Calculator
Use the settings below, then add as many coefficients as needed. The page stays in a single vertical flow, while the inputs shift to 3 columns on large screens, 2 on smaller screens, and 1 on mobile.
Formula Used
General linear predictor: η = β0 + β1x1 + … + βkxk
Confidence interval for one coefficient: β ± zα/2 × SE(β)
Identity link: μ = η, so a predictor change Δx gives Δμ = β × Δx
Logit link: log(p / (1 − p)) = η, so odds ratio = exp(β × Δx)
Log link: log(μ) = η, so multiplicative factor = exp(β × Δx)
Relative change under log or logit exponentiation: (exp(β × Δx) − 1) × 100%
Updated prediction: apply the inverse link to the baseline profile after adding β × Δx to the linear predictor.
How to Use This Calculator
- Select the model family and the exact link used in your fitted model.
- Enter an outcome label, such as event probability, count, rate, or mean score.
- Optional: provide a baseline outcome for the reference profile to translate coefficients into updated predictions.
- Add one row for each coefficient you want to interpret.
- Enter the estimated coefficient, standard error, p-value if known, and the predictor change Δx you care about.
- Use Δx = 1 for binary indicators, or larger values for meaningful shifts like 5 years or 10 units.
- Submit the form to generate coefficient intervals, exponentiated effects, narrative interpretations, and the graph.
- Use the CSV and PDF buttons to export the output.
Example Data Table
| Coefficient name | Estimate β | SE | p-value | Entered Δx | Context note |
|---|---|---|---|---|---|
| Treatment | 0.620 | 0.180 | 0.001 | 1 | Treated vs control |
| Age | 0.090 | 0.030 | 0.004 | 5 | Per five years |
| BMI | 0.040 | 0.020 | 0.045 | 2 | Per two BMI units |
FAQs
1. What does a positive coefficient mean in a logit model?
A positive logit coefficient raises log-odds. After exponentiation, the odds ratio becomes greater than one, which means the event becomes more likely for the entered predictor change, holding all other variables constant.
2. Why does the calculator exponentiate some coefficients?
Logit and log links operate on transformed scales. Exponentiation converts those effects into odds ratios or multiplicative mean or rate factors, which are usually easier to explain than raw log-scale coefficients.
3. When should I enter a baseline outcome?
Enter a baseline outcome when you want a translated prediction, such as a new probability, mean, or rate for a reference profile. Without it, the calculator still interprets coefficients and intervals correctly.
4. Can I interpret categorical predictors here?
Yes. For a dummy-coded variable, set Δx to 1 and describe the contrast in the context note, such as treated versus control or urban versus rural.
5. What if the confidence interval crosses zero?
If a coefficient interval includes zero, the coefficient-level evidence is weaker at that confidence level. For exponentiated effects, the comparable reference value becomes one instead of zero.
6. Does this replace full marginal effects analysis?
No. This tool provides disciplined coefficient interpretations and reference-profile translations. Full marginal effects can still be better when nonlinear probability changes across covariate patterns matter strongly.
7. Can I use this with Poisson, gamma, or quasi-Poisson models?
Yes, use the log link for those models when appropriate. The calculator then reports multiplicative factors and percent changes that match common interpretations of counts, rates, and positive means.
8. What is the purpose of the entered change Δx field?
Δx lets you interpret practically meaningful predictor shifts. Instead of only reporting one-unit effects, you can evaluate five years, ten dollars, two standard deviations, or any custom difference.