#StackBounty: #mixed-model difference in standard errors between 2 seemingly equivalent models

Bounty: 250

Consider a crossed design with 3 operators and 4 instruments.
Interest is in the instrument effect.

Could you explain me the difference in standard errors of the fixed effects between the two seemingly equivalent models below?

Model 1

  • fixed effect: instrument
  • random effect: operator, operator*instrument

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Model 2

  • fixed effect: instrument
  • random effect: operator*instrument

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Get this bounty!!!

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