ShinyItemAnalysis provides analysis of educational tests (such as admission tests)
and its items. For demonstration purposes, 20-item dataset
**GMAT**
from
R
`library(difNLR)`

is used. You can change the dataset
(and try your own one) on page
**Data.**

For selected cut-score, blue part of histogram shows students with total score above the cut-score, grey column shows students with Total Score equal to cut-score and red part of histogram shows students below the cut-score.

Traditional item analysis uses proportions of correct answers or correlations to estimate item properties.

Displayed is difficulty (red) and discrimination (blue) for all items. Items are ordered by difficulty.

**Difficulty**
of items is estimated as percent of students who answered correctly to that item.

**Discrimination**
is described by difference of percent correct
in upper and lower third of students (Upper-Lower Index, ULI). By rule of thumb it should not be lower than 0.2
(borderline in the plot), except for very easy or very difficult items.

**Explanation:Difficulty**
Difficulty of item is estimated as percent
of students who answered correctly to that item.
**SD**
standard deviation,
**RIT**
Pearson correlation between item and Total score,
**RIR**
Pearson correlation between item and rest of items,
**ULI**
- Upper-Lower Index,
**Alpha Drop**
- Cronbach's alpha of test without given item.

Traditional item analysis uses proportions of correct answers or correlations to estimate item properties.

In distractor analysis, we are interested in how test takers select the correct answer and how the distractors (wrong answers) were able to function effectively by drawing the test takers away from the correct answer.

Various regression models may be fitted to describe
item properties in more detail.
**Logistic regression**
can model dependency of probability of correct answer on total score by
s-shaped logistic curve. Parameter
**b0**
describes horizontal position of the fitted curve,
parameter
**b1**
describes its slope.

Various regression models may be fitted to describe
item properties in more detail.
**Logistic regression**
can model dependency of probability of correct answer on
standardized total score (Z-score) by s-shaped logistic curve. Parameter
**b0**
describes
horizontal position of the fitted curve (difficulty), parameter
**b1**
describes its slope at
inflection point (discrimination).

Various regression models may be fitted to describe
item properties in more detail.
**Logistic regression**
can model dependency of probability of correct answer on
standardized total score (Z-score) by s-shaped logistic curve. Note change in parametrization - the IRT parametrization
used here corresponds to the parametrization used in IRT models.
Parameter
**b**
describes horizontal position of the fitted curve (difficulty),
parameter
**a**
describes its slope at inflection point (discrimination).

Various regression models may be fitted to describe
item properties in more detail.
**Nonlinear regression**
can model dependency of probability of correct answer on
standardized total score (Z-score) by s-shaped logistic curve. The IRT parametrization used here corresponds
to the parametrization used in IRT models. Parameter
**b**
describes horizontal position of the fitted curve (difficulty),
parameter
**a**
describes its slope at inflection point (discrimination). This model allows for nonzero lower left asymptote
**c**
(pseudo-guessing).

Various regression models may be fitted to describe
item properties in more detail.
**Multinomial regression**
allows for simultaneous modelling of probability of choosing
given distractors on standardized total score (Z-score).

Item Response Theory (IRT) models are mixed-effect regression models in which student ability (theta) is assumed to be a random effect and is estimated together with item paramters. Ability (theta) is often assumed to follow normal distibution.

In
**1PL IRT model,**
all items are assumed to have the same slope in inflection point – the
same discrimination
**a.**
Items can differ in location of their inflection point – in item difficulty
**b.**
More restricted version of this model, the
**Rasch model,**
assumes discrimination
**a**
is equal to 1.

Item Response Theory (IRT) models are mixed-effect regression models in which student ability (theta) is assumed to be a random effect and is estimated together with item paramters. Ability (theta) is often assumed to follow normal distibution.

**2PL IRT model,**
allows for different slopes in inflection point – different
discriminations
**a.**
Items can also differ in location of their inflection point – in item difficulty
**b.**

Item Response Theory (IRT) models are mixed-effect regression models in which student ability (theta) is assumed to be a random effect and is estimated together with item paramters. Ability (theta) is often assumed to follow normal distibution.

**3PL IRT model,**
allows for different discriminations of items
**a,**
different item difficulties
**b,**
and allows also for nonzero left asymptote – pseudo-guessing
**c.**

Differential item functioning (DIF) occurs when people from different groups (commonly gender or ethnicity) with the same underlying true ability have a different probability of answering the item correctly. If item functions differently for two groups, it is potentially unfair.

