1. State what is being compared
Two classification histories can differ because of their inputs, release cutoffs, revisions, transformations, thresholds or fitted models. Decide which dimension the comparison is meant to test. To isolate threshold sensitivity, hold everything else fixed. To compare complete research procedures, allow their declared differences but report them. Neither exercise automatically identifies a superior model. The transparent two-feature threshold setting considered here is a rule-based classification exercise on synthetic information, not evidence of historical prediction. Discussion of fitted methods is conceptual and does not imply that a probabilistic model has been trained.
2. Establish a common comparison population
Match decision cutoffs and observation identities before comparing outputs. Determine whether both methods used the same available vintage and whether both had enough eligible inputs. Report the full scheduled population, each method's available cases and the intersection used for label agreement. Excluding all difficult cases can make agreement look reassuring while hiding poor coverage. Retain missing-input and abstention statuses outside the economic label set. A classification produced from revised data should not be compared with an earlier as-known classification as though only the classification rule differed.
3. Use a cross-tab without inventing ground truth
A cross-tab counts how often each label from method A occurs with each label from method B. Scikit-learn documents confusion matrices with true labels on one axis and predicted labels on the other. When neither regime history is independently established truth, use neutral axis names instead and describe the diagonal as agreement. Show counts before percentages and state whether any normalisation is by row, column or total. A large diagonal may reflect a dominant shared label. It does not establish that either method correctly identifies an unobserved economic state.
4. Align names only when the meanings justify it
Arbitrary cluster numbers can be permuted without changing a partition. Scikit-learn's adjusted Rand score compares pairwise assignments in a way that is unchanged by label permutation. That can help compare fitted partitions, but it does not validate economic names. For threshold quadrants with predefined meanings, preserve the definitions rather than relabelling states to maximise agreement. If a fitted state's meaning must be mapped to a named category, establish that mapping using the permitted development information. Repeatedly renaming states after seeing evaluation outcomes can conceal instability rather than resolve it.
5. Work through a fictional disagreement
The table contains four invented observations, not market evidence. Method A assigns higher growth at zero or above; method B uses 0.2. Both use an inflation threshold of zero, and every fictional inflation feature is -0.5. Growth values are -0.2, 0.1, 0.3 and 0.4. The methods agree on three of four rows, giving 75% agreement, and disagree only at 0.1. This calculation measures the consequences of different boundaries on these chosen inputs. It is not a probability that either method is correct or an estimate of future agreement.
6. Inspect sequences as well as totals
The same agreement rate can arise from isolated disagreements or one prolonged episode. Inspect run lengths, state occupancy, transition timing and distances from boundaries. Keep repeated labels based on unchanged inputs distinct from independent updates. A method that responds later may switch less often without being more accurate; a method that switches more often may simply have a narrower boundary margin. Where fitted comparisons require evaluation, preserve temporal order. Scikit-learn's TimeSeriesSplit documentation warns against training on future data and evaluating on the past; chronology alone still does not repair revised-data leakage.
7. Conclude with a bounded finding
A defensible conclusion identifies the compared rules, information policy, common sample, coverage, agreement counts and main reasons for disagreement. Keep economic interpretation, classification stability and any later decision evaluation separate. Do not select a method because its labels produce a pleasing retrospective narrative. If the exercise uses synthetic observations, its findings concern those assumptions and arithmetic only. Claims about historical performance would require an independently specified, chronologically valid study with appropriate uncertainty reporting. This guide explains method comparison; it is not investment advice or evidence that a regime label supports a particular exposure.
Inspect the comparison
| Fictional row | Growth feature | A: growth threshold 0 | B: growth threshold 0.2 |
|---|---|---|---|
| One | -0.2 | Lower growth / lower inflation | Lower growth / lower inflation |
| Two | 0.1 | Higher growth / lower inflation | Lower growth / lower inflation |
| Three | 0.3 | Higher growth / lower inflation | Higher growth / lower inflation |
| Four | 0.4 | Higher growth / lower inflation | Higher growth / lower inflation |
Primary references
References support the stated methods and data conventions. Original fictional examples are not observations from the cited sources.