Calculator inputs
Choose one estimation method, enter the needed values, and compute the standard error, z statistic, interval, and related diagnostics.
Example data table
These sample rows show how coefficient estimates, variances, and intervals can look in a fitted generalized linear model report.
| Predictor | Estimate | Variance | SE | z | 95% CI Lower | 95% CI Upper |
|---|---|---|---|---|---|---|
| Intercept | -1.2540 | 0.0900 | 0.3000 | -4.1800 | -1.8420 | -0.6660 |
| Age | 0.8420 | 0.0484 | 0.2200 | 3.8273 | 0.4108 | 1.2732 |
| Income | 0.1350 | 0.0064 | 0.0800 | 1.6875 | -0.0218 | 0.2918 |
| Treatment | -0.4680 | 0.0289 | 0.1700 | -2.7529 | -0.8012 | -0.1348 |
Formula used
Standard error from a variance element
SE(β̂j) = √(Vjj × φ × m)
Standard error from an information diagonal
SE(β̂j) = √((1 / Ijj) × φ × m)
Standard error from a reported z statistic
SE(β̂j) = |β̂j / z| × √(φ × m)
Standard error from confidence interval width
SE(β̂j) = (Upper − Lower) / (2 × zα/2) × √(φ × m)
Wald confidence interval
β̂j ± zα/2 × SE(β̂j)
Here, Vjj is the coefficient variance, Ijj is the diagonal Fisher information, φ is the dispersion scale, and m is the robust variance multiplier. The calculator reports a Wald style interval around the entered coefficient estimate.
How to use this calculator
Enter the coefficient name, model family, and link function. Choose one estimation method that matches the information you already have from your model output.
Type the coefficient estimate and confidence level. Then enter either the variance element, the information diagonal, the reported z statistic, or the confidence interval bounds.
Add dispersion and robust variance adjustments only when your analysis requires them. Keep both values at 1 for a standard covariance based calculation.
Click the calculate button. The result box appears above the form and shows the standard error, z statistic, p value, confidence interval, and a Plotly uncertainty graph.
Use the CSV and PDF buttons to export the computed report. The example table below the calculator can help you validate your inputs against a realistic GLM output layout.
Frequently asked questions
1. What does the standard error measure in a GLM?
It measures the sampling uncertainty around one estimated coefficient. Smaller standard errors usually indicate more precise estimates, while larger values suggest greater instability or weaker information in the data.
2. When should I use the variance element method?
Use it when your software already reports the coefficient covariance matrix or the diagonal variance for a specific parameter. This is the most direct route to the standard error.
3. Why does the calculator offer an information diagonal option?
Some model summaries or optimization routines report Fisher information rather than covariance. Since variance is the reciprocal of the information diagonal, the calculator can derive the standard error from it.
4. Can I recover a standard error from a z statistic?
Yes. If you know the coefficient estimate and its reported z statistic, the standard error can be back solved as the absolute coefficient divided by the absolute z value.
5. What does the dispersion scale change?
It rescales the coefficient variance before taking the square root. This matters in models where dispersion is estimated separately or when quasi likelihood adjustments are used.
6. What is the robust variance multiplier for?
It lets you inflate or adjust the base variance when you want a quick sensitivity check against robust or sandwich style variance changes without rebuilding the model.
7. Are the confidence intervals exact?
No. They are Wald style intervals based on the normal approximation. These are common and useful, but they may differ from profile likelihood or bootstrap intervals.
8. What does relative SE percent tell me?
It compares the standard error to the size of the coefficient estimate. Lower percentages imply a more stable estimate, while high percentages suggest notable relative uncertainty.