Questions tagged [item-response-theory]

Item Response Theory (IRT) is a set of statistical methods for modeling responses to test items. Use this tag for on-topic questions about (a) the theory itself (b) models appropriate for a specific case (c) implementing IRT in a specific tool such as an R package.

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Reliability in IRT Style

Reporting 'reliability' in IRT is more to 'informations' obtained and a bit different from a classical way using such as Cronbach alpha and KR20. Therefore, how to report the test reliability in ...
Hisham's user avatar
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22 votes
3 answers
12k views

Item Response Theory vs Confirmatory Factor Analysis

I was wondering what the core, meaningful differences are between Item Response Theory and Confirmatory Factor Analysis. I understand that there are differences in the calculations (focusing more on ...
SimonsSchus's user avatar
9 votes
3 answers
4k views

What is Item Response Theory (IRT) called for continuous response?

I would like to model my problem using something similar to Item Response Theory, but my responses are not binary. They are continuous in $[0, 1]$. What are these models/the research field called?
user1141785's user avatar
26 votes
6 answers
20k views

How to get started with applying item response theory and what software to use?

Context I have been reading about item response theory, and I find it fascinating. I believe I understand the basics, but I am left wondering how to apply statistical techniques related to the area. ...
Behacad's user avatar
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8 votes
2 answers
7k views

Estimating ability using IRT when the model parameters are known

I have 3PL model parameters (guessing, difficulty and discrimination item parameters). Is there any function with which I can estimate individual ability from item response data? I tried the function <...
KH Kim's user avatar
  • 1,221
4 votes
1 answer
604 views

Item information in IRT

According to item information curves, item information for a 2PL IRT model is $I(\theta)=a^2_i p_i(\theta) q_i(\theta)$ To determine $p_i(\theta)$ and $q_i(\theta)$, do you just use the observed ...
Jack Tanner's user avatar
  • 4,832
2 votes
1 answer
255 views

2PLM IRT modeling of rare event behavioral data: Why changing discrimination and difficulty values?

I am using the 2PLM (2-parameter logistic model) IRT model to examine how sets of very rare (negative/aversive) maternal behaviors (towards their children) are associated with a priori ...
Jhaltiga68's user avatar
1 vote
1 answer
69 views

Interdependence of hyperparameters of bernouilli laws [closed]

Suppose that you have $N$ people passing an exam having 2 type of questions (type A and type B) which all have correct/uncorrect outcomes. After seeing the results, I want to modelize the probability ...
Rodolphe LAMPE's user avatar
1 vote
1 answer
271 views

How do I appropriately examine the dimensionality of binary data?

I have 72 binary variables and, at a theoretical level, I am trying to identify groups of variables that seem to vary together. In practice, I am struggling with how to analyze this data properly. I ...
Cameron Stumpf's user avatar
8 votes
4 answers
3k views

Simulating responses to a test for item-response theory

I am developing an online assessment system and I need to calibrate the bank of questions but I do not have enough people to implement a pilot test. That is why I decided to simulate the responses of ...
Erika Hernández's user avatar
8 votes
1 answer
971 views

Analyzing a partially crossed design

I have a data set from a test (see below). The scoring algorithm gives each item (item_id) a score (y) that is continuous from $...
Simon Harmel's user avatar
7 votes
2 answers
1k views

What is the probability that a student gets a better score than another on a test with randomly selected questions?

Suppose there is a set $S$ of $100$ questions and there are $2$ students $a$ and $b$. Let $P_{ai}$ be the probability that $a$ answers the question $i$ correctly, and $P_{bi}$ the same for $b$. All $...
Daniel's user avatar
  • 205
6 votes
1 answer
317 views

Predict person parameters in explanatory IRT with lme4

I am using glmer from lm4 in R to run an explanatory IRT analysis. The aim is to model person parameters with items nested in persons and to control for age (the test scale has 10 items; all persons ...
Wolfgang Lenhard's user avatar
6 votes
1 answer
350 views

IRT/Rasch modeling with very large N

I want to fit a 1-parameter IRT model on a questionaire with 15 questions and about six million people. Considering the large N, standard errors aren't essential. It looks like the IRT world is sort ...
DavidShor's user avatar
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6 votes
1 answer
3k views

Internal consistency reliability in item response theory models

How can internal consistency reliability of a test and of individual test items be quantified in Item Response Theory models? I know I can resort to Classical Test Theory, Cronbach's alpha, and other ...
Jack Tanner's user avatar
  • 4,832
6 votes
2 answers
4k views

Longitudinal item response theory models in R

I'm trying to fit longitudinal item response theory (IRT) models in R. I have a test that was administered at multiple measurement occasions. I'd like to examine individuals' growth curves of factor ...
itpetersen's user avatar
5 votes
1 answer
4k views

