`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.

Download figure`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`score <- apply(data, 1, sum) # Total score`

`# Summary of total score`

`summary(score)`

`# Histogram`

`hist(score, breaks = 0:ncol(data)) `

`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`score <- apply(data, 1, sum) # Total score`

`tosc <- sort(unique(score)) # Levels of total score`

`perc <- cumsum(prop.table(table(score))) # Percentiles`

`sura <- 100 * (tosc / max(score)) # Success rate`

`zsco <- sort(unique(scale(score))) # Z-score`

`tsco <- 50 + 10 * zsco # T-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.

Chronbach's alpha is an estimate of the reliability of a psychometric test. It is a function of the number of items in a test, the average covariance between item-pairs, and the variance of the total score (Cronbach, 1951).

**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.

`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`# Difficulty and discrimination plot`

`DDplot(data)`

`# Table`

```
tab <- round(data.frame(item.exam(data, discr = TRUE)[, c(4, 1, 5, 2, 3)],
psych::alpha(data)$alpha.drop[, 1]), 2)
```

`tab`

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.

Download figure

`library(difNLR)`

`data(GMATtest)`

`data <- GMATtest[, colnames(GMATtest) != "group"]`

`data(GMATkey)`

`key <- GMATkey`

`# Combinations - plot for item 1 and 3 groups`

```
plotDistractorAnalysis(data, key, num.group = 3, item = 1,
multiple.answers = T)
```

`# Distractors - plot for item 1 and 3 groups`

```
plotDistractorAnalysis(data, key, num.group = 3, item = 1,
multiple.answers = F)
```

`# Table with counts and margins - item 1 and 3 groups`

`DA <- DistractorAnalysis(data, key, num.groups = 3)[[1]]`

`dcast(as.data.frame(DA), response ~ score.level, sum, margins = T, value.var = "Freq")`

`# Table with proportions - item 1 and 3 groups`

`DistractorAnalysis(data, key, num.groups = 3, p.table = T)[[1]]`

`tab`

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.

Points represent proportion of correct answer with respect to total score. Their size is determined by count of respondents who answered item correctly.

Download figure`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`score <- apply(data, 1, sum)`

`# Logistic model for item 1`

`fit <- glm(data[, 1] ~ score, family = binomial)`

`# Coefficients`

`coef(fit)`

`# Function for plot`

`fun <- function(x, b0, b1){exp(b0 + b1 * x) / (1 + exp(b0 + b1 * x))}`

`# Plot of estimated curve`

```
curve(fun(x, b0 = coef(fit)[1], b1 = coef(fit)[2]), 0, 20,
xlab = "Total score",
ylab = "Probability of correct answer",
ylim = c(0, 1))
```

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).

Points represent proportion of correct answer with respect to standardized total score. Their size is determined by count of respondents who answered item correctly.

Download figure`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`stand.score <- scale(apply(data, 1, sum))`

`# Logistic model for item 1`

`fit <- glm(data[, 1] ~ stand.score, family = binomial)`

`# Coefficients`

`coef(fit)`

`# Function for plot`

`fun <- function(x, b0, b1){exp(b0 + b1 * x) / (1 + exp(b0 + b1 * x))}`

`# Plot of estimated curve`

```
curve(fun(x, b0 = coef(fit)[1], b1 = coef(fit)[2]), -3, 3,
xlab = "Standardized total score",
ylab = "Probability of correct answer",
ylim = c(0, 1))
```

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).

Points represent proportion of correct answer with respect to standardized total score. Their size is determined by count of respondents who answered item correctly.

Download figure`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`stand.score <- scale(apply(data, 1, sum))`

`# Logistic model for item 1`

`fit <- glm(data[, 1] ~ stand.score, family = binomial)`

`# Coefficients - tranformation`

`coef <- c(a = coef(fit)[2], b = - coef(fit)[1] / coef(fit)[2])`

`coef`

`# Function for plot`

`fun <- function(x, a, b){exp(a * (x - b)) / (1 + exp(a * (x - b)))}`

`# Plot of estimated curve`

```
curve(fun(x, a = coef[1], b = coef[2]), -3, 3,
xlab = "Standardized total score",
ylab = "Probability of correct answer",
ylim = c(0, 1))
```

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).

Points represent proportion of correct answer with respect to standardized total score. Their size is determined by count of respondents who answered item correctly.

