases of my data set. — lisaarthur, Nov 12 '23 at 17:57
@whuber Stress is an ordinal variable as it goes from 'Least' to 'Most'. However, spss treats it as a categorical variable. I coded the 10 levels of stress the same way as they appeared on the scales for participants. Like a Likert Scale. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. 1 - Least stressed, 10 - most stressed. That's how I coded it in spss. The 'reference category' of all categorical covariates (gender, stress, marital status) is 'First' (as opposed to 'Last'). Not sure if people not familiar with spss will understand this feature. — lisaarthur, Nov 12 '23 at 18:02
This is all standard and not unique to SPSS. What is strange are the contradictions between your descriptions and what the output is showing. For instance, the values "seven," "eight," "nine," and "most" do not correspond to a ten-level ordinal variable you claim has values between 1 and 10 inclusive. — whuber, Nov 12 '23 at 20:29

score 4 · Answer 1 · answered Nov 12 '23 at 18:17

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It doesn’t seem like you should be restricting answers to only SPSS users as this is a broad misunderstanding of statistics and interpreting a model and not anything specific about implementing SPSS software.

With that being said, it doesn’t seem like your stress variable is being treated as ordinal. An ordinal categorical factor would have orthogonal polynomial contrasts, with the number of comparisons being the number of levels of the ordinal factor minus 1. So if you have 4 levels of stress you’d have a linear, a quadratic, and a cubic comparison. But that doesn’t seem to be what’s depicted as it’s being reported as stress(1), stress(2), stress(3) which reads to me like it’s being coded as a dummy coded categorical factor which means all levels are compared to level 0, the reference level. This is probably not the right way to code this factor especially if you want to model and interpret it as ordinal.

In terms of interpreting logistic regression, coefficients are reported as log odds which is borderline uninterpretable so you may want to refer to the later column with exp(B) which is the odds ratio.

Also, you said there are 10 levels to your stress ordinal variable but it appears your frequencies are only 7 8 9 most. did people only respond for those 4 levels? I am guessing your current model is comparing 8 9 Most to 7 and is dummy coded

