[R-sig-ME] Standard Error of a coef. in a 2-level model vs. 2 OLS models
Harold Doran
h@ro|d@dor@n @end|ng |rom c@mb|um@@@e@@ment@com
Wed Sep 16 23:45:27 CEST 2020
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 using 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 using 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 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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