Interpreting the signs of GLM ordinal logistic regression

lindor1310

In the ordinal logistic regression of GLM in JASP, I don't know how to interpret the sign of the estimated value, so I would like some advice. 

Specifically, I will present a tentative hypothesis and variables and explain. 

It is a “self-interested hypothesis”, which would be that "the higher the income, the more opposed the redistribution." If the dependent variable is a ternary variable indicating support for or opposition to redistribution (1: in favor, 2: neutral, 3: opposed), and the independent variable is household income (1: low income, 2: medium income, 3: high income), 

then whether the estimated value is positive or negative would make this self-interested hypothesis valid? 

In my opinion, if we adopt the cumulative odds assumption, a negative coefficient means that the probability of belonging to a higher category (in this case, "opposite") is higher, but I am not sure about this and would like to hear your expert opinion.

I'm not an English speaker, so my explanation may not be very clear, but please forgive me.

EJ

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

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