| Title: | Rasch Model Parameters by Pairwise Algorithm |
|---|---|
| Description: | Performs the explicit calculation -- not estimation! -- of the Rasch item parameters for dichotomous and polytomous item responses, using a pairwise comparison approach. Person parameters (WLE) are calculated according to Warm's weighted likelihood approach. |
| Authors: | Joerg-Henrik Heine <[email protected]> |
| Maintainer: | Joerg-Henrik Heine <[email protected]> |
| License: | GPL-3 |
| Version: | 0.6.1-0 |
| Built: | 2025-03-10 02:47:04 UTC |
| Source: | https://github.com/cran/pairwise |
Performs the explicit calculation – not estimation! – of the Rasch item parameters for dichotomous and polytomous response formats using a pairwise comparison approach (see Heine & Tarnai, 2015) a procedure that is based on the principle for item calibration introduced by Choppin (1968, 1985). On the basis of the item parameters, person parameters (WLE) are calculated according to Warm's weighted likelihood approach (Warm, 1989). Item- and person fit statistics and several functions for plotting are available.
In case of dichotomous answer formats the item parameter calculation for the Rasch Model (Rasch, 1960), is based on the construction of a pairwise comparison matrix Mnij with entries fij representing the number of respondents who got item i right and item j wrong according to Choppin's (1968, 1985) conditional pairwise algorithm.
For the calculation of the item thresholds and difficulty in case of polytomous answer formats, according to the Partial Credit Model (Masters, 1982), a generalization of the pairwise comparison algorithm is used. The construction of the pairwise comparison matrix is therefore extended to the comparison of answer frequencies for each category of each item. In this case, the pairwise comparison matrix Mnicjc with entries ficjc represents the number of respondents who answered to item i in category c and to item j in category c-1 widening Choppin's (1968, 1985) conditional pairwise algorithm to polytomous item response formats. Within R this algorithm is simply realized by matrix multiplication.
In general, for both polytomous and dichotomous response formats, the benefit in applying this algorithm lies in it's capability to return stable item parameter 'estimates' even when using data with a relative high amount of missing values, as long as the items are still proper linked together.
The recent version of the package 'pairwise' computes item parameters for dichotomous and polytomous item responses – and a mixture of both – according the partial credit model using the function pair.
Based on the explicit calculated item parameters for a dataset, the person parameters may thereupon be estimated using any estimation approach. The function pers implemented in the package uses Warm's weighted likelihood approach (WLE) for estimation of the person parameters (Warm, 1989). When assessing person characteristics (abilities) using (rotated) booklet designs an 'incidence' matrix should be used, giving the information if the respective item was in the booklet (coded 1) given to the person or not (coded 0). Such a matrix can be constructed (out of a booklet allocation table) using the function make.incidenz.
Item- and person fit statistics, see functions pairwise.item.fit and pairwise.person.fit respectively, are calculated based on the squared and standardized residuals of observed and the expected person-item matrix. The implemented procedures for calculating the fit indices are based on the formulas given in Wright & Masters, (1982, p. 100), with further clarification given at http://www.rasch.org/rmt/rmt34e.htm.
Further investigation of item fit can be done by using the function ptbis for point biserial correlations. For a graphical representation of the item fit, the function gif for plotting empirical and model derived category probability curves, or the function esc for plotting expected (and empirical) score curves, can be used.
The function iff plots or returns values of the item information function and the function tff plots or returns values of the test information function.
To detect multidimensionality within a set of Items a rasch residual factor analysis proposed by Wright (1996) and further discussed by Linacre (1998) can be performed using the function rfa.
For a 'heuristic' model check the function grm makes the basic calculations for the graphical model check for dicho- or polytomous item response formats. The corresponding S3 plotting method is plot.grm.
Joerg-Henrik Heine <[email protected]>
Choppin, B. (1968). Item Bank using Samplefree Calibration. Nature, 219(5156), 870-872.
Choppin, B. (1985). A fully conditional estimation procedure for Rasch model parameters. Evaluation in Education, 9(1), 29-42.
Heine, J. H. & Tarnai, Ch. (2015). Pairwise Rasch model item parameter recovery under sparse data conditions. Psychological Test and Assessment Modeling, 57(1), 3–36.
Heine, J. H. & Tarnai, Ch. (2011). Item-Parameter Bestimmung im Rasch-Modell bei unterschiedlichen Datenausfallmechanismen. Referat im 17. Workshop 'Angewandte Klassifikationsanalyse' [Item parameter determination in the Rasch model for different missing data mechanisms. Talk at 17. workshop 'Applied classification analysis'], Landhaus Rothenberge, Muenster, Germany 09.-11.11.2011
Heine, J. H., Tarnai, Ch. & Hartmann, F. G. (2011). Eine Methode zur Parameterbestimmung im Rasch-Modell bei fehlenden Werten. Vortrag auf der 10. Tagung der Fachgruppe Methoden & Evaluation der DGPs. [A method for parameter estimation in the Rasch model for missing values. Paper presented at the 10th Meeting of the Section Methods & Evaluation of DGPs.] Bamberg, Germany, 21.09.2011 - 23.09. 2011.