Download figure`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`stand.score <- scale(apply(data, 1, sum))`

`# NLR model for item 1`

`fun <- function(x, a, b, c){c + (1 - c) * exp(a * (x - b)) / (1 + exp(a * (x - b)))}`

```
fit <- nls(data[, 1] ~ fun(stand.score, a, b, c), algorithm = "port",
start = startNLR(data, GMAT[, "group"])[1, 1:3])
```

`# Coefficients`

`coef(fit)`

`# Plot of estimated curve`

```
curve(fun(x, a = coef(fit)[1], b = coef(fit)[2], c = coef(fit)[3]), -3, 3,
xlab = "Standardized total score",
ylab = "Probability of correct answer",
ylim = c(0, 1))
```

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).

Points represent proportion of selected option with respect to standardized total score. Their size is determined by count of respondents who selected given option.

Download figure`library(difNLR)`

`library(nnet)`

`data(GMAT)`

`data.scored <- GMAT[, colnames(GMAT) != "group"]`

`stand.score <- scale(apply(data, 1, sum))`

`data(GMATtest)`

`data <- GMATtest[, colnames(GMATtest) != "group"]`

`data(GMATkey)`

`key <- GMATkey`

`# multinomial model for item 1`

`fit <- multinom(relevel(data[, 1], ref = paste(key[1])) ~ stand.score)`

`# Coefficients`

`coef(fit)`

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 parameters. Ability (theta) is often assumed to follow normal distribution.

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.

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`# Model`

`fit <- rasch(data)`

`# Item Characteristic Curves`

`plot(fit)`

`# Item Information Curves`

`plot(fit, type = "IIC")`

`# Test Information Function`

`plot(fit, items = 0, type = "IIC")`

`# Coefficients`

`coef(fit)`

`# Factor scores vs Standardized total scores`

`df1 <- ltm::factor.scores(fit, return.MIvalues = T)$score.dat`

`FS <- as.vector(df1[, "z1"])`

`df2 <- df1`

`df2$Obs <- df2$Exp <- df2$z1 <- df2$se.z1 <- NULL`

`STS <- as.vector(scale(apply(df2, 1, sum)))`

`df <- data.frame(FS, STS)`

```
plot(FS ~ STS, data = df,
xlab = "Standardized total score",
ylab = "Factor 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 parameters. Ability (theta) is often assumed to follow normal distribution.

**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.**

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`# Model`

`fit <- ltm(data ~ z1)`

`# Item Characteristic Curves`

`plot(fit)`

`# Item Information Curves`

`plot(fit, type = "IIC")`

`# Test Information Function`

`plot(fit, items = 0, type = "IIC")`

`# Coefficients`

`coef(fit)`

`# Factor scores vs Standardized total scores`

`df1 <- ltm::factor.scores(fit, return.MIvalues = T)$score.dat`

`FS <- as.vector(df1[, "z1"])`

`df2 <- df1`

`df2$Obs <- df2$Exp <- df2$z1 <- df2$se.z1 <- NULL`

`STS <- as.vector(scale(apply(df2, 1, sum)))`

`df <- data.frame(FS, STS)`

```
plot(FS ~ STS, data = df,
xlab = "Standardized total score",
ylab = "Factor 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 parameters. Ability (theta) is often assumed to follow normal distribution.

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

`data(GMAT)`

`data <- GMAT[, colnames(GMAT) != "group"]`

`# Model`

`fit <- tpm(data)`

`# Item Characteristic Curves`

`plot(fit)`

`# Item Information Curves`

`plot(fit, type = "IIC")`

`# Test Information Function`

`plot(fit, items = 0, type = "IIC")`

`# Coefficients`

`coef(fit)`

`# Factor scores vs Standardized total scores`

`df1 <- ltm::factor.scores(fit, return.MIvalues = T)$score.dat`

`FS <- as.vector(df1[, "z1"])`

`df2 <- df1`

`df2$Obs <- df2$Exp <- df2$z1 <- df2$se.z1 <- NULL`

`STS <- as.vector(scale(apply(df2, 1, sum)))`

`df <- data.frame(FS, STS)`

```
plot(FS ~ STS, data = df,
xlab = "Standardized total score",
ylab = "Factor score")
```

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.
In general, two type of DIF can be recognized: if the item has different
difficulty for given two groups with the same discrimination,
**uniform**
DIF is present (left figure). If the item has different
discrimination and possibly also different difficulty for given two groups,
**non-uniform**
DIF is present (right figure)

In most DIF detection methods testing procedure is performed item by item. To control family-wise error rate or false discovery rate, wide range of correction methods is offered. Default option is set to Benjamini-Hochberg (Benjamini & Hochberg, 1995).

** Remember, when using your own dataset, DIF analysis is only available if you also upload group vector! **

DIF is not about total scores! Two groups may have the same distribution of total scores, yet, some item may function differently for two groups. Also, one of the groups may have significantly 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.

