Minimum bias is still useful for fitting and explaining a multiplicative rating plan, but it offers no accuracy advantage over an equivalent Poisson GLM. Its appeal is that the factor updates are easy to follow and the fitted totals are easy to reconcile; that reconciliation is shared by the GLM and does not prove either model predicts well.
| Question | Answer | Practical consequence |
|---|---|---|
| Does minimum bias give a different fit? | No, when the specifications match. | Choose the implementation for convenience and transparency. |
| Does balance validate the model? | No. Class totals can match while combinations are poorly fitted. | Check residual patterns, factor stability and performance on new data. |
| Does a wrong variance invalidate the factors? | Not automatically, if the conditional mean is correct. | Separate uncertainty problems from problems with the mean. |
When the fitted answer is the same
For claim counts, the model is:
Expected claims = exposure × base frequency × classification factors.
Without additional unequal observation weights, the balance version of multiplicative minimum bias adjusts factors until observed and fitted claim totals agree within each level of every included classification variable. Extra observation weights instead produce weighted balance. A Poisson GLM solves the same equations when it uses the same observations, exposure treatment, weights and multiplicative terms, with a log link and no penalty or credibility adjustment. With a finite, identifiable solution and convergence, the fitted means agree, as do the relativities after consistent normalization. Brown derives this equivalence; Mildenhall develops the wider relationship between minimum-bias criteria and GLMs.
This applies to the balance procedure, not everything called minimum bias. Changing the criterion, constraints or weights can change the answer.
What balance actually buys you
Balance makes a model easy to reconcile to its training data. If a reviewer asks whether fitted claims reproduce a territory's observed total, the answer is directly checkable. It does not establish that the territory factor works equally well for each class inside it.
Here is an illustrative example, with equal exposure in each cell:
| Territory | Class 1 observed / fitted | Class 2 observed / fitted | Total observed / fitted |
|---|---|---|---|
| Territory A | 70 / 60 | 30 / 40 | 100 / 100 |
| Territory B | 20 / 30 | 30 / 20 | 50 / 50 |
| Class totals | 90 / 90 | 60 / 60 | 150 / 150 |
Every margin balances, yet each cell differs from its observed count by 10. That could be noise or a missing territory-by-class interaction. Matching the totals cannot distinguish the two. Check whether the pattern persists across samples or in held-out data before treating it as a model defect.
Wrong variance and wrong mean are different problems
Using the Poisson equations does not require believing that claim-count variance equals the mean. When the conditional mean is correctly specified, Poisson pseudo-maximum likelihood can consistently estimate its coefficients under the usual sampling and regularity conditions. This is a large-sample result, not a promise of correct factors in every dataset. A wrong working variance can cost efficiency and invalidate conventional standard errors; uncertainty estimates must reflect the data's variance and dependence. Santos Silva and Tenreyro explain these conditions.
Quasi-Poisson allows variance to equal a common dispersion factor times the mean. That factor cancels from the coefficient equations, so it changes estimated uncertainty without changing fitted means under the same specification. Clark explains the distinction.
A wrong mean structure is more consequential for the factors themselves. Omitted interactions or overly broad groups can leave systematic errors. Different working variance functions then give those errors different weights and can select different fitted compromises. Adjusting standard errors alone cannot fix that.
What I would choose
I would keep minimum bias where its transparency makes the work easier, and use an equivalent Poisson GLM where its software and diagnostics are more convenient. Neither deserves preference because its class totals balance: both do.
If factors are unstable or predictions fail on new data, reconsider the variables, interactions, weighting or credibility treatment. Gross and Evans illustrate adding credibility to minimum bias, but that changes the comparison. The deciding evidence is whether the factors are stable and the predictions hold up.