Heine, J. H., & Tarnai, Ch. (2013). Die Pairwise-Methode zur Parameterschätzung im ordinalen Rasch-Modell. Vortrag auf der 11. Tagung der Fachgruppe Methoden & Evaluation der DGPs. [The pairwise method for parameter estimation in the ordinal Rasch model. Paper presented at the 11th Meeting of the Section Methods & Evaluation of DGPs.] Klagenfurt, Austria, 19.09.2013 - 21.09. 2013.
Linacre, J. M. (1998). Detecting multidimensionality: which residual data-type works best? Journal of outcome measurement, 2, 266–283.
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danmarks pædagogiske Institut.
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54(3), 427–450.
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
Wright, B. D. (1996). Comparing Rasch measurement and factor analysis. Structural Equation Modeling: A Multidisciplinary Journal, 3(1), 3–24.
The Andersen likelihood ratio test is based on splitting the dataset into subgroups of persons. One can argue that it is a significance testable version of the more descriptive graphical model check - see grm.
andersentest.pers( pers_obj, split = "median", splitseed = "no", pot = NULL, zerocor = NULL )andersentest.pers( pers_obj, split = "median", splitseed = "no", pot = NULL, zerocor = NULL )
pers_obj |
an object of class |
split |
Specifies the splitting criterion. Basically there are three different options available - each with several modes - which are controlled by passing the corresponding character expression to the argument. 1) Using the rawscore for splitting into subsamples with the following modes: 2) Dividing the persons in 3) The third option is using a manifest variable as a splitting criterion. In this case a vector with the same length as number of cases in |
splitseed |
numeric, used for |
pot |
optional argument, at default ( |
zerocor |
optional argument, at default ( pot=pers_obj$pair$fuargs$pot, zerocor=pers_obj$pair$fuargs$zerocor |
Andersen (1973) proposed to split the dataset by [raw] score groups, which can be achieved setting the argument split = "score". However as pointed out by Rost (2004) there might be several different splitting criteria for testing subsample invariance of the raschmodel. Thus the argument split provides some other options for splitting the data - see description of arguments.
A (list) object of class "andersentest.pers" ...
Andersen, E. B. (1973). A goodness of fit test for the rasch model. Psychometrika, 38(1), 123–140.
Rost, J. (2004). Lehrbuch Testtheorie - Testkonstruktion (2 nd Ed.) Huber: Bern.
## Not run: data(bfiN) # loading example data set data(bfi_cov) # loading covariates to bfiN data set model <- pers(pair(bfiN,m=6)) andersentest.pers(model, split = bfi_cov$gender) andersentest.pers(model, split = "random") andersentest.pers(model, split = "median") ### unsing simulated data: data("sim200x3") model2 <- pers(pair(sim200x3)) andersentest.pers(model2, split = "median") ## End(Not run)## Not run: data(bfiN) # loading example data set data(bfi_cov) # loading covariates to bfiN data set model <- pers(pair(bfiN,m=6)) andersentest.pers(model, split = bfi_cov$gender) andersentest.pers(model, split = "random") andersentest.pers(model, split = "median") ### unsing simulated data: data("sim200x3") model2 <- pers(pair(sim200x3)) andersentest.pers(model2, split = "median") ## End(Not run)
Covaraites to the data from 2800 subjects answering to 5 neuroticism items of the bfi dataset originally included in the R-package {psych} - see https://cran.r-project.org/package=psych.
data(bfi_cov)data(bfi_cov)
A "data.frame" containing 3 variables (gender, education, and age) for 2800 obsevations.
The covariates are in the same row (person) order as the responses to the 5 neuroticism items in the seperate datasets bfiN and bfiN_miss.
The coding is as follows:
genderMales = 1, Females =2
education1 = HS, 2 = finished HS, 3 = some college, 4 = college graduate 5 = graduate degree
ageage in years
https://cran.r-project.org/package=psych
Revelle, William (2015), psych: Procedures for Psychological, Psychometric, and Personality Research.R package version 1.5.1
data(bfi_cov) dim(bfi_cov) ############################################################## names(bfi_cov) # show all variable names of datadata(bfi_cov) dim(bfi_cov) ############################################################## names(bfi_cov) # show all variable names of data
Data from 2800 subjects answering to 5 neuroticism items with 6 answer categories (0-5) of the bfi dataset originally included in the R-package {psych} - see https://cran.r-project.org/package=psych.
data(bfiN)data(bfiN)
A "data.frame" containing 5 variables and 2800 obsevations.
The other variables from the original bfi dataset were skipped and the categories are 'downcoded' to '0,1,2,3,4,5' to have a simple, ready to use example data frame. For further Information on the original dataset see R-package {psych}.
