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 ...

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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 ...
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As a rule of thumb, difference in amount of administered items: classically scored vs adaptive (irt-based) tests?

I am thinking of developing a new adaptive test. One of the main goals is to shorten existing, classically scored tests. Is there a rule of thumb about how many items are needed to administered ...
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25 views

Understanding and applying Item Response Theory

In the process of designing a quiz application that can assess the student for understanding of a particular concept, I came across Item Response Theory. I have absolutely no clue whether applying ...
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37 views

Are there local maxima in the standard 2-pl model or is there proof that there aren't?

I'm looking to use iterative logistic regression to find the parameter values of the 2 pl model: $ P = \sigma(\alpha_{i} (\theta_{s} - \beta_{i})) $ where $ \sigma(x) = \frac{1}{1+e^{-x}} $ I know ...
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Latent Class Analysis vs Rasch Analysis

I hope everybody is well :) I was wondering if anybody could explain the core, philosophical/conceptual differences between Latent Class Analysis and Rasch Analysis. I'm not necessarily referring to ...
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28 views

The probability of a student getting a given question correct and the associated uncertainty (Item response theory)

I'm doing some statistics on multiple choice test scores (with item response theory, (http://en.wikipedia.org/wiki/Item_response_theory). I want to know the probability that a student with a certain ...
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50 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 ...
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43 views

IRT how to graph the Item Information Function

Following the Stata Manual - Item–response theory (IRT) models' example 28g — One-parameter logistic IRT (Rasch) model: use http://www.stata-press.com/data/r13/gsem_cfa , clear gsem (MathAb -> ...
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89 views

How to fit Graded Response Model with lme4::glmer

Thanks to Rijmen et al.(2003), we can fit GRM to the data with lme4::glmer. I think Rasch model is straightforward, with ...
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34 views

Longitudinal data format in WinBUGS or OpenBUGS, different number of items per time point

I am working with longitudinal data, where there are a different number of "items" per time point. I am working with the MCMCdynamicIRT1d function in ...
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1answer
64 views

Interpreting discrimination values in IRT polytomous (grm) models. Are there any cut-offs or anchors?

I am working on a project that is looking at the discriminative properties of 6, 5-point Likert items in a scale. I am using the ltm package in R to examine this within a item response theory (irt) ...
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107 views

How to obtain Item Information Curves for the Partial Credit Model?

I have estimated a Partial Credit Model in Stata following Zheng, X. and Rabe-Hesketh, S. (2007) "Estimating parameters of dichotomous and ordinal item response models using gllamm". I'd like to ...
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59 views

Multigroup Longitudinal Item Response WinBUGS OpenBUGS

I was able to fit the Longitudinal IRT model in Winbugs for an ordinal response by extending the BUGS code I took from the paper by Curtis in JSS http://www.jstatsoft.org/v36/c01/paper/ However, I am ...
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1answer
95 views

Implementing nominal model from Polytomous Item Response Theory

I am attempting to map out the probabilities of observing different categories given different person ability using the Nominal Model. From the handbook of Polymous Item Response Theory 2010, the ...
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214 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 ...
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127 views

Is it possible to fit a Graded Response Model in Stata?

I've been reading about Item Response Theory during the past few weeks and I'd like to use it to examine how my scales are functioning. The response categories are ordinal. If I understood well, the ...
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35 views

Item Response Theory alternatives

What are other approaches than Item Response Theory to model learning of students in standardised tests?
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22 views

Splines, latent variables and model identification

For $J$ units of observations my basic model contains latent variables $\theta_j, j = 1, ..., J$ identified by the marginal assumption $\theta \sim N(0,1)$. The latent variables are connected to a ...
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Datasets for exploring Cognitive Diagnosis Modelling [closed]

I recently became interested in Cognitive Diagnosis Modelling, which classifies respondents to skill profiles based on their responses and a hypothesized relation between skills and items (Q- or ...
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62 views

BUGS/JAGS for Nominal Response Model

I am a beginner with BUGS/JAGS and I was hoping to gather the opinion of you, experts. I am trying to implement a Nominal Item Response Analysis (Polytomous, not ordered, like a multiple-choice exam) ...
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206 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 ...
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1answer
150 views

Mixing dichotomous and polytomous items in one test

I have to evaluate a test paper which contains both dichotomous and polytomous items. I am currently using R. But in R IRT models for scoring of dichotomous and polytomous items are different and I ...
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121 views

Item reliability or fit in IRT-based adaptive tests?

