item_fit {irt}

Calculate item-fit indices

Description

item_fit calculates the fit of an item to a given psychometric model.

Usage

item_fit(ip, resp, theta = NULL, type = "Q1", item_id = NULL, n_groups = NULL)

Arguments

ip

An Itempool-class object.

resp

A Response_set-class object, matrix or data.frame containing the item responses.

theta

An vector containing ability parameters. When type = "Q1" and theta = NULL or an invalid theta vector provided, theta values will be estimated using item parameters and responses. In order to speed up the function for large data sets, theta values can be supplied.

type

The type of the item-fit index. Currently the following indices are available:

"Q3"

Yen's Q3 index (Yen, 1984)

"Q1"

Yen's Q1 index (Yen, 1981). Only available for unidimensional dichotomous items.

"G2"

PARSCALE's fit statistic. See DeMars (2005) for details.

The default value is "Q1".

item_id

A string vector that is holding the ID's of the item for which item fit should be calculated. The default value is NULL where item fit statistic of all items will be calculated.

n_groups

An integer representing the number of groups of examinees. When type = "Q1" and n_groups = NULL, the default value will be 10 (as specified in Yen (1981)). For example, if there are 900 examinees, when n_groups = 10, first examinees will be sorted according to their theta scores and separated into 10 equally sized groups of approximately 90 examinees each. The same default value is used when type = "G2".

Details

# Yen's Q3

The details of Yen's Q3 can be found in Yen (1984). It is mainly used as a measure of local dependence between two set of items.

# Yen's Q1

The details of Yen's Q1 can be found in Yen (1981). Please note that Q1 can have inflated Type-I error rates (Orlando & Thissen, 2000).

# PARSCALE's G2

PARSCALE's fit statistic G2 is explained in Kang and Chen (2008) and DeMars (2005) in detail. DeMars also detailed the situations when G2 index yields inflated Type-I error rates. Specifically, she did not recommend this index for short tests.

Value

A vector of item-fit index values for Q1 and G2. A correlation matrix will be returned for Q3.

Author(s)

Emre Gonulates

References

DeMars, C. E. (2005). Type I error rates for PARSCALE's fit index. Educational and psychological measurement, 65(1), 42-50.

Kang, T., & Chen, T. T. (2008). Performance of the generalized S-X2 item fit index for polytomous IRT models. *Journal of Educational Measurement*, 45(4), 391–406. <doi:10.1111/j.1745-3984.2008.00071.x>

Orlando, M., & Thissen, D. (2000). New item fit indices for dichotomous item response theory models. Applied Psychological Measurement, 24, 50–64.

Yen, W. M. (1981). Using simulation results to choose a latent trait model. *Applied Psychological Measurement*, 5(2), 245–262. <doi:10.1177/014662168100500212>

Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. *Applied Psychological Measurement*, 8(2), 125–145.

Examples

ip <- generate_ip(model = "3PL", n = 10)
theta <- rnorm(1000)
resp <- sim_resp(ip = ip, theta = theta, output = "response_set")

### Yen's Q1 ###
# Calculate Yen's Q1 for all items
item_fit(ip = ip, resp = resp, theta = theta, type = "Q1")

# Calculate Yen's Q1 for only selected items
item_fit(ip = ip, resp = resp, theta = theta, type = "Q1",
         item_id = c("Item_3", "Item_5"))

# Change the number of groups examinees will be separated into:
item_fit(ip = ip, resp = resp, theta = theta, type = "Q1", n_groups = 15)