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I have random factors such as Flower, Allotment and Gardener. Gardeners scored the flowers.

Flower Crossed in Allotment. Flower Nested in Gardener, and Allotment Nested in Gardner.

Can I analyse each notion separately, or do I need to estimate variances across all levels of the design within a single, comprehensive model? All factors are random effects.

user330
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1 Answers1

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If I understand your terminology correctly:

  • "Flower Nested in Gardener": each Gardener scored several Flowers, but each Flower was scored by only one Gardener
  • "Allotment Nested in Gardener": each Gardener scored Flowers in several Allotments, but Flowers in each Allotment were scored by only one Gardener
  • "Flower Crossed in Allotment": each Flower occurred in more than one Allotment, and each Allotment had more than one Flower
  • We would also assume that there were multiple scores for Flowers within each Allotment — otherwise (if there is a single observation per Allotment/Flower combination), then we typically handle the variation at this level as part of the residual variance; indeed, if there is only a single observation then software packages should warn you (but don't always) that the model is overparameterized (the residual variance is confounded/jointly unidentifiable with the Allotment:Flower random effect)

If this description is correct (adding a diagram of your experimental design to your question, as in this answer, might help), then the maximal model would be

(1 | Gardener/(Allotment * Flower))

however, this syntax might not won't work: you need to expand it out to

(1 | Gardener) + (1 | Gardener : Allotment) + (1 | Gardener : Flower ) +
  (1 | Gardener : Allotment : Flower)
  • if you only have one observation per Allotment/Flower, you would drop the last term
  • don't forget that effects other than the intercept may vary among grouping variables, depending on your design (see e.g. Schielzeth and Forstmeier 2009)

Schielzeth, Holger, and Wolfgang Forstmeier. 2009. “Conclusions beyond Support: Overconfident Estimates in Mixed Models.” Behavioral Ecology 20 (2): 416–20. https://doi.org/10.1093/beheco/arn145.

Ben Bolker
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  • Thank you very much for your response. For better clarification: assume 100 different flowers are crossed within 30 allotments. Different flowers are nested with gardeners (with approximately 30 gardeners distributed across the allotments), and different allotments are nested with gardeners. Does this configuration work with your syntax? – user330 Mar 24 '24 at 22:50
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    Your description here doesn't help me much beyond what you said in your original question. To make sure we're on the same page it would help to describe your design without using the terms "nested" and "crossed" (i.e., common language as in my answer). Or, you could say whether the description I give in my answer seems correct. – Ben Bolker Mar 24 '24 at 23:13
  • Thank you. Your answer seems correct, But there is only one thing I don't understand. You stated: "but Flowers in each Allotment were scored by only one gardener. Within each allotment, we have different gardeners; for example, in Allotment 1, 10 Gardners scored 100 flowers. – user330 Mar 24 '24 at 23:23
  • In that case, Allotment can't be nested in Gardener. "A nested in G" means that each particular A (allotment) is observed with a single level of G (gardener). (This is why I wanted to make sure that the language is clear.) A figure, or an example data set showing your design, would help ... – Ben Bolker Mar 25 '24 at 00:46
  • When I say "Allotments nested in Gardeners," it means that each allotment is specifically cared for by a gardener, and different allotments are under the care of different gardeners. This relationship indicates that the allotments are indeed nested within the gardeners, showing that each gardener has their own designated allotment(s) they are responsible for. This setup creates a structure where gardeners are directly linked to their specific allotments within the garden,. – user330 Mar 25 '24 at 01:39
  • "each gardener has their own designated allotments", but if flowers in each allotment are scored by more than one gardener ("for example, in Allotment 1, 10 Gardeners scored 100 flowers"), then allotments are not nested within gardeners according to the statistical meaning of the word. – Ben Bolker Mar 25 '24 at 02:00
  • Perhaps I haven't made my point clear, and for that, I apologize. It's a bit complex, but I am completely certain that, in the statistical sense of the term eplanied, allotments ARE NESTED within gardeners. Thank you for the time you've spent discussing this with me. – user330 Mar 25 '24 at 02:25