My background is in machine learning and statistics, but I am relatively new to psychometrics and testing. Nearly all of the literature I've found on item reliability refers to Chronbach's alpha or ...
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55 views

Change in output depending on mirt version

I have a matrix which I'm trying to run through the mirt function of the mirt package: ...
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1answer
37 views

Inferring testlet structure in item response theory

Is it possible to infer the testlet structure in a set of items using item response theory? Specifically, I've created a lot of variations on the story recall task, each variation being scored on 25 ...
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1answer
122 views

How can I handle missing values when fitting IRT model?

I am conducting a study for analyzing male involvement in Family planning. It is of interest to develop an index for the involvement of male. I am currently having difficulties fitting an IRT model ...
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74 views

Calculating the space/distance between scale points (IRT)?

I am working with a seven item Likert Scale (1, 2......6, 7) for a classroom management. How can I calculate the distance between these seven scale points? This is for instrument reliability ...
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Comparing the Goodness of fit of two polytomous set of items not nested

I'm working on two identical set of items that only differ in their frequency-of-occurence dimension (in the first is max.7 while in the second is max.4). They are both fit with the Generalised ...
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130 views

Using Ltm package to calclate 3PL some lines of data seem to go missing

I am hoping someone can help with the following: I have been trying to use the ltm package in R to get person fit estimates using a 3PL model. The problem I have been having is that I start off ...
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156 views

Machine learning with trinomial features

I have 100,000 students who have each answered some multiple choice questions. Given their performance I want to work out what the chances are of a particular student answering the next question ...
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135 views

Computationally singular error using MIRT package

We've got a 524*40 data frame of responses to a likert-type scale questionnaire (7 response categories on 40 items). We want to do exploratory multidimensional IRT using the MHRM method to identify ...
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108 views

Applications of Item Response Theory

As far as I know, item response theory is mainly used within psychology to analyse survey data, personality questionaires or in educational setting. Are there other areas (possibly outside of ...
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87 views

Dealing with least and maximum score in IRT

Generally when I do IRT modelling (using R software, 2PL model, ltm package) I remove records of students who have scored either 0 or 100%. The logic being that we do not have enough information about ...
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210 views

Item response theory vs. summative Likert scale

If the items to be "summed" or combined to create an overall index are collectively the underlying construct (i.e. I am trying to measure compliance to an intervention which has different ...
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560 views

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

I am sorry for a more basic question, but I was unable to find any good sources on google. How is a bifactor IRT model different from a factor analysis? How would you describe their key differences? ...
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3answers
391 views

Is R output reliable (specially IRT package ltm)

This may seem like a foolish question, but it is critical for me to have some expert advice on this. I am doing some research on students' learning levels in India. I am using R software (...
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134 views

Overall goodness-of-fit/p-value for multiple items IRT model in R (ltm)

The data set which I am trying to analyse is Student Test Data. I have a data of responses (either 1/correct response or 0/incorrect response) on some questions of a set of students. I have fitted a ...
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1answer
339 views

IQ adaptive test items in 1pl, 2pl or 3pl IRT model?

Some adapative test systems (e.g. school assessment tools) use the 1pl IRT model, while others use the 2pl or the 3pl. When developing an adaptive IQ test, is there a rule of thumb about which model ...
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199 views

How to select next item in polytomous CAT / MIRT?

To make a Computerized Adaptive Test out of a sample of 20 dichotomous items a typical course of action would be to: 1) calibrate respondent data with a R package like mirt or ltm using Rasch, 2PL ...
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1answer
86 views

IRT model and ceiling effect

I did some experiment in which tests are taken twice, pretest and posttest. I found there might be ceiling effect because the average of posttest is close to maximum test score possible. If I assume ...
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1answer
147 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 ...
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1answer
854 views

IRT in R: Does anyone know of an IRT item calibration function that can cope with NA's?

I have a dataset that looks like this. ...
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166 views

How to extract factor scores for each observation in IRT?

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 ...
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2answers
1k views

Error message from grm() in ltm: subscript out of bounds

I am analyzing a survey data set. One of the items in the survey is: ...
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1answer
256 views

Error using ltm R package

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 ...
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43 views

How do I extract difficulty and discrimination from a non-parametric IRT model

I've been using the KernSmoothIRT module in R to do non-parametric analysis of some items. I'm trying to find a way to quantify the difficulty and discrimination ...
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177 views

Item information in IRT with item covariates (linear logistic test model)

Short question: How does the calculation and interpretation of IRT item information and test information change in the presence of item properties? Long question: There's a variation on IRT called ...
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166 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 ...
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702 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 ...
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How to calculate absolute fit indices (RMSEA, GFI…) from relative ones (AIC, BIC…)?

I have conducted an IRT analysis with Conquest in order to compare two models (1-dimensional vs. 8-dimensional) applied to a given data set (41 items of a questionnaire, N=195). Comparing the ...