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This is a definition question. In the standard normal regression model

$y_i=a+bx_i+e_i$

where $e_i\sim N(0,s)$, $a$ and $b$ are fixed effects and $e_i$ is a random effect. So is this a mixed model? Or $e_i$ is not considered a random effect? This page says that random effects are estimated with partial pooling, so is $e_i$ not a random effect because it is not estimated with partial pooling?

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  • $e_i$ is not a random effect. You need a categorical variable to be able to talk about "random effects". – amoeba May 26 '17 at 08:30

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A mixed-effects model generally has both a random effect and an error term, both with mean $0$. I see the error term and you have a covariate effect in there ($bx_i$). So, I don't think it's a mixed effects model, it looks like a fixed effects model with two parameters (a,b) and design matrix $[\mathbf{1},\mathbf{X}]$