DIF is not about total scores! Two groups may have the same distribution of total scores, yet, some item may function differently dor the two groups. Also, one of the groups may have signifficantly lower total score, yet, it may happen that there is no DIF item!

For selected cut-score, blue part of histogram shows students with total score above the cut-score, grey column shows students with Total Score equal to cut-score and red part of histogram shows students below the cut-score.

Delta plot (Angoff and Ford, 1993) compares the proportions of correct answers per item in the two groups. It displays non-linear transformation of these proportions using quantiles of standard normal distributions (so called delta scores) for each item for the two genders in a scatterplot called diagonal plot or delta plot (see Figure). Item is under suspicion of DIF if the delta point considerably departs from the diagonal.

Logistic regression allows for detection of uniform and non-uniform DIF (Swaminathan and Rogers, 1990) by adding a group
specific intercept
**bDIF**
(uniform DIF) and group specific interaction
**aDIF**
(non-uniform DIF) into model and
by testing for their significance.

Logistic regression allows for detection of uniform and non-uniform DIF by adding a group
specific intercept
**bDIF**
(uniform DIF) and group specific interaction
**aDIF**
(non-uniform DIF) into model and
by testing for their significance.

Nonlinear regression model allows for nonzero lower asymptote - pseudoguessing
**c.**
Similarly to logistic regression, also nonlinear regression allows for detection of uniform
and non-uniform DIF by adding a group
specific intercept
**bDIF**
(uniform DIF) and group specific interaction
**aDIF**
(non-uniform DIF) into the model and by testing for their significance.

Nonlinear regression model allows for nonzero lower asymptote - pseudoguessing
**c.**
Similarly to logistic regression, also nonlinear regression allows for detection of uniform
and non-uniform DIF (Drabinova and Martinkova, 2016) by adding a group
specific intercept
**bDIF**
(uniform DIF) and group specific interaction
**aDIF**
(non-uniform DIF) into the model and by testing for their significance.

Lord statistic (Lord, 1980) is based on IRT model (1PL, 2PL, or 3PL with the same guessing). It uses the difference between item parameters for the two groups to detect DIF. In statistical terms, Lord statistic is equal to Wald statistic.

Raju statistic (Raju, 1988, 1990) is based on IRT model (1PL, 2PL, or 3PL with the same guessing). It uses the area between the item charateristic curves for the two groups to detect DIF.

For demonstration purposes, 20-item dataset
`GMAT`

and datasets
`GMATkey`

and
`GMATgroups`

from
R
`library(difNLR)`

are used. On this page, you may select your own dataset (see below).
To return to demonstration dataset, refresh this page in your browser
**(F5)**
.

Used dataset
`GMAT`

is generated based on parameters of real Graduate Management
Admission Test (GMAT) data set (Kingston et al., 1985). However, first two items were
generated to function differently in non-uniform and uniform way respectively.
The data set represents responses of 1,000 subjects to multiple-choice test of 20 items.

Main dataset should contain responses of individual students (rows) to given items (collumns). Header may contain item names, no row names should be included. If responses are in ABC format, the key provides correct respomse for each item. If responses are scored 0-1, key is vecor of 1s.

ShinyItemAnalysis Version 0.2

ShinyItemAnalysis Version 0.1 is available here.

ShinyItemAnalysis provides analysis of tests and their items. It is based on the Shiny R package.

For demonstration purposes, practice dataset from
`library(difNLR)`

is used.
On page
**Data**
you may select your own dataset

`library(CTT)`

`library(deltaPlotR)`

`library(difNLR)`

`library(ggplot2)`

`library(gridExtra)`

`library(ltm)`

`library(moments)`

`library(nnet)`

`library(psychometric)`

`library(reshape2)`

`library(shiny)`

`library(shinyAce)`

Patricia Martinkova, Institute of Computer Science, Czech Academy of Sciences

Adela Drabinova

If you discover a problem with this application please contact the project maintainer at martinkova(at)cs.cas.cz

Project was supported by grant funded by Czech Science foundation under number GJ15-15856Y

Copyright 2016 Patricia Martinkova, Ondrej Leder and Adela Drabinova

This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the License or at your option any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.