The category meanings (after downcoding) are as follows:
score 0Very Inaccurate
score 1Moderately Inaccurate
score 2Slightly Inaccurate
score 3Slightly Accurate
score 4Moderately Accurate
score 5Very Accurate
The Item meanings are as follows:
N1Get angry easily.
N2Get irritated easily.
N3Have frequent mood swings.
N4Often feel blue.
N5Panic easily.
The covariates like gender, education and age are in a seperate dataset cov_bfi
https://cran.r-project.org/package=psych
Revelle, William (2015), psych: Procedures for Psychological, Psychometric, and Personality Research.R package version 1.5.1
data(bfiN) dim(bfiN) ############################################################## names(bfiN) # show all variable names of data.frame bfiN range(bfiN,na.rm=TRUE) # checking the valid response rangedata(bfiN) dim(bfiN) ############################################################## names(bfiN) # show all variable names of data.frame bfiN range(bfiN,na.rm=TRUE) # checking the valid response range
Data from 2800 subjects answering to 5 neuroticism items with 6 answer categories (0-5) of the bfi dataset originally included in the R-package {psych} with artificial missing data (see details).
data(bfiN_miss)data(bfiN_miss)
A "data.frame" containing 5 variables and 2800 obsevations.
This dataset is the same like the dataset {bfiN} included in this package, exept for the amount of missing data, which were additional created in that way, having aprox. 15% missing for each of the 5 variables by random.
The other variables from the original bfi dataset were skipped and the categories are 'downcoded' to '0,1,2,3,4,5' to have a simple, ready to use example data frame. For further Information on the original dataset see R-package {psych}.
The covariates like gender, education and age are in a seperate dataset cov_bfi
https://cran.r-project.org/package=psych
Revelle, William (2015), psych: Procedures for Psychological, Psychometric, and Personality Research.R package version 1.5.1
data(bfiN_miss) dim(bfiN_miss) ############################################################## names(bfiN_miss) # show all variable names of data.frame bfiN_miss range(bfiN_miss,na.rm=TRUE) # checking the valid response range colSums(is.na(bfiN_miss))/dim(bfiN_miss)[1] # percentage of missing per variabledata(bfiN_miss) dim(bfiN_miss) ############################################################## names(bfiN_miss) # show all variable names of data.frame bfiN_miss range(bfiN_miss,na.rm=TRUE) # checking the valid response range colSums(is.na(bfiN_miss))/dim(bfiN_miss)[1] # percentage of missing per variable
plotting function for plotting category probability curves.
catprob(pair_obj, itemnumber = 1, ra = 4, plot = TRUE, ...)catprob(pair_obj, itemnumber = 1, ra = 4, plot = TRUE, ...)
pair_obj |
an object of class |
itemnumber |
an integer, defining the number of the item to plot the respective category probability for. This is set to an arbitrary default value of |
ra |
an integer, defining the (logit) range for x-axis |
plot |
a logical (default |
... |
arguments passed to plot |
no details in the moment.
a plot or a matrix with category probabilities.
######## data(sim200x3) result <- pair(sim200x3) catprob(pair_obj = result, itemnumber = 2 ) data(bfiN) result <- pair(bfiN) catprob(pair_obj = result, itemnumber = 3 )######## data(sim200x3) result <- pair(sim200x3) catprob(pair_obj = result, itemnumber = 2 ) data(bfiN) result <- pair(bfiN) catprob(pair_obj = result, itemnumber = 3 )
Data from the german sample of the PISA 2003 survey, containing 31 dichotomous items from the math task.
data(cog)data(cog)
A data frame containing 34 variables and 4660 obsevations.
The first 3 variables are ID variables. For further Information on variables and their meaning see the codebook PDF file
available at https://www.oecd.org/pisa/pisaproducts/PISA12_cogn_codebook.pdf
Database - PISA 2003, Downloadable Data, https://www.oecd.org/pisa/data/pisa2012database-downloadabledata.htm
data(cog) dim(cog) ############################################################## names(cog) # show all variable names of data.frame cog names(cog[,4:34]) # show the variable names of the math items names(cog[,1:3]) # show the variable names of the ID variablesdata(cog) dim(cog) ############################################################## names(cog) # show all variable names of data.frame cog names(cog[,4:34]) # show the variable names of the math items names(cog[,1:3]) # show the variable names of the ID variables
a data.frame containing a booklet allocation table for the cognitive Data cog in this package, which holds 31 dichotomous items from the math task from the german sample of the PISA 2003 survey.
data(cogBOOKLET)data(cogBOOKLET)
A data.frame containing 31 rows.
