[R-sig-ME] Standard Error of a coef. in a 2-level model vs. 2 OLS models

[Simon Harmel]

Just a clarification.

For `ols1` model, I can approximate its SE of the sector coefficient by
using the within and between variance components from the HLM model:
sqrt(( 6.68  + 39.15  )/45)/(160*.25))

BUT  For `ols2` model, how can I approximate its SE of the sector
coefficient by using the within and between variance components from the
HLM model?

On Sun, Sep 13, 2020 at 6:37 PM Simon Harmel <sim.harmel using gmail.com> wrote:

> Dear All,
>
> I have fit two ols models (ols1 & ols2) and an mixed-effects model (m1).
> ols1 is a simple lm() model that ignores the second-level. ols2 is a simple
> lm() model that ignores the first-level.
>
> For `ols1` model,  `sigma(ols1)^2` almost equals sum of variance
> components in the `m1` model: 6.68 (bet.) + 39.15 (with.)
> For `ols2` model, I wonder what does `sigma(ols2)^2` represents when
> compared to the `m1` model?
>
> Here is the fully reproducible code:
>
> library(lme4)
> library(tidyverse)
>
> hsb <- read.csv('
> https://raw.githubusercontent.com/rnorouzian/e/master/hsb.csv')
> hsb_ave <- hsb %>% group_by(sch.id) %>% mutate(math_ave = mean(math)) %>%
> slice(1) # data that only considers grouping but ignores lower level
>
> ols1 <- lm(math ~ sector, data = hsb)
> summary(ols1)
>
> m1 <- lmer(math ~ sector + (1|sch.id), data = hsb)
> summary(m1)
>
> # `sigma(ols1)^2` almost equals 6.68 (bet.) + 39.15 (with.) from lmer
>
> But if I fit another ols model that only considers the grouping structure
> (ignoring lower level):
>
> ols2 <- lm(math_ave ~ sector, data = hsb_ave)
> summary(ols2)
>
> Then what does `sigma(ols2)^2` should amount to when compared to the `m1`
> model?
>

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