How to check goodness of fit for a graded response model in R

I am using the grm function in the ltm package in R. There is no function to check the goodness of fit of the output. How can I ...
Deepak Agarwal's user avatar
5 votes
1 answer
2k views

Difference between IRT and EFA to find factors

I am learning about Item Response Theory in which items are used to assess ability. In principle, multiple latent abilities may exist and some items test the one, while other items test another. This ...
LBogaardt's user avatar
  • 582
5 votes
1 answer
2k views

How to extract factor scores for each observation in IRT? [closed]

library(ltm) fit <- rasch(LSAT) factor.scores(fit) This code can generate latent trait scores for response patterns. How can I extract latent trait scores for ...
Rach's user avatar
  • 51
4 votes
1 answer
322 views

Do 1PL IRT models measure both ability and difficulty, or just difficulty?

I'm trying to better understand Item response Theory (IRT) from a Bayesian perspective. Hypothetically, suppose I want to use a 1PL model and my data is a binary matrix ...
jbuddy_13's user avatar
  • 2,940
4 votes
2 answers
4k views

Acceptable values for discrimination parameter - 2PL IRT Model

What is the acceptable range for discrimination parameters with the two-parameter IRT model? I have information from Baker (2001) but would love additional information. I have heard discrimination ...
Daniel's user avatar
  • 53
4 votes
2 answers
2k views

Meaning of large values of parameter b (|b| >>) 4 in IRT theory

I'm working with a data set of 100 itens, 5 alternatives, medicine test and analyzing them by means of IRT (. The IRT - 3 parameter model yielded some values of b that are very large (...
Caco's user avatar
  • 143
3 votes
1 answer
1k views

Item response theory for continuous variables, and estimating standard error of measurement

I really like how traditional item response theory (IRT) packages tell you the standard error of measurement conditional on one's ability level, and from that, you can calculate the test information ...
user3084100's user avatar
3 votes
1 answer
637 views

Is it acceptable/common practice to report IRT theta scores as a percentile?

I have been teaching myself IRT. I think I get it, however, I've not yet reached a point where I would say that I'm totally confident. In assuming that the latent trait is normally distributed with ...
faustus's user avatar
  • 265
3 votes
1 answer
2k views

How is a bifactor IRT model different from a factor analysis?

How is a bifactor IRT model different from a factor analysis? How would you describe their key differences? Any references you could direct me to would be very helpful. Thank you for sharing your ...
Xander's user avatar
  • 416
3 votes
1 answer
870 views

Is it possible to do IRT distractor analysis using R?

I've been using the mirt package to analyse a few response matrixes I have through IRT. However, every time I need to perform distractor analysis, I end up having ...
Douglas De Rizzo Meneghetti's user avatar
3 votes
1 answer
175 views

Pros/cons of estimating parameters for missing observations?

Some people are playing a game online. Every time a person plays, a new game board is generated randomly. On generation of a new board, the player can also choose a special weapon. (The choice of ...
Jack Tanner's user avatar
  • 4,832
2 votes
1 answer
1k views

Is empirical reliability in IRT the counterpart of internal consistency in CTT?

In IRT it is not meaningful to compute internal consistency coefficients such as Cronbachs alpha, because standard error of measurement (and thus measurement precision) is not assumed uniform across ...
jmjr's user avatar
  • 133
2 votes
0 answers
59 views

Item Information Distorting Scale

I'm refining a psychometric questionnaire and working to estimate (2PL) IRT parameters for the items in order to score the items. It's a small scale consisting of 5 questions. The MAP and VSS-1 ...
Sue Doh Nimh's user avatar
2 votes
1 answer
523 views

Unidimensionality in IRT

I recently came across the definition of unidimensionality (in the context of IRT and internal consistency reliability, specifically Cronbach's alpha). Johnsosn (2007) states that There is a one-...
user1607's user avatar
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2 votes
2 answers
2k views

Error using ltm R package [closed]

I'm using the R package ltm to create a 2-parameter logistic regression. The input matrix is sparse - many users have taken a small subset of the items in the item bank. For some of my data sets i'm ...
Samir's user avatar
  • 71
0 votes
1 answer
177 views

IRT analysis: duplicate columns?

I am trying to create a 2-parameter logistic regression model. My data has no NA's, 233 rows (plus 1 header row), and 458 columns of 0's and 1's only (but many ...
Vijay's user avatar
  • 1
0 votes
1 answer
404 views

Get different IRT model result when use functions from different R package?

Reproducible example as below: ...
kittygirl's user avatar
  • 294