This function performs an item analysis with certain statistics that are useful for scale or index development. The resulting tables are shown in the viewer pane resp. webbrowser or can be saved as file. Following statistics are computed for each item of a data frame:

• percentage of missing values

• mean value

• standard deviation

• skew

• item difficulty

• item discrimination

• Cronbach's Alpha if item was removed from scale

• mean (or average) inter-item-correlation

Optional, following statistics can be computed as well:

• kurstosis

• Shapiro-Wilk Normality Test

If factor.groups is not NULL, the data frame df will be splitted into groups, assuming that factor.groups indicate those columns of the data frame that belong to a certain factor (see return value of function sjt.pca as example for retrieving factor groups for a scale and see examples for more details).

sjt.itemanalysis(df, factor.groups = NULL, factor.groups.titles = "auto",
scale = FALSE, min.valid.rowmean = 2, altr.row.col = TRUE,
sort.column = NULL, show.shapiro = FALSE, show.kurtosis = FALSE,
show.corr.matrix = TRUE, CSS = NULL, encoding = NULL, file = NULL,
use.viewer = TRUE, no.output = FALSE, remove.spaces = TRUE)

## Arguments

df A data frame with items. If not NULL, df will be splitted into sub-groups, where the item analysis is carried out for each of these groups. Must be a vector of same length as ncol(df), where each item in this vector represents the group number of the related columns of df. See 'Examples'. Titles for each factor group that will be used as table caption for each component-table. Must be a character vector of same length as length(unique(factor.groups)). Default is "auto", which means that each table has a standard caption Component x. Use NULL to suppress table captions. Logical, if TRUE, the data frame's vectors will be scaled when calculating the Cronbach's Alpha value (see reliab_test). Recommended, when the variables have different measures / scales. Minimum amount of valid values to compute row means for index scores. Default is 2, i.e. the return values index.scores and df.index.scores are computed for those items that have at least min.valid.rowmean per case (observation, or technically, row). See mean_n for details. Logical, if TRUE, alternating rows are highlighted with a light gray background color. Numeric vector, indicating the index of the column that should sorted. by default, the column is sorted in ascending order. Use negative index for descending order, for instance, sort.column = -3 would sort the third column in descending order. Note that the first column with rownames is not counted. Logical, if TRUE, a Shapiro-Wilk normality test is computed for each item. See shapiro.test for details. Logical, if TRUE, the kurtosis for each item will also be shown (see kurtosi and describe in the psych-package for more details. Logical, if TRUE (default), a correlation matrix of each component's index score is shown. Only applies if factor.groups is not NULL and df has more than one group. First, for each case (df's row), the sum of all variables (df's columns) is scaled (using the scale-function) and represents a "total score" for each component (a component is represented by each group of factor.groups). After that, each case (df's row) has a scales sum score for each component. Finally, a correlation of these "scale sum scores" is computed. A list with user-defined style-sheet-definitions, according to the official CSS syntax. For more details, see this package-vignette, or 'Details' in sjt.frq. String, indicating the charset encoding used for variable and value labels. Default is NULL, so encoding will be auto-detected depending on your platform (e.g., "UTF-8" for Unix and "Windows-1252" for Windows OS). Change encoding if specific chars are not properly displayed (e.g. German umlauts). Destination file, if the output should be saved as file. If NULL (default), the output will be saved as temporary file and openend either in the IDE's viewer pane or the default web browser. Logical, if TRUE, the HTML table is shown in the IDE's viewer pane. If FALSE or no viewer available, the HTML table is opened in a web browser. Logical, if TRUE, the html-output is neither opened in a browser nor shown in the viewer pane and not even saved to file. This option is useful when the html output should be used in knitr documents. The html output can be accessed via the return value. Logical, if TRUE, leading spaces are removed from all lines in the final string that contains the html-data. Use this, if you want to remove parantheses for html-tags. The html-source may look less pretty, but it may help when exporting html-tables to office tools.

## Value

Invisibly returns

• df.list: List of data frames with the item analysis for each sub.group (or complete, if factor.groups was NULL)

• index.scores: A data frame with of standardized scale / index scores for each case (mean value of all scale items for each case) for each sub-group.

• ideal.item.diff: List of vectors that indicate the ideal item difficulty for each item in each sub-group. Item difficulty only differs when items have different levels.

• cronbach.values: List of Cronbach's Alpha values for the overall item scale for each sub-group.

• knitr.list: List of html-tables with inline-css for use with knitr for each table (sub-group)

• knitr: html-table of all complete output with inline-css for use with knitr

• complete.page: Complete html-output.

If factor.groups = NULL, each list contains only one elment, since just one table is printed for the complete scale indicated by df. If factor.groups is a vector of group-index-values, the lists contain elements for each sub-group.

## Details

See 'Details' in sjt.frq.

## Note

• The Shapiro-Wilk Normality Test (see column W(p)) tests if an item has a distribution that is significantly different from normal.

• Item difficulty should range between 0.2 and 0.8. Ideal value is p+(1-p)/2 (which mostly is between 0.5 and 0.8).

• For item discrimination, acceptable values are 0.20 or higher; the closer to 1.00 the better. See reliab_test for more details.

• In case the total Cronbach's Alpha value is below the acceptable cut-off of 0.7 (mostly if an index has few items), the mean inter-item-correlation is an alternative measure to indicate acceptability. Satisfactory range lies between 0.2 and 0.4. See also mic.

See 'Notes' in sjt.frq.

## References

• Jorion N, Self B, James K, Schroeder L, DiBello L, Pellegrino J (2013) Classical Test Theory Analysis of the Dynamics Concept Inventory. (web)

• Briggs SR, Cheek JM (1986) The role of factor analysis in the development and evaluation of personality scales. Journal of Personality, 54(1), 106-148. doi: 10.1111/j.1467-6494.1986.tb00391.x

• McLean S et al. (2013) Stigmatizing attitudes and beliefs about bulimia nervosa: Gender, age, education and income variability in a community sample. International Journal of Eating Disorders. doi: 10.1002/eat.22227

• Trochim WMK (2008) Types of Reliability. (web)

## Examples

# Data from the EUROFAMCARE sample dataset
library(sjmisc)
library(sjlabelled)
data(efc)

# retrieve variable and value labels
varlabs <- get_label(efc)

# recveive first item of COPE-index scale
start <- which(colnames(efc) == "c82cop1")
# recveive last item of COPE-index scale
end <- which(colnames(efc) == "c90cop9")

# create data frame with COPE-index scale
mydf <- data.frame(efc[, start:end])
colnames(mydf) <- varlabs[start:end]# NOT RUN {
sjt.itemanalysis(mydf)

# auto-detection of labels
sjt.itemanalysis(efc[, start:end])

# Compute PCA on Cope-Index, and perform a
# item analysis for each extracted factor.
factor.groups <- sjt.pca(mydf, no.output = TRUE)\$factor.index
sjt.itemanalysis(mydf, factor.groups)
# }