Interpreting the signs of GLM ordinal logistic regression

Comments

• EJ

  October 23

  I've asked our expert, but ChatGPT answer your question as follows:

  Short answer: with your coding (1 = in favor, 2 = neutral, 3 = opposed), a positive income coefficient in a cumulative‐logit (proportional odds) model means higher income → more opposition, which supports the self-interest hypothesis. A negative coefficient means the opposite.

  Why:

  Most software (incl. JASP’s ordinal GLM) fits the proportional-odds model as

  [

  \text{logit},\Pr(Y \le k \mid x)=\tau_k - \beta x, \quad k=1,2.

  ]

  • If β > 0, then for every 1-step increase in income, the odds of being at or below any cutpoint (k) decrease by a factor (e^{\beta}). Equivalently, the odds of being above that cutpoint (i.e., in a higher category) increase by (e^{\beta}). With your ordering (higher values = more opposed), probability mass shifts upward → more opposition.
  • If β < 0, odds shift toward lower categories → more support.

  Interpretation you can quote:

  • “Each one-level increase in income multiplies the odds of being more opposed (i.e., in category (>k)) by (e^{\beta}) for every cutpoint (k).”

  Example: if (\beta=0.40), then (e^{0.40}\approx 1.49): each step up in income increases the odds of being more opposed by ~49% (holding other predictors constant).

  Practical checks/tips:

  • Make sure the dependent variable is ordered exactly as you intend (1=favor < 2=neutral < 3=oppose). If you reverse the order, the sign flips.
  • Treating income as 1–2–3 assumes a linear step effect. If you want separate effects for medium vs high income, use dummy variables.
  • The proportional-odds assumption implies the same (\beta) works for both cutpoints (1|2 and 2|3). If that’s doubtful, consider testing/relaxing it (partial proportional odds).

  So: with your coding and the cumulative odds link, positive = more opposition; negative = more support.
• JohnnyB

  October 23

  Haha, I don't think I can improve on chatGPT's answer :'-)

  When the coefficient is positive, it means the predictor will increase the chances of landing in a higher category.

  Cheers,

  Johnny
• lindor1310

  November 2

  Thank you for your response. I appreciate it very much.☺️

  The data I used was from a Japanese social survey. If income is used as the independent variable, expressed as a linear value (1 low, 2 medium, 3 high), and several other variables are controlled for, with support for or opposition to redistribution (1, in favor, 2, neutral, 3, opposed) as the dependent variable, the hypothesis that "the higher the income, the more people oppose redistribution" seems intuitive. However, when I perform this using JASP's Ordinal glm, the sign of the estimate is negative and significant. This, in light of your responses, indicates that my hypothesis does not hold. On the other hand, when I perform the analysis using the same value assignments in the "mass::polr" package in R, the sign is positive and significant. (It's possible that I'm not using R correctly.)

  I also asked ChatGPT about this, and they replied:

  
  

  1. Cumulative Logit Mechanism (JASP's GLM)

  JASP's "ordinal logistic regression (GLM)" uses cumulative logit, and the model takes the following form:

  \text{logit}\{P(Y \leq j)\} = \theta_j - \beta X

  The key here is that it models the "probability of remaining below that value (≤ j)."

  2. Interpretation of OR

  • OR = exp(β) > 1

  → As X increases, the "odds of remaining in the lower category" increase.

  → More likely to remain in the lower category.

  • OR = exp(β) < 1

  → As X increases, the "odds of remaining in the lower category" decrease.

  → Less likely to remain in the lower category = More likely to shift to the higher category.

  3. Your Case

  • DV: Pro or Con of Redistribution (1 = Pro, 3 = Oppose)

  • B = –0.013, OR ≈ 0.89

  Interpretation:

  • As income increases, the odds of remaining in the pro or neutral (lower category) category decrease by 0.89.

  • In other words, it becomes more difficult to remain in pro or neutral, and the probability of shifting to the oppose (3) category increases.

  This answer seems to support my hypothesis.

  When I ask this question to other generative AIs (Gemini, Claude, etc.), the answer is either that my hypothesis is supportable or not (there are cases where it is and where it isn't), and the answer is not the same. I don't know what to trust.

  I would appreciate some help...
• Rhars

  November 8

  The confusion stems from different (opposite!) parameterizations in JASP vs polr.

  I'm absolutely not an expert in JASP, but as far as I can tell, JASP uses vglm from the VGAM package to estimate this model. Running the same model on the same data between JASP vs polr indeed gives opposite sign coefficients (I tried). This makes sense, as the VGAM documentation -I hope linking is allowed- specifies that by default VGAM focuses on P(Y<=j). In other words, positive coefficients imply one is more likely to land in category j or lower, see: https://www.rdocumentation.org/packages/VGAM/versions/1.1-13/topics/cumulative

  In VGAM, this can be switched around if the reverse=TRUE option is enabled. The documentation specifies that reverse=TRUE focuses on P(Y>j), direction-wise, i.e. positive coefficients imply one is more likely to land in higher categories.

  Running polr gives exactly the same coefficients as running VGAM with reverse=TRUE. In other words, positive coefficients in polr suggest that higher scores on your predictor are associated with landing in a higher category. If higher values in your case represent 'more opposition', then a positive coefficient in polR suggests an increase in your predictor is associated with a higher 'opposition' category (as higher values=more opposition). In other words, both results are telling you the same thing, but in a different way. VGAM/JASP is just telling you you're less likely to land in lower (i.e. pro/neutral) categories.
• JohnnyB

  November 10

  Hi @Rhars ,

  Thanks for your input, that is very helpful! I think it makes sense to use the reversed function call, but it would be good to make this more explicit in the helpfiles.

  Cheers

  Johnny
• lindor1310

  November 14

  Thank you for your thoughtful reply✨

  I was confused at first, but I feel like my thoughts are starting to clear up.

  The two options I should focus on in the formula for ordinal logistic regression analysis are P(Y<=j) or P(Y>j), and since JASP is likely using the Vglm default for its analysis, the former, P(Y<=j), applies.

  Therefore, can I interpret this as meaning that my hypothesis,

  "In JASP's ordinal logistic regression analysis, the estimated value is negative, and as the number of independent variables increases, the dependent variable tends to fall into a higher category," is correct, and that this does not contradict the fact that Mass::polr output a positive estimated value in the same analysis"?

  I'd like to thank everyone who has provided their research and support and sent me messages.

  Lindor
• Rhars

  November 15 edited November 15

  Yes, that is indeed the conclusion. In polr, positive betas imply higher categories, in Jasp/vglm, negative betas imply higher categories.

  Though it's not about the number of independent variables, but the value of the independent variables. (I think that's what you meant, though!)

  To be a bit more precise: both packages actually focus on logit(P(Y<=j)) on the left hand side by default. It's just that Polr uses α_j-Xβ on the right hand side (see 'details' in https://www.rdocumentation.org/packages/MASS/versions/7.3-65/topics/polr While vgam (and therefore jasp) uses α_j+Xβ (see Yee's 2008 paper in the R Journal, p28). The sign flip (+ vs -) also flips the coefficient interpretation.
• Dmartin427

  November 16

  I had this exact nightmare of interpretation when I was building an advanced research statistics course for my health science students. Long story short, the interpretation of the coefficient signs are the opposite of what you would initially expect them to be in JASP.