For further Information on variables and their meaning see the codebook PDF file
available at https://www.oecd.org/pisa/pisaproducts/PISA12_cogn_codebook.pdf
Database - PISA 2003, Downloadable Data, https://www.oecd.org/pisa/data/pisa2012database-downloadabledata.htm
data(cogBOOKLET) cogBOOKLETdata(cogBOOKLET) cogBOOKLET
Calculation of delta parameters or rather item step parameters from thurstonian threshold parameters returned by the function pair.
deltapar(object, sigma = TRUE)deltapar(object, sigma = TRUE)
object |
an object of class |
sigma |
a logical whether to return item difficulties (sigma) or not |
The "Thurstone threshold" or rather thurstonian threshold for a category corresponds to a point on the latent variable at which the probability of being observed in that category or above equals that of being observed in the categories below. Thus these thurstonian threshold parameters can be interpreted in an strait forward and easy way. However, some other computer programs related to Rasch analysis don't return thurstonian threshold parameters from their estimation procedure, but rather so called delta parameters for the item steps. The later are also known as "step measures", "step calibrations", "step difficulties", "tau parameters", and "Rasch-Andrich thresholds". For a better comparability between different Rasch software and estimation procedures the thurstonian threshold parameters can be converted into delta or rather items step parameters.
If sigma=TRUE an object of class c("data.frame", "deltapar") containing delta parameters for items and their difficultie (first column). Otherwise a matrix containing only the delta parameters.
Linacre J.M. (1992). Rasch-Andrich Thresholds and Rasch-Thurstone Thresholds. Rasch Measurement Transactions, 5:4, 191. https://www.rasch.org/rmt/rmt54r.htm
Linacre J.M. (2001). Category, Step and Threshold: Definitions & Disordering. Rasch Measurement Transactions, 15:1, 794. https://www.rasch.org/rmt/rmt151g.htm
Adams, R. J., Wu, M. L., & Wilson, M. (2012). The Rasch Rating Model and the Disordered Threshold Controversy. Educational and Psychological Measurement, 72(4), 547–573. https://doi.org/10.1177/0013164411432166
Linacre J.M. (2006). Item Discrimination and Rasch-Andrich Thresholds. Rasch Measurement Transactions, 20:1, 1054. https://www.rasch.org/rmt/rmt201k.htm
###################### data(sim200x3) # loading reponse data ip <- pair(sim200x3,m = c(2,3,3)) # compute item parameters summary(ip) # have a look at the results (thurstonian thresholds) deltapar(ip) # compute delta parameters from these###################### data(sim200x3) # loading reponse data ip <- pair(sim200x3,m = c(2,3,3)) # compute item parameters summary(ip) # have a look at the results (thurstonian thresholds) deltapar(ip) # compute delta parameters from these
Selectetd data for 5001 'subjects' who participated in the PISA 2012 survey.
data(DEU_PISA2012)data(DEU_PISA2012)
A list containing ... .
The data is based on freely down loadable data on the official OECD page - see source. The general structure of the data in list format, is described in an PDF document available in the User guides, package vignettes and other documentation section.
Database - PISA 2003, Downloadable Data, https://www.oecd.org/pisa/data/pisa2012database-downloadabledata.htm
############################################################## data(DEU_PISA2012) str(DEU_PISA2012)############################################################## data(DEU_PISA2012) str(DEU_PISA2012)
plotting function for plotting expected score curves.
esc(pers_obj, itemnumber = 1, integ = 6, ra = 4, nodes = 100, lwd = 2, ...)esc(pers_obj, itemnumber = 1, integ = 6, ra = 4, nodes = 100, lwd = 2, ...)
pers_obj |
an object of class |
itemnumber |
an integer, defining the number of the item to plot the respective categoy probability for. This is set to an arbitrary default value of |
integ |
either an integer defining the number of (ability) groups to integrate the empirical theta vector or the character expression |
ra |
an integer, defining the (logit) range for x-axis |
nodes |
numer of integration nodes |
lwd |
see |
... |
arguments passed to plot |
no details in the moment.
######## data(bfiN) result <- pers(pair(bfiN)) esc(pers_obj=result,1,lwd=2) # plot for first item esc(pers_obj=result,2,lwd=2) # plot for second item for(i in 1:5){esc(pers_obj=result,i,lwd=2)} ######### esc(pers_obj=result,2,integ="all",lwd=2) # plot for secod item######## data(bfiN) result <- pers(pair(bfiN)) esc(pers_obj=result,1,lwd=2) # plot for first item esc(pers_obj=result,2,lwd=2) # plot for second item for(i in 1:5){esc(pers_obj=result,i,lwd=2)} ######### esc(pers_obj=result,2,integ="all",lwd=2) # plot for secod item
function tabulating (answer) categories in X.
ftab(X, catgories = NULL, na.omit = FALSE)ftab(X, catgories = NULL, na.omit = FALSE)
X |
Data as a |
catgories |
optional a vector ( |
na.omit |
logical (default: |
X can either be a ("numeric" or "character") "matrix" containing response vectors of persons (rows) or a "data.frame" containing "numeric", "character" or "factor" variables (columns).
