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

[Harold Doran]

Simon

Crossposting like this is frowned on a bit, but I’ve been in your shoes trying to get an answer before. I think you might be a bit confused. I saw your questions in both places and you’re asking how to get the standard errors of the OLS model using by fitting a mixed model and using the variance components from that mixed model to get the standard errors from an OLS model.

This is what we refer to in statistics as “bass-ackwards”. 😊

If you want the standard errors of the fixed effects from an OLS model, compute them as follows:

ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2, 10, 20, labels = c("Ctl","Trt"))
weight <- c(ctl, trt)
lm.D9 <- lm(weight ~ group)
X <- model.matrix(lm.D9)

### Compute Standard errors of fixed effects
sqrt(diag(solve(crossprod(X)) * .6964^2))

### use built in extractor function to get them instead
sqrt(diag(vcov(lm.D9)))

Similarly, get the standard errors of the mixed model from its own variance/covariance matrix.


From: Simon Harmel <sim.harmel using gmail.com>
Sent: Wednesday, September 16, 2020 5:54 PM
To: Harold Doran <harold.doran using cambiumassessment.com>
Cc: 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

Hi Harold,

I improved my question, and asked it on CrossValidated: (https://stats.stackexchange.com/questions/487363/using-variance-components-of-a-mixed-model-to-obtain-std-error-of-a-coef-from-a)

I would appreciate your answer, either here or on CrossValidated.

Many thanks, Simon

On Wed, Sep 16, 2020 at 4:45 PM Harold Doran <harold.doran using cambiumassessment.com<mailto:harold.doran using cambiumassessment.com>> wrote:
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<mailto: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<mailto: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<mailto: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<http://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<http://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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