20 Rasch Measurement Error

One of our principles of measurement is that we should be able to quantify error. The standard errors of both person ability and item difficulty can be obtained.

rm(list=ls())  #remove all variables in the R environment
library(TAM)  #load the package TAM so we can use the functions in TAM
library(tidyverse)

# load in the dataset
responses <- read_csv('data/responses.csv')
# keep the scores
responses <- responses %>% select(ends_with('score'))
mod1 <- tam.jml(responses,bias=FALSE)
fit1 <- tam.jml.fit(mod1,trim_val = NULL)
item_fit <- tibble(fit1$fit.item)
item_fit <- item_fit %>% bind_cols(mod1$item1)
item_fit <- item_fit %>% arrange(xsi)

How would you describe the relationship between the standard error of the item difficulty and the item difficulty?

p <- ggplot(item_fit, aes(x=xsi, y=se.xsi))
p <- p + geom_point()
p

Figure 20.1: Standard Error of Item Measurement