a "matrix" with category frequencies
######## data(bfiN) ftab(bfiN) data(sim200x3) ftab(sim200x3)######## data(bfiN) ftab(bfiN) data(sim200x3) ftab(sim200x3)
plotting function for plotting empirical and model derived category probability curves.
gif(pers_obj, itemnumber = 1, ra = 4, integ = "raw", kat = "all", ...)gif(pers_obj, itemnumber = 1, ra = 4, integ = "raw", kat = "all", ...)
pers_obj |
an object of class |
itemnumber |
an integer, defining the number of the item to plot the respective categoy probability for. This is set to an arbitrary default value of |
ra |
an integer, defining the (logit) range for x-axis |
integ |
either an integer, defining the number of integration points along the (logit) range on the x-axis to integrate the empirical theta values, or the character expression |
kat |
either an integer, defining for which category the empirical category probabilities should be plotted over the model derived category probability curves, or the character expression |
... |
arguments passed to plot |
no details in the moment.
a plot with category probabilities.
######## data(bfiN) pers_obj <- pers(pair(bfiN)) #### plot empirical category probabilities gif(pers_obj = pers_obj, itemnumber = 1 ) gif(pers_obj = pers_obj, itemnumber = 1 , integ=8) # integration over 8 points gif(pers_obj = pers_obj, itemnumber = 1 , integ=8, kat=1) # only for category number 1######## data(bfiN) pers_obj <- pers(pair(bfiN)) #### plot empirical category probabilities gif(pers_obj = pers_obj, itemnumber = 1 ) gif(pers_obj = pers_obj, itemnumber = 1 , integ=8) # integration over 8 points gif(pers_obj = pers_obj, itemnumber = 1 , integ=8, kat=1) # only for category number 1
This function makes the basic calculations for the graphical model check for dicho- or polytomous item response formats. It is more or less a wraper function, internaly calling the function pairSE. Several splitting options are available (see arguments).
grm( daten, m = NULL, w = NULL, split = "random", splitseed = "no", verbose = FALSE, ... )grm( daten, m = NULL, w = NULL, split = "random", splitseed = "no", verbose = FALSE, ... )
daten |
a data.frame or matrix with optionaly named colums (names of items), potentially with missing values, comprising polytomous or dichotomous (or mixed category numbers) responses of |
m |
an integer (will be recycled to a vector of length k) or a vector giving the number of response categories for all items - by default |
w |
an optional vector of case weights. |
split |
Specifies the splitting criterion. Basically there are three different options available - each with several modes - which are controlled by passing the corresponding character expression to the argument. 1) Using the rawscore for splitting into subsamples with the following modes: 2) Dividing the persons in 3) The third option is using a manifest variable as a splitting criterion. In this case a vector with the same length as number of cases in |
splitseed |
numeric, used for |
verbose |
logical, if |
... |
additional arguments |
The data is splitted in two or more subsamples and then item thresholds, the parameter (Sigma) and their standard errors (SE) for the items according the PCM are calculated for each subsample. Additional arguments (see description of function pairSE) for parameter calculation are passed through.
WARNING: When using data based on booklet designs with systematically missing values (by design) you have to ensure that in each of the booklet the maximum raw value to reach is equal while using the raw value as splitting criterion.
A (list) object of class c("grm","list") containing the item difficulty parameter sigma and their standard errors for two or more subsamples.
Estimation of standard errors is done by repeated calculation of item parameters for subsamples of the given data. This procedure is mainly controlled by the arguments nsample and size (see arguments). With regard to calculation time, the argument nsample is the 'time killer'. On the other hand, things (estimation of standard errors) will not necessarily get better when choosing large values for nsample. For example choosing nsample=400 will only result in minimal change for standard error estimation in comparison to (nsample=30) which is the default setting (see examples).
description of function pairSE{pairwise}.
