Neither mixed models nor permutation tests are universally better for spatial case–control analysis. Choose according to the inference you need, how cases and controls were sampled, whether the data include meaningful replication or grouping, and what spatial dependence the analysis must preserve. A mixed model represents structured variation through model terms such as random effects; a permutation test evaluates a specified null by rearranging data in ways that must respect the study design. In many applications, they answer different questions rather than serving as interchangeable alternatives.
Start by defining the question and sampling design
Before choosing a method, define the outcome, the spatial units or locations represented by the data, how cases and controls entered the study, and the result you need. “Spatial case–control analysis” can refer to distinct targets:
- Association or risk-surface estimation: whether case status varies with location, or how that variation appears across a mapped area.
- Global clustering: whether the overall spatial pattern is more clustered than expected under a null model.
- Local cluster detection: whether a particular area or focus has an unusual concentration of cases.
A smoothed geographic risk surface, a global clustering test, and a local cluster statistic are not the same estimand. A method that performs well for one target should not be assumed to answer another. Also establish whether case and control counts were fixed by design, whether observations are grouped or repeated, and which aspects of the spatial arrangement could plausibly vary under the null.
What each approach represents
| Consideration | Mixed model | Permutation test |
|---|---|---|
| Core idea | Represents structured variation with model terms, including random effects for relevant grouping or replication. | Builds a null reference distribution by rearranging observations or labels under a specified randomization scheme. |
| Question it can address | Depends on the model and its effects; may estimate associations while accounting for modeled grouping or spatial variation. | Tests a statistic against the outcomes expected under the particular null encoded by the permitted rearrangements. |
| Design feature to inspect | Whether repeated, replicated, clustered, or otherwise grouped observations call for explicit random effects. | Whether the rearrangements preserve the sampling design and are valid under the null. |
| Main interpretive caution | Spatial random effects can overlap with smooth covariates, complicating fixed-effect interpretation. | Dependence can make observations non-exchangeable; unrestricted shuffling may not produce a valid null distribution. |
This comparison is about the methods’ roles, not a ranking. The model or test statistic, the sampling process, and the null hypothesis determine what the result means.
Do these 3 things before closing this tab:
1Scan for outdated or missing drivers - takes under a minute2Repair Windows errors before they cause bigger problems3Fix the driver behind crashes, sound loss and screen glitches#1 Best Overall
When a mixed model is a plausible choice
A mixed model is worth considering when the data contain replication or grouping that the analysis should represent—for example, replicated spatial point patterns or repeated spatial units. Bell and Grunwald’s 2004 work develops mixed models for replicated spatial point patterns using maximum pseudolikelihood and generalized linear mixed modeling, and compares fixed- and mixed-effect formulations. That evidence applies to the replicated point-pattern setting; it does not establish a general preference for mixed models in all case–control studies.
Check what the random effects stand for
Use random effects to represent a real feature of the data structure, such as grouping or replication, rather than treating them as a generic fix for spatial dependence. State which grouping is modeled and how that affects the interpretation of the remaining effects. The intended inferential target still matters: a model designed to account for replication does not automatically provide a global clustering test or local cluster location.
Rank #2
- This guide is a perfect overview for the topics covered in introductory statistics courses.
Consider spatial confounding
When a model includes spatial random effects, smooth covariates may follow a similar geographic pattern. This spatial confounding can make fixed-effect interpretation sensitive to modeling choices. Restricted spatial regression is discussed in the cited literature as one approach, but it is not a universal solution; explain the modeling choice and its implications rather than implying that the issue has been removed.
When permutation inference is plausible
Permutation inference is useful when you can state a defensible null randomization and implement it while preserving the design. A permutation test does not get its validity simply from repeating a shuffle many times: the allowed rearrangements define the null being tested. Specify what is rearranged, what is held fixed, and why those changes would be plausible if the null were true.
Rank #3
A case–control GAM example
In a 2006 population-based case–control mapping application, investigators used a generalized additive model (GAM) with a bivariate spatial smoother. They tested whether case status depended on location by comparing model deviances with and without the spatial smoothing term. To form the null distribution, they conditioned on the case and control counts, randomized locations, and refit the models for each permutation. The article reports 999 permutations for that analysis; this is a study-specific implementation, not a universal minimum or recommendation.
This example illustrates one conditional randomization design, not a template that is automatically valid for every case–control study. Whether locations, labels, or another element can be randomized depends on how subjects were sampled and on the null hypothesis of interest.
Check exchangeability before shuffling
Permutation inference relies on exchangeability under the null: the observations being rearranged must be interchangeable in the way the test assumes. Spatial correlation, repeated measures, or other dependence can violate that condition. FSL’s permutation documentation warns that correlated data can break exchangeability and notes that blocks can accommodate some repeated-measures designs. Blocks do not make every permutation valid by themselves; the restrictions must match the design and null.
A spatial random-shift study documents a related risk: in its setting, a procedure that disrupted spatial correlation produced liberal tests. The practical implication is to justify the randomization scheme for the actual dependence structure, rather than assuming that a spatial shuffle is harmless.
Free tools Windows power users keep installed
One-click scans. No signup required.
Best Value
How to choose for a particular analysis
- Write down the estimand. Decide whether you need a covariate association, a smoothed risk surface, a global clustering result, or a local cluster around a focus.
- Describe the sampling process. Record what was sampled, whether case and control totals were fixed, and which locations, labels, or units could vary under the null.
- Map the dependence and replication. Identify repeated observations, groups, replicated patterns, or spatial correlation that could affect model structure or exchangeability.
- Match the method to that structure. Consider random effects when meaningful replication or grouping needs representation. Consider permutation inference when a design-consistent null randomization can be specified.
- State the inferential limits. For a mixed model, describe spatial-confounding concerns if spatial random effects and smooth covariates overlap. For a permutation test, state the exchangeability assumptions and exact restrictions on rearrangement.
- Check the alternative you care about. A compact cluster, a point source, and a line source are different spatial patterns; evidence for one pattern does not settle performance for another.
If both methods appear possible, compare them only after aligning their estimands and assumptions. A model-based association estimate and a permutation p-value for a particular null need not be competing answers to the same question.
What published performance comparisons do—and do not—show
A simulation study compared permutation-based GAM approaches with a spatial scan statistic, not with mixed models. Its relative power changed with the simulated alternative: the scan statistic had the highest power for the study’s circular-cluster scenario, while GAM methods performed better for its point- and line-source scenarios. GAM methods had greater sensitivity than the scan statistic in all three simulated cases. These results are specific to that study’s simulations and comparison; they do not show that permutation-based GAMs generally outperform mixed models, nor do they establish a universal winner among spatial methods.
Use comparative evidence only when the study’s sampling design, spatial alternative, target statistic, and performance measure are relevant to your own analysis. If those differ, the published ranking may not transfer.
Quick Recap
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
Recommended Free Tools
