# Formulating a mixed model with nested fixed and random effects

I'm analysing the results of an experiment using a mixed (fixed and random-effects) ANOVA with nested effects and I just need someone to confirm that I have the right model.

The effects in the design are:

• Product--fixed, 5 levels--this is the main effect of interest
• Batch--random, 3 levels--nested within product
• Day--random,6 levels--this is a blocking factor in the design. On each day, multiple samples from each product/batch are tested in a random order.

So we have a complete, balanced experiment within each day.

Here is the ANOVA model that I think I need:

Day
+ Product
+ Batch(Product)
+ Day x Batch(Product)


Am I right in thinking that the appropriate error term for Product is the Batch-within-Product Mean Square?

I have used type III sums of squares.

I'm only really interested in testing for difference between products, so the model in the random factors is mostly only important to ensure that I get the correct residual for this comparison. However, tests for effects due to Day and Batch-within-Product are of secondary interest.

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