Questions tagged [irt]

The Item Response Theory framework encompasses a wide range of psychometric methods and mathematical models (latent trait models) to study individual responses to items defining a measurement instrument (multi-item scales such as questionnaires or tests) that is used to assess a specific construct (e.g., examinee proficiency or liability to depression).

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24
votes
5answers
17k 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. ...
4
votes
2answers
2k views

How 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]. How are these models/the research field called?
6
votes
2answers
7k views

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 ...
4
votes
1answer
403 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 ...
2
votes
1answer
180 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 ...
16
votes
3answers
7k 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 ...
5
votes
2answers
3k 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 ...
7
votes
2answers
5k 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 <...
7
votes
1answer
209 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 $...
7
votes
4answers
2k 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 ...
6
votes
1answer
2k 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 ...
3
votes
1answer
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 ...
5
votes
1answer
1k 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 ...
5
votes
1answer
318 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 ...
3
votes
2answers
2k 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 ...
2
votes
0answers
55 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 ...
7
votes
2answers
188 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 $...
4
votes
1answer
3k 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 ...
3
votes
1answer
166 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 ...
3
votes
1answer
544 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 ...
2
votes
1answer
582 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 ...
1
vote
1answer
49 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 ...
1
vote
1answer
218 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 ...
1
vote
1answer
80 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-...
0
votes
1answer
83 views

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

Reproducible example as below: ...