Standard Error of a coef. in a 2-level model vs. 2 OLS models

This is not how standard errors are computed for linear or mixed linear
models. I'm not sure what you're goal is, but the SEs are the square roots
of the diagonal elements of the variance/covariance matrix of the fixed
effects.

See ?vcov on how to extract that matrix.

-----Original Message-----
From: R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> On
Behalf Of Simon Harmel
Sent: Sunday, September 13, 2020 7:51 PM
To: r-sig-mixed-models <r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] Standard Error of a coef. in a 2-level model vs. 2
OLS models

External email alert: Be wary of links & attachments.


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 at 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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