answered Nov 12 '23 at 18:17

JElder

919

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I stopped writing my answer after seeing yours (+1). I have a vague memory, however, that SPSS (which I don't use) chooses the highest rather than the lowest level of a categorical predictor as reference, unlike R. A comment (easy to overlook) and a later edit to the question confirm your suspicion that only 4 levels of Stress were represented in the data set. – EdM Nov 12 '23 at 18:26
@EdM You can choose whether you want the lowest or the highest level to be the reference, and I chose the lowest (called 'first' in spss) as someone suggested that that would be best. – lisaarthur Nov 12 '23 at 18:28
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@lisaarthur this page linked in the first comment on your question is a good start for seeing the different ways that ordinal predictors can be handled in a model. I'm not sure which are readily available in SPSS. – EdM Nov 12 '23 at 18:35
@JElder Thank you for your response, very appreciated. Yes spss sees it as categorical. Yes, people only selected 7, 8, 9, and 10 (Most) on the stress scale. What do I do? Do I recode 7, 8, 9, and Most in spss so I can then can identify it in the results output? But will it create a mess? I need my reference category to be the lowest level of stress (number 1). – lisaarthur Nov 12 '23 at 18:35
@JElder "In terms of interpreting logistic regression, coefficients are reported as log odds which is borderline uninterpretable so you may want to refer to the later column with exp(B) which is the odds ratio." - Textbooks interpret the coefficients and also add a bit about the exp(B). – lisaarthur Nov 12 '23 at 18:41
@JElder 'I am guessing your current model is comparing 8 9 Most to 7 and is dummy coded' - Omg. So Stress(1) would be a comparison of 7 to what? – lisaarthur Nov 12 '23 at 18:46
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@lisaarthur You said, “ need my reference category to be the lowest level of stress (number 1).” I think what EdM and I are saying is that there are multiple ways of treating/coding a categorical factor and what you’re describing and what you did is the incorrect approach. You can do orthogonal polynomial contrasts in SPSS and I would strongly recommend you do that for your ordinal factor. It gives you linear contrasts (and other contrasts) – JElder Nov 12 '23 at 18:57
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@lisaarthur “Textbooks interpret the coefficients and also add a bit about the exp(B).” I am not sure what you mean here. Can you tell me how to interpret log odds? I sure can’t! The logit transformation allows for a linear relationship between the response and the coefficients but it isn’t very interpretable. If your textbook interprets log odds coefficients, I’d love to hear how they do it! – JElder Nov 12 '23 at 18:59
@JElder orthogonal polynomial contrasts in SPSS - My research methods textbooks don't cover this so I checked youtube and there does not seem to be one done for logistic regression. Yes, I do use youtube for these things because textbooks don't cover it (for SPSS and social sciences) and any resource online will be something confusing and incomprehensible. I found a video on Linear contrast analysis on youtube, is this what my case falls under? – lisaarthur Nov 12 '23 at 19:30
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@lisaarthur: Orthogonal Polynomial contrasts can be done for any regression model. There are different contrast coding schemes for categorical independent variables. This does not depend on whether it's a generalized linear model or general linear model. This document refers to it in SPPS and this link refers to it in SPSS: https://web.wlu.ca/bgebotys/book/conspss.pdf | https://www.researchgate.net/post/How_can_I_run_a_Polynomial_orthogonal_contrasts_analysis_by_SPSS – JElder Nov 12 '23 at 20:01
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@lisaarthur I have provided thorough answers to your original question and all of your follow-ups-- I'd appreciate if you could accept my answer if the responses have been helpful! Please consider implementing your independent variable as either (1) numeric or preferably () using an orthogonal poly contrast for the IV factor. – JElder Nov 12 '23 at 20:04
I have looked at your resources, thank you. A lot is unclear to me still. So I analyse the relationship between the stress independent variable and the DV (prosocial behaviour) separately from the logistic regression? I can turn the stress variable into a numeric one? That sounds easier than doing this orthogonal polynomial contrast thing. – lisaarthur Nov 12 '23 at 20:10
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@lisaarthur: None of this is separate from regression. To use a categorical factor in a regression model, you have to make a decision about how you will contrast code it. A dummy coded contrast (what you were using) is not meaningful for a ordinal factor, while a orthogonal polynomial contrast is much more interpretable as it tells you "Is my outcome more likely as stress increases?". Your current contrast code says "Is my outcome more likely for 9 compared to 7?" etc. which doesn't make a ton of sense. To reiterate, this is all a part of the regression model and a decision you have to make. – JElder Nov 12 '23 at 20:30
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@lisaarthur I would not personally recommend treating stress as numeric as it is only four levels and it is ordinal (which is not numeric) but people often do incorrectly treat ordinal variables as numeric. Your inferences should probably be pretty much the same whether you treat as numeric or categorical with orthogonal polynomial contrasts though. To be clear, you have to decide on a CONTRAST for ALL CATEGORICAL IVs. This is not overcomplicating the model. It is the case with any categorical IV. Does that make sense? – JElder Nov 12 '23 at 20:33
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https://www.youtube.com/watch?v=9tBLXJjZPZs – JElder Nov 12 '23 at 20:33
@JElder thank you so much for all this. Sorry, I wanted to accept your answer and close the question but it got closed before I could do. – lisaarthur Nov 14 '23 at 17:47
@JElder Just one last question, you say that "To be clear, you have to decide on a CONTRAST for ALL CATEGORICAL IVs." - Do I have to create these contrasts for my gender (male, female) and marital status (married, single) IVs, too? I thought they were already coded fine as they are binary? Thank you. – lisaarthur Nov 14 '23 at 18:32
@JElder I will also have to re-define the ordinal variable in the Variable View in SPSS no? So I would give my 'seven', 'eight', 'nine', and 'most' labels a numerical value of 7, 8, 9, and 10. – lisaarthur Nov 14 '23 at 18:42
@JElder. I'm so sorry, I don't understand the youtube video you sent me at all. It is showing dummy coding and contrast coding for gender but I don't see why I need to dummy code or contrast code the gender variable? It already is coded fine, it's binary and I can compare the 2 levels fine. – lisaarthur Nov 14 '23 at 19:01
@JElder. The gender variable in the video is contrast coded like this: if female = female gender coding = 1. if female = male gender coding = -1. How do I translate this to my stress variable with 4 levels? It is totally incomphrehensible to me. – lisaarthur Nov 14 '23 at 19:04

Binary logistic regression results interpretation when one IV is ordinal

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