data(bfiN) # loading example data set data(bfi_cov) # loading covariates to bfiN data set # calculating itemparameters and SE for two random allocated subsamples grm_gen <- grm(daten=bfiN, split = bfi_cov$gender) summary(grm_gen) #### plot(grm_gen) grm_med <- grm(daten=bfiN, split = "median") summary(grm_med) #### plot(grm_med) grm_ran<-grm(daten=bfiN, split = "random") summary(grm_ran) # some examples for plotting options # plotting item difficulties for two subsamples against each other # with elipses for a CI = 95% . #### plot(grm_ran) # using triangles as plotting pattern #### plot(grm_ran,pch=2) #plotting without CI ellipses #### plot(grm_ran,ci=0,pch=2) # plotting with item names #### plot(grm_ran,itemNames=TRUE) # Changing the size of the item names #### plot(grm_ran,itemNames=TRUE, cex.names = 1.3) # Changing the color of the CI ellipses plot(grm_ran,itemNames=TRUE, cex.names = .8, col.error="green") ###### example from details section 'Some Notes on Standard Errors' ######## ## Not run: grm_def<-grm(daten=bfiN, split = "random",splitseed=13) plot(grm_def) ###### grm_400<-grm(daten=bfiN, split = "random", splitseed=13 ,nsample=400) plot(grm_400) ## End(Not run)data(bfiN) # loading example data set data(bfi_cov) # loading covariates to bfiN data set # calculating itemparameters and SE for two random allocated subsamples grm_gen <- grm(daten=bfiN, split = bfi_cov$gender) summary(grm_gen) #### plot(grm_gen) grm_med <- grm(daten=bfiN, split = "median") summary(grm_med) #### plot(grm_med) grm_ran<-grm(daten=bfiN, split = "random") summary(grm_ran) # some examples for plotting options # plotting item difficulties for two subsamples against each other # with elipses for a CI = 95% . #### plot(grm_ran) # using triangles as plotting pattern #### plot(grm_ran,pch=2) #plotting without CI ellipses #### plot(grm_ran,ci=0,pch=2) # plotting with item names #### plot(grm_ran,itemNames=TRUE) # Changing the size of the item names #### plot(grm_ran,itemNames=TRUE, cex.names = 1.3) # Changing the color of the CI ellipses plot(grm_ran,itemNames=TRUE, cex.names = .8, col.error="green") ###### example from details section 'Some Notes on Standard Errors' ######## ## Not run: grm_def<-grm(daten=bfiN, split = "random",splitseed=13) plot(grm_def) ###### grm_400<-grm(daten=bfiN, split = "random", splitseed=13 ,nsample=400) plot(grm_400) ## End(Not run)
plotting function for plotting the Item information function(IIF).
iff( pair_obj, itemnumber = 1, x = NULL, plot = TRUE, cat = FALSE, lwd = 2, col = 1, ... )iff( pair_obj, itemnumber = 1, x = NULL, plot = TRUE, cat = FALSE, lwd = 2, col = 1, ... )
pair_obj |
an object of class |
itemnumber |
an integer, defining the number of the item to plot the respective item information function for. This is set to an arbitrary default value of |
x |
The value(s) of the latent variable, at which the IIF will be evaluated. |
plot |
a logical (default |
cat |
a logical (default |
lwd |
see parameters for |
col |
see parameters for |
... |
arguments passed to plot |
no details in the moment.
a plot, a matrix or a single numeric with values of the Item information function.
######## data(sim200x3) result <- pair(sim200x3) # IFF plot for Item No. 2 iff(pair_obj = result, itemnumber = 2 ) # IFF plot for Categories of Item No. 2 iff(pair_obj = result, itemnumber = 2 ,cat=TRUE) # IFF at theta=0 for Item No. 2 iff(pair_obj = result, itemnumber = 2 ,x=0) # IFF at theta=0 for Categories of Item No. 2 iff(pair_obj = result, itemnumber = 2 ,x=0,cat=TRUE) # IFF of Item No. 2 for a given range of thetas iff(pair_obj = result, itemnumber = 2 ,x=seq(0,4,.1)) # ... etc. iff(pair_obj = result, itemnumber = 2 ,x=seq(0,4,.1),cat=TRUE) ##### examples with other data ... data(bfiN) result <- pair(bfiN) iff(pair_obj = result, itemnumber = 3 ) iff(pair_obj = result, itemnumber = 3 ,cat=TRUE)######## data(sim200x3) result <- pair(sim200x3) # IFF plot for Item No. 2 iff(pair_obj = result, itemnumber = 2 ) # IFF plot for Categories of Item No. 2 iff(pair_obj = result, itemnumber = 2 ,cat=TRUE) # IFF at theta=0 for Item No. 2 iff(pair_obj = result, itemnumber = 2 ,x=0) # IFF at theta=0 for Categories of Item No. 2 iff(pair_obj = result, itemnumber = 2 ,x=0,cat=TRUE) # IFF of Item No. 2 for a given range of thetas iff(pair_obj = result, itemnumber = 2 ,x=seq(0,4,.1)) # ... etc. iff(pair_obj = result, itemnumber = 2 ,x=seq(0,4,.1),cat=TRUE) ##### examples with other data ... data(bfiN) result <- pair(bfiN) iff(pair_obj = result, itemnumber = 3 ) iff(pair_obj = result, itemnumber = 3 ,cat=TRUE)
Data from the Book 'Best Test Design' from Wright & Stone (1979, p. 31, table 2.3.1) comprising responses from 35 subjects scored in 18 dichotomous items.
data(KCT)data(KCT)
A "data.frame" containing 18 numeric variables (coded 0,1) and 35 obsevations.
The so called 'Knox Cube Test' was initially developed as a cube imitation test around 1913 by Howard A. Knox as a nonverbal test of intelligence to screen and identify potential immigrants with mental deficits at the Ellis Island immigration station in New York Harbor – see Richardson (2005) for a historical review.
