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How to combine linear mixed model results across different test subjects?

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Suppose I have three test subjects and for each I have collected data and formulated a linear mixed-effects model using fitlme. (Assume the effects, both fixed and random, are the same for each.)
If LME is the resulting model for a particular individual, the command anova(LME), gives me a p-value for each fixed effect, indicating its significance in determining the response outcome.
How can I combine the three anova analyses to test whether the fixed effect in general plays a role in determining the response?

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