catSurv (version 1.5.0)

obsInf: Observed Information

Description

Calculates the observed information of the likelihood of a respondent's ability \(\theta\) for a given item.

Usage

obsInf(catObj, theta, item)

Value

The function obsInf returns a numeric value of the observed information of the likelihood, given \(\theta\), for a given question item.

Arguments

catObj

An object of class Cat

theta

A numeric or an integer indicating the value for \(\theta\)

item

An integer indicating the index of the question item

Author

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

Details

The observed information is equivalent to the negative second derivative of the log-likelihood evaluated at \(\theta\). This function should never be called when the respondent has answered no questions as the likelihood is not defined.

See Also

estimateTheta, expectedObsInf

Examples

## Loading ltm Cat object
data(ltm_cat)

## Store example answers
setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35))

## Calculate observed information for different ability parameters and items
obsInf(ltm_cat, theta = 1, item = 10)
obsInf(ltm_cat, theta = 1, item = 11)
obsInf(ltm_cat, theta = 0, item = 10)
obsInf(ltm_cat, theta = 0, item = 11)