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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11 views

Theta (thetaEst) estimates in CatR with known item parameters - assessing a whole dataset

To my R angels, After a recent voyage of discovery, I have been using IRT to develop a set of GRM derived item parameters on a large dataset of 40000 questionnaire responses. I would like to use these ...
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32 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 ...
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61 views

Bayesian Multiple Item Response Models?

I am trying to extend the ideas of item response theory to multiple responses. Consider a marketing survey, which asks customers, "what's the deciding factor in whether or not you purchase ...
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71 views

How to incorporate multiple likelihoods in a probabilistic graphical model with Stan?

Data composition: In beta testing of a video game, users were assigned tasks in a many-to-many relationship. At the end of every day, users were asked to self evaluate (for each task) whether they ...
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50 views

What is the role of non-anchor items when equating scales across studies using IRT?

I'm trying to use IRT to equate scales across 5 datasets. Three of them use the same scale (A); the other ones use different ones (B and C) There are items that overlap between A and C, A and B, but ...
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Are there supposed to be bounds on parameters in 2PL Item Response Theory models?

Recently I've been studying Item Response Theory (IRT) and have come across some issues with the application side of it. I currently have a dataset of ~200 respondents x 7405 questions (quite ...
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32 views

How many parameters are estimated in a 2PL model?

I'm familiar with 1PL IRT models, where you have some data matrix, and you model the latent factors, theta (the trait/ability) and (item) difficulty. ...
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interpretation of item tree analysis plot

Two quick questions about Item-Tree analysis plot. (1) For the red plot, I know items {1L, 3L, 5L, 6L} are equally informative and thus not plotted. Does this mean ...
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60 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 ...
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42 views

Intuitions behind item response theory?

I'm relatively new to Item Response Theory. After having read some materials on 1PL and 2PL, I have a few thoughts and questions. Say you have a questionnaire that a social psychologist will complete ...
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Item response theory with any cdf link

The IRT applications mostly use as link functions the logit and the probit, which are the cumulative distribution function (cdf) of the logistic and normal distributions, the resulting models gives ...
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70 views

IRT: What is enough information? And can a test provide too much?

I was wondering what makes for a good test information value in IRT, and came across this: Reliability: Item and test information functions graphically reflect how reliably the individual items and ...
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How to best summarize Likert data (to use as an independent variable in a regression)?

I want to run a regression where one of the explanatory variables is a "summary" (details below) of a set of questionnaire questions that are answered on a Likert scale (although there are ...
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What is the source of the IRT 1PL discrimination constant?

For a 1PL IRT model you would use the 1.702 constant for the discrimination parameter. My questions are why, what is the source of this constant?
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196 views

Data With Ordinal Responses: Calculate ICC & Assess Model Fit

I have a data set of animal responses with repeated measures. The responses are on a 9-point scale. Here, I present an example data set that is very similar to mine: ...
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48 views

Calculating Theta scores for identified subjects (using R package ltm) [closed]

I am using the R package ltm to calculate a 2PL IRT model. goal: creating a list of subjects IDs with the calculated Theta scores. problem: ltm requires that the input includes only item scores, and ...
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Testing the fit of polychoric correlation

I’m using polychoric correlations for my work. According to Kampen and Weeren (2017): In order to prevent this questionable research practice, it is recommended that in applications of the ...
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Post-Processing Explanatory IRT Models in lme4

I have fit several different explanatory IRT models using lme4, and the final model includes item, person, and item-by-person covariates. The issue I'm now encountering is that I don't know how to get ...
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113 views

Difference between CFA using WLSMV estimator and IRT

I am trying to understand the differences (or similarities) between conducting CFA on categorical data using the WLSMV estimator in SEM and item response theory analysis. I would appreciate any input. ...
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29 views

item response theory - criteria for selecting items

I'm trying to use IRT to select the best items for a one-factor scale that has 20 items. I was wondering what I need to be looking at if I wanted to select 5 or so items from these items (for a short ...
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304 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 $...
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Determine characteristics of test raters who systematically score higher or lower on a series of items

I have a survey that asks for respondents' subjective view on the presence of a marker (1/0). I have approximately 50 respondents and 40 marker questions. I want to tell what respondent ...
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72 views

Item response theory (IRT) for continuous responses

I hope this message finds everyone safe and well. I want to estimate the Rasch item difficulty parameters for my test items (dataset below). However, I have two challenges: (1) Item scores are ...
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23 views

Adding Post-stratified Weights to IRT 3PL Model

I am using IRT, 3 Parameter Logistic Model (3PL) for parameter estimation of my question parameters. As my data is biased I calculated Post-stratified weights using sample and population data. I want ...
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DIF: validity of carrying out a t-test on the final sample?

I have run a DIF analysis of a questionnaire, to see how autistic men and women answer differently, with a total sample of 530 autistic men and 530 autistic women. I have a general hypothesis that the ...
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DIF: match sample randomly or by age?

