Build reliable estimates across groups with random intercepts. Paste data, choose variables, view diagnostics fast. Export clean summaries for homework, research, and audits easily.
| group | y | x1 | x2 |
|---|---|---|---|
| A | 12 | 3 | 8 |
| A | 13 | 4 | 7 |
| A | 15 | 6 | 6 |
| B | 9 | 2 | 5 |
| B | 10 | 3 | 4 |
| B | 11 | 4 | 4 |
| C | 20 | 8 | 9 |
| C | 22 | 9 | 10 |
| C | 21 | 7 | 9 |
This calculator fits a random-intercept model for grouped observations: yit = β0 + x′itβ + ui + εit.
Random effects regression is designed for clustered or panel data where each group has its own baseline level. Instead of estimating one intercept per group, the model treats group intercepts as random draws with variance σ²u. This approach keeps more degrees of freedom than fixed effects, supports time-invariant predictors, and often improves efficiency when the random-effects assumption holds. The calculator summarizes θ, σ²e, and σ²u so you can judge how much variation sits within versus between groups.
Prepare a CSV with a group identifier, one numeric outcome, and one or more numeric predictors. Groups should have repeated observations; two or more groups are required, and more is better for stable variance estimates. Rows with missing values are removed, so keep your data clean and consistently typed. Balanced panels are not required, but highly uneven group sizes can influence the estimated average group size n̄ used in θ.
The calculator uses a feasible GLS workflow for a random-intercept model. First, it computes within-group deviations to estimate the within variance σ²e. Next, it runs a weighted between regression on group means to approximate the composite variance at the group level, then extracts σ²u by method of moments. Finally, it quasi-demeans y and X using θ and fits OLS on transformed variables to obtain coefficients and standard errors.
Coefficients report the average effect of each predictor after accounting for shared group structure. Standard errors are derived from the transformed design matrix and an estimated residual variance, producing t statistics and approximate two-sided p values. R² is shown for the transformed regression and is best used for quick comparisons across model variants rather than absolute fit claims. If σ²u is near zero, group effects are weak and results will resemble pooled regression.
Use the export buttons to download the coefficient table as CSV for spreadsheets or as a PDF for sharing. Choose a precision level before exporting to match your reporting standard. The exported table includes terms, coefficients, standard errors, t values, and p values, which are typically enough for a methods appendix. For publication workflows, pair the output with a short note stating the model is random intercept with feasible GLS and method-of-moments variance components.
It fits a random-intercept regression for grouped data, estimating one shared slope vector while allowing each group to have its own intercept drawn from a common distribution.
Use random effects when you can reasonably assume group effects are not correlated with predictors, and you need estimates for time-invariant variables or want higher efficiency.
These summarize the variance split and the quasi-demeaning strength. θ controls how much group means are removed; σ²e is within variance and σ²u is between-group variance.
It is an approximate two-sided p value from a Student-t distribution using N−p degrees of freedom, based on the coefficient divided by its standard error.
Include a header row, then one row per observation. Provide a group id column, a numeric outcome column, and numeric predictor columns that match the names you enter.
Rows with missing group, outcome, or predictor values are removed to keep the matrix calculations stable and prevent biased results from partial records.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.