Quoted from Wright & Stone (1979):
"Success on this subtest requires the application of visual attention and short-term memory to a simple sequencing task. It appears to be free from school-related tasks and hence to be an indicator of nonverbal intellectual capacity." (Wright & Stone 1979, p. 28).
Wright, B. D. & Stone, M. H. (1979). Best Test Design: Rasch Measurement. Chicago: MESA Press.
Richardson, J. T. E. (2005). Knox’s cube imitation test: A historical review and an experimental analysis. Brain and Cognition, 59(2), 183–213. https://doi.org/10.1016/j.bandc.2005.06.001
data(KCT) dim(KCT) ############# some item calibrations ############### data(KCT) IP_pair <- pair(daten = KCT[,4:17], m = 2) summary(IP_pair) #################################################### #################################################### #########MIKE error message never received########## #################################################### ####################################################data(KCT) dim(KCT) ############# some item calibrations ############### data(KCT) IP_pair <- pair(daten = KCT[,4:17], m = 2) summary(IP_pair) #################################################### #################################################### #########MIKE error message never received########## #################################################### ####################################################
Data for 300 subjects answering to 5 dichotomous items out of 'Kognitiver Fähigkeits Test' [Cognitive Skills Test] (KFT - Gaedike & Weinläder, 1976) . This data is used as an example in the textbook by J. Rost (2004) to demonstrate some principles of rasch measurement.
data(kft5)data(kft5)
A "matrix" containing 5 columns (variables) and 300 rows (obsevations).
The instrument KFT and the data are described in Rost (2004) at page 95.
Rost, J. (2004). Lehrbuch Testtheorie - Testkonstruktion (2 nd Ed.) Huber: Bern.
Heller, K, Gaedike, A.-K & Weinläder, H. (1976). Kognitiver Fähigkeits-Test (KFT 4-13). Weinheim: Beltz.
data(kft5) dim(kft5) ########### # frequencies ftab(kft5) # Itemparameter to be compared with Rost (2004), page 120. summary(pair(kft5)) # Itemparameter to be compared with Rost (2004), page 120. summary(pers(pair(kft5)))data(kft5) dim(kft5) ########### # frequencies ftab(kft5) # Itemparameter to be compared with Rost (2004), page 120. summary(pair(kft5)) # Itemparameter to be compared with Rost (2004), page 120. summary(pers(pair(kft5)))
S3 logLik method to extract the log-likelihood for object of class"pers"
## S3 method for class 'pers' logLik(object, sat = FALSE, p = FALSE, ...)## S3 method for class 'pers' logLik(object, sat = FALSE, p = FALSE, ...)
object |
object of class |
sat |
a "logical" with default set to |
p |
a "logical" with default set to |
... |
not used jet. |
Function to perform a likelihood ratio test for the estimated model 'against' the saturated model for object of class"pers".
lrtest.pers(object, ...)lrtest.pers(object, ...)
object |
an object of class |
... |
not used jet. |
This function converts a booklet allocation table (like in cogBOOKLET) into a incidence matrix used in the function pers.
make.incidenz(tab, bookid, item_order = NULL, info = FALSE)make.incidenz(tab, bookid, item_order = NULL, info = FALSE)
tab |
a booklet allocation table as a |
bookid |
a integer vector with the same length as the number of persons in the response data giving the information which booklet was assigned to each person. |
item_order |
optional a character vector with the item names in the order of the items in the response data (from first to last column in the response data). By default it is assumend that the item order in the booklet allocation table is already the same as in the response data. |
info |
logical default: |
It is assumed that there is an equal replicate factor for each item used, when constructing the bookletdesign - so every items occures with the same frequency over all booklets of the entire set of booklets.
an incidence matrix as an object of class "matrix" with 0,1 coding or a "list" with detailed information.
######################### data(cog);data(cogBOOKLET) # loading reponse and allocation data table(cog$BOOKID)# show n persons per booklet names(table(c(as.matrix(cogBOOKLET[,2:5])))) # show booklets in allocation data d<-(cog[cog$BOOKID!=14,]) # skip persons which got booklet No.14. inc<-make.incidenz(tab=cogBOOKLET, bookid=d$BOOKID) # make just the incidence matrix inc make.incidenz(tab=cogBOOKLET, bookid=d$BOOKID, info=TRUE) # get some info too # in this case not necessary but just to show # using the (item) names in cog to secure the item order in incidence matrix: make.incidenz(tab=cogBOOKLET, bookid=d$BOOKID, item_order=names(cog)[4:34]) ################################################ data(cog);data(cogBOOKLET) # loading reponse and allocation data table(cog$BOOKID)# show n persons per booklet names(table(c(as.matrix(cogBOOKLET[,2:5])))) # show booklets in allocation data d<-(cog[cog$BOOKID!=14,]) # skip persons which got booklet No.14. inc<-make.incidenz(tab=cogBOOKLET, bookid=d$BOOKID) # make just the incidence matrix inc make.incidenz(tab=cogBOOKLET, bookid=d$BOOKID, info=TRUE) # get some info too # in this case not necessary but just to show # using the (item) names in cog to secure the item order in incidence matrix: make.incidenz(tab=cogBOOKLET, bookid=d$BOOKID, item_order=names(cog)[4:34]) #######################
Data for 1000 subjects answering to 5 polytomous items assessing neuroticism contained in the german version of the NEO–five–factor–inventory (NEOFFI) by Borkenau and Ostendorf (1991). This data is used as an example in the textbook by J. Rost (2004) to demonstrate some principles of rasch measurement.
