How to run a EIV regresison

June 27, 2023

I am trying to run an EIV regression but I am having troubles understanding the sigma error required
I have a data frame like this (example data):

y	x	x.sd
46.5	4.3	0.52
54.2	4.6	0.71
56.7	5.1	1.01
49.4	4.9	0.54
51.1	3.9	1.1

y=dependent variable

x=independent variable

x.sd= standard deviation of x

I tried:

library(eivtools)

eivreg(y~x, data, Sigma_error = x.sd)

But I get an error. Sigma must be a matrix
I am a bit confused now because I thought Sigma was the sd of the variable

Could someone please explain what us exactly the sigma value here?
Any help is highly appreciate it

>Solution :

You have to compute a named matrix Sigma_error of the regressors, in this case a 1×1 matrix.
Note that the lm and unadjusted eiv coefficients are equal.

data <- "y  x   x.sd
46.5    4.3     0.52
54.2    4.6     0.71
56.7    5.1     1.01
49.4    4.9     0.54
51.1    3.9     1.1"
data <- read.table(text = data, header = TRUE)

library(eivtools)
#> Loading required package: R2jags
#> Loading required package: rjags
#> Loading required package: coda
#> Linked to JAGS 4.3.1
#> Loaded modules: basemod,bugs
#> 
#> Attaching package: 'R2jags'
#> The following object is masked from 'package:coda':
#> 
#>     traceplot

# Sys.setenv(JAGS_HOME="C:/PROGRA~1/JAGS/JAGS-4.3.1")

S2 <- matrix(var(data$x.sd), dimnames = list("x", "x"))
fit_lm <- lm(y ~ x, data)
fit_eiv <- eivreg(y ~ x, data, Sigma_error = S2)

summary(fit_lm)
#> 
#> Call:
#> lm(formula = y ~ x, data = data)
#> 
#> Residuals:
#>      1      2      3      4      5 
#> -4.006  2.455  2.890 -3.584  2.245 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   32.750     19.247   1.702    0.187
#> x              4.129      4.202   0.983    0.398
#> 
#> Residual standard error: 4.013 on 3 degrees of freedom
#> Multiple R-squared:  0.2435, Adjusted R-squared:  -0.008679 
#> F-statistic: 0.9656 on 1 and 3 DF,  p-value: 0.3982
summary(fit_eiv)
#> 
#> Call:
#> eivreg(formula = y ~ x, data = data, Sigma_error = SE)
#> 
#> Error Covariance Matrix
#>         x
#> x 0.07133
#> 
#> Residuals:
#>      1      2      3      4      5 
#> -3.317  2.349  1.458 -4.486  3.996 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   20.657     25.663   0.805    0.480
#> x              6.781      5.545   1.223    0.309
#> Number of observations used: 5 
#> Latent residual standard deviation: 3.574 
#> Latent R-squared: 0.3999, (df-adjusted: -0.0002294)
#> 
#> EIV-Adjusted vs Unadjusted Coefficients:
#>             Adjusted Unadjusted
#> (Intercept)   20.657     32.750
#> x              6.781      4.129

^{Created on 2023-06-27 with reprex v2.0.2}