Download figure Download figure`library(difNLR)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Summary table`

`sc_zero <- apply(data[group == 0, ], 1, sum); summary(sc_zero) # total scores of reference group`

`sc_one <- apply(data[group == 1, ], 1, sum); summary(sc_one) # total scores of focal group`

`# Histograms`

`hist(sc_zero, breaks = 0:20)`

`hist(sc_one, breaks = 0:20)`

Delta plot (Angoff & Ford, 1973) 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. The detection threshold is either fixed to value 1.5 or based on bivariate normal approximation (Magis & Facon, 2012).

`library(difNLR)`

`library(deltaPlotR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Delta scores with fixed threshold`

```
deltascores <- deltaPlot(data.frame(data, group), group = "group",
focal.name = 1, thr = 1.5)
```

`deltascores`

`# Delta plot`

`diagPlot(deltascores, thr.draw = T)`

`# Delta scores with normal threshold`

```
deltascores <- deltaPlot(data.frame(data, group), group = "group",
focal.name = 1, thr = "norm")
```

`deltascores`

`# Delta plot`

`diagPlot(deltascores, thr.draw = T)`

Mantel-Haenszel test is DIF detection method based on contingency tables that are calculated for each level of total score (Mantel & Haenszel, 1959).

`library(difNLR)`

`library(deltaPlotR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Mantel-Haenszel test`

```
fit <- difMH(Data = data, group = group, focal.name = 1,
p.adjust.method = "BH")
```

`fit`

Mantel-Haenszel test is DIF detection method based on contingency tables that are calculated for each level of total score (Mantel & Haenszel, 1959).

`library(difNLR)`

`library(deltaPlotR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Contingency table for item 1 and score 12`

`df <- data.frame(data[, 1], group)`

`colnames(df) <- c("Answer", "Group")`

`df$Answer <- relevel(factor(df$Answer, labels = c("Incorrect", "Correct")), "Correct")`

`df$Group <- factor(df$Group, labels = c("Reference Group", "Focal Group"))`

`score <- apply(data, 1, sum)`

`df <- df[score == 12, ]`

```
tab <- dcast(data.frame(xtabs(~ Group + Answer, data = df)),
Group ~ Answer,
value.var = "Freq",
margins = T,
fun = sum)
```

`tab`

`# Mantel-Haenszel estimate of OR`

```
fit <- difMH(Data = data, group = group, focal.name = 1,
p.adjust.method = "BH")
```

`fit$alphaMH`

Logistic regression allows for detection of uniform and non-uniform DIF (Swaminathan & Rogers, 1990) by adding a group
specific intercept
**b2**
(uniform DIF) and group specific interaction
**b3**
(non-uniform DIF) into model and
by testing for their significance.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Logistic regression DIF detection method`

```
fit <- difLogistic(Data = data, group = group, focal.name = 1,
type = "both",
p.adjust.method = "BH")
```

`fit`

Logistic regression allows for detection of uniform and non-uniform DIF by adding a group
specific intercept
**b2**
(uniform DIF) and group specific interaction
**b3**
(non-uniform DIF) into model and
by testing for their significance.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Logistic regression DIF detection method`

```
fit <- difLogistic(Data = data, group = group, focal.name = 1,
type = "both",
p.adjust.method = "BH")
```

`fit`

`# Plot of characteristic curve for item 1`

```
plotDIFLogistic(data, group,
type = "both",
item = 1,
IRT = F,
p.adjust.method = "BH")
```

`# Coefficients`

`fit$logitPar`

Logistic regression allows for detection of uniform and non-uniform DIF (Swaminathan & 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.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`scaled.score <- scale(score)`

`# Logistic regression DIF detection method`

```
fit <- difLogistic(Data = data, group = group, focal.name = 1,
type = "both",
match = scaled.score,
p.adjust.method = "BH")
```

`fit`

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.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`scaled.score <- scale(score)`

`# Logistic regression DIF detection method`

```
fit <- difLogistic(Data = data, group = group, focal.name = 1,
type = "both",
match = scaled.score,
p.adjust.method = "BH")
```

`fit`

`# Plot of characteristic curve for item 1`

```
plotDIFLogistic(data, group,
type = "both",
item = 1,
IRT = T,
p.adjust.method = "BH")
```

`# Coefficients for item 1 - recalculation`

`coef_old <- fit$logitPar[1, ]`

`coef <- c()`

`# a = b1, b = -b0/b1, adif = b3, bdif = -(b1b2-b0b3)/(b1(b1+b3))`

`coef[1] <- coef_old[2]`

`coef[2] <- -(coef_old[1] / coef_old[2])`

`coef[3] <- coef_old[4]`

```
coef[4] <- -(coef_old[2] * coef_old[3] + coef_old[1] * coef_old[4] ) /
(coef_old[2] * (coef_old[2] + coef_old[4]))
```

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.