I am carrying out a DIF analysis comparing the scores of men and women on a questionnaire. A preliminary ANOVA revealed that when comparing total scores on the test, there is a significant effect of ...
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24 views

Latent Bayesian IRT model with unbalanced panels

I'm using JAGS to estimate an IRT model in which individuals appear multiple times in the dataset but where panels are unbalanced (some individuals appear more often than others. To give you a sense ...
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Differential Item Functioning with Autistic and control samples

I'm carrying out a DIF analysis of a self-report questionnaire which measures 'systemising', or the drive to construct/understand complex systems such as technology/maths/buildings/etc, to check for ...
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25 views

Wright-Map with multiple values for one item

To give some context: I'm quite new to quantitative research in social sciences and learned about IRT, Rasch Reliability and Wright-Maps yesterday. Today a colleague sent me this image: and asked ...
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34 views

Estimating IRT item parameters when ability is known

I'm reading the Fundamentals of IRT book by Hambleton et al. In this book they demonstrate the invariance of item parameters in a 3PL model by: First building the model on the full sample, deriving ...
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61 views

Person's parameter (ability) calibration using R's package ltm

I have a user response ($0/1$) matrix user_item_matrix, which has $1000$ rows (users) and $30$ columns (items/questions). There is a lot of missing data (more than $...
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72 views

Using Co-variates in Item Response Theory 3PL model?

I am using Item Response theory(IRT) using 3 Parameter Logistic Model(3PL) for Logic test. After training the model, I use the posterior means of the item parameters 𝛼, β and γ to estimate person ...
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27 views

Can I do a repeated measures logistic regression for 16 students who answered different questions on a test?

I had 15 students take a vocabulary test with 100 items at the end of a course and were scored "1" (correct) or "0" (incorrect) for each item. I would like to predict the likelihood of them getting a ...
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71 views

Relationship between parameters of Factor Analysis with categorical data and IRT-parameters

I have a problem in understanding the relationship between parameters of Factor Analysis with categorical paramters and IRT-parameters. The relationship is clearly defined, for example in Kamata, ...
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38 views

IRT degrees of freedom of item fit statistics

I'm fitting Rasch models with the mirt package. Upon measuring item-wise $Q_1$ using mirt::itemfit(model, fit_stats="X2"), I ...
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Downsides to “naive” estimation of longitudinal IRT factor scores?

I have a questionnaire administered at two time points. I would like to estimate a latent factor score (theta) at each administration using Item Response Theory. The ideal approach would be to model ...
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434 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 ...
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216 views

Standard errors of parameters in IRT

DeMars's Item Response Theory makes the following claims about parameter estimation in 3PL models: The standard error of $b$ (difficulty) will be smaller when there are more examinees with $\theta$ (...
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697 views

Difference between empirical and marginal reliability of an IRT model

I am using the mirt library in R to fit an instrument (binary responses) comprising two dimensions. In the mirt documentation are mentioned two types of reliability. I would like to ask what is the ...
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24 views

Generalizability study of subscaled rating instrument

I have a school rating ($1$ thru $4$) instrument that consists of $9$ subscales (e.g., classroom instruction, school management etc.). Under each subscale, I have $6$ items on which rating occurs. I ...
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78 views

Should subscales be analyzed separately under the IRT Graded Response model?

Suppose I have a Likert scale type questionnaire that assesses the amount of social support a patient receives. The questionnaire is divided into four subscales that measure: Emotional support ...
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105 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-...
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184 views

Differential Item Functioning (DIF) Anchor Selection

I have a conceptual question regarding item anchor selection that seems to be so basic to the literature that authors of various online and print resources assume the reader understands. Namely, I am ...
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22 views

Bifactor model and infit statistics?

Good afternoon, I am currently in the process of calibrating an item bank using a GPCM model. So, am I right to assume that the bifactor model allows me to work with my general factor by ...
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278 views

How should we select between various Item Response Theory Models? (E.g. RSM, GRM, LRSM, PCM)

If you ask me what's the application scenario difference between NRM and GRM, I will answer ...
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103 views

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

Reproducible example as below: ...
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102 views

Testing for IRT assumptions with large samples and short scales

I’m using R’s mirt package to fit some (unidimensional) GPC models to a set of Likert-style items with five levels in each. I’m looking for some advice on how to test for the standard IRT assumptions. ...
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53 views

Why item discriminations are missing in IRT GRM, estimated as a part of the Structural Equation Model? [closed]

I have run a Structural Equation Model that has four latent constructs (FI, SC, EM and RB) in R. All of the factors are continuous. Meanwhile, indicators are all ordered categorical variables measured ...
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38 views

Item Response Theory model to recover the item locations

I can't seem to find a model to solve the following problem. It seems to be closely related to IRT, but not exactly. I have a list of users and items, I know the preference between users and items, ...
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315 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 ...

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