`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Nonlinear regression DIF method`

```
fit <- difNLR(data = data, group = group, type = "both",
p.adjust.method = "BH")
```

`fit`

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 & 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.

`library(difNLR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# Nonlinear regression DIF method`

```
fit <- difNLR(data = data, group = group, type = "both",
p.adjust.method = "BH")
```

`# Plot of characteristic curve of item 1`

`plot(fit, item = 1)`

`# Coefficients`

`fit$coef`

Lord test (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.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# 2PL IRT MODEL`

```
fit <- difLord(Data = data, group = group, focal.name = 1,
model = "2PL",
p.adjust.method = "BH")
```

`fit`

Lord test (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.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# 2PL IRT MODEL`

```
fit <- difLord(Data = data, group = group, focal.name = 1,
model = "2PL",
p.adjust.method = "BH")
```

`fit`

`# Coefficients for item 1`

`tab_coef <- fit$itemParInit[c(1, ncol(data) + 1), 1:2]`

`# Plot of characteristic curve of item 1`

`plotDIFirt(parameters = tab_coef, item = 1)`

Raju test (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.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# 2PL IRT MODEL`

```
fit <- difRaju(Data = data, group = group, focal.name = 1,
model = "2PL",
p.adjust.method = "BH")
```

`fit`

Raju test (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.

`library(difNLR)`

`library(difR)`

`data(GMAT)`

`data <- GMAT[, 1:20]`

`group <- GMAT[, "group"]`

`# 2PL IRT MODEL`

```
fit <- difRaju(Data = data, group = group, focal.name = 1,
model = "2PL",
p.adjust.method = "BH")
```

`fit`

`# Coefficients for item 1`

`tab_coef <- fit$itemParInit[c(1, ncol(data) + 1), 1:2]`

`# Plot of characteristic curve of item 1`

`plotDIFirt(parameters = tab_coef, item = 1, test = "Raju")`

For demonstration purposes, 20-item dataset
`GMAT`

and dataset
`GMATkey`

from
`difNLR`

R package are used.
On this page, you may select one of three dataset offered in
`difNLR`

package or you may upload 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 uniform and non-uniform way respectively.
The data set represents responses of 2,000 subjects to multiple-choice test of 20 items.
The distribution of total scores is the same for both groups.

Dataset
`GMAT2`

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

Dataset
`Medical`

is a subset of real admission test to medical school. First item was previously
detected as functioning differently. The data set represents responses of
1,407 subjects (484 males, 923 females) to multiple-choice test of 20 items. For more details of item selection see
Drabinova & Martinkova (2016).

Main dataset should contain responses of individual students (rows) to given items (columns). Header may contain item names, no row names should be included. If responses are in ABC format, the key provides correct response for each item. If responses are scored 0-1, key is vector of 1s. Group is 0-1 vector, where 0 represents reference group and 1 represents focal group. Its length need to be the same as number of individual students in main dataset.

ShinyItemAnalysis Version 1.0

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(difR)`

`library(foreign)`

`library(ggplot2)`

`library(gridExtra)`

`library(ltm)`

`library(moments)`

`library(nnet)`

`library(psych)`

`library(psychometric)`

`library(reshape2)`

`library(shiny)`

`library(shinyAce)`

`library(stringr)`

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

Adela Drabinova

Jakub Houdek

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, Adela Drabinova, Ondrej Leder and Jakub Houdek

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.

Angoff, W. H., & Ford, S. F. (1973). Item‐Race Interaction on a Test of Scholastic Aptitude. Journal of Educational Measurement, 10(2), 95-105.

Benjamini, Y., & Hochberg, Y. (1995). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society. Series B (Methodological), 289-300.

Cronbach, L. J. (1951). Coefficient Alpha and the Internal Structure of Tests. Psychometrika, 16(3), 297-334.

Drabinova, A., & Martinkova, P. (2016). Detection of Differential Item Functioning Based on Non-Linear Regression. Technical Report V-1229 .

Lord, F. M. (1980). Applications of Item Response Theory to Practical Testing Problems. Routledge.

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Raju, N. S. (1988). The Area between Two Item Characteristic Curves. Psychometrika, 53 (4), 495-502.

Raju, N. S. (1990). Determining the Significance of Estimated Signed and Unsigned Areas between Two Item Response Functions. Applied Psychological Measurement, 14 (2), 197-207.