data(Neoffi5)data(Neoffi5)
A "matrix" containing 5 columns (variables) and 1000 rows (obsevations).
An detailed description of the data can be found in Rost (2004) at page 202.
Rost, J. (2004). Lehrbuch Testtheorie - Testkonstruktion (2 nd Ed.) Huber: Bern.
Borkenau. P. & Ostendorf F. (1991). Ein Fragebogen zur Erfassung fünf robuster Persönlichkeitsfaktoren. Diagnostica, 37, (1), 29–41.
data(Neoffi5) dim(Neoffi5) ########### # frequencies ftab(Neoffi5) # Itemparameter to be compared with Rost (2004), page 211. summary(pair(Neoffi5)) # Itemparameter to be compared with Rost (2004), page 213. summary(pers(pair(Neoffi5)))data(Neoffi5) dim(Neoffi5) ########### # frequencies ftab(Neoffi5) # Itemparameter to be compared with Rost (2004), page 211. summary(pair(Neoffi5)) # Itemparameter to be compared with Rost (2004), page 213. summary(pers(pair(Neoffi5)))
This is the (new) main function for calculation of the item parameter for the dichotomous Rasch Model (Rasch, 1960) and its extension for polytomous items (thurstonian thresholds) according to the Partial Credit Model (Masters, 1982).
The function implements a generalization (see Heine & Tarnai, 2015) of the pairwise comparison approach, that is based on the principle for item calibration introduced by Choppin (1968, 1985) – see also (Wright & Masters, 1982). The number of (response) categories may vary across items.
Missing values up to an high amount in data are allowed, as long as items are proper linked together.
pair( daten, m = NULL, w = NULL, pot = TRUE, zerocor = TRUE, ccf = FALSE, likelihood = NULL, pot2 = 2, delta = TRUE, conv = 1e-04, maxiter = 3000, progress = TRUE, init = NULL, zerosum = TRUE, ... )pair( daten, m = NULL, w = NULL, pot = TRUE, zerocor = TRUE, ccf = FALSE, likelihood = NULL, pot2 = 2, delta = TRUE, conv = 1e-04, maxiter = 3000, progress = TRUE, init = NULL, zerosum = TRUE, ... )
daten |
a single |
m |
an integer (will be recycled to a vector of length k) or a vector giving the number of response categories for all items - by default |
w |
an optional vector of case weights. |
pot |
either a logical or an integer >= 2 defining the power to compute of the pairwise comparison matrix. If TRUE (default) a power of three of the pairwise comparison matrix is used for further calculations. If FALSE no powers are computed. |
zerocor |
either a logical or an numeric value between >0 and <=1. If (in case of a logical) zerocor is set to TRUE (default) unobserved combinations (1-0, 0-1) in the data for each pair of items are given a frequency of one conf. proposal by Alexandrowicz (2011, p.373). As an alternative option a numeric value between >0 and <=1 can be assigned to unobserved combinations (1-0, 0-1) in the data for each pair of items (conf. to personal communication with A. Robitzsch; 29-03-2021). |
ccf |
logical with default |
likelihood |
either NULL (default) or a a character expression defining a likelihood estimation approach based on the pairwise comparison matrix. Currently only the so called MINCHI approach as described in Fischer (2006) is implemented , which can be selected by setting |
pot2 |
ignored when |
delta |
ignored when |
conv |
ignored when |
maxiter |
ignored when |
progress |
ignored when |
init |
ignored when |
zerosum |
ignored when |
... |
additional parameters passed through. |
Parameter calculation is based on the construction of a paired comparison matrix Mnicjc with entries ficjc representing the number of respondents who answered to item i in category c and to item j in category c-1 widening Choppin's (1968, 1985) conditional pairwise algorithm to polytomous item response formats. This algorithm is simply realized by matrix multiplication.
To avoid numerical problems with off diagonal zero's when constructing the pairwise comparison matrix Mnij, powers of the Mnicjc matrix, can be used (Choppin, 1968, 1985). Using powers k of Mnicjc - argument pot=TRUE (default), replaces the results of the direct comparisons between i and j with the sum of the indirect comparisons of i and j through an intermediate k.
In general, it is recommended to use the argument with default value pot=TRUE.
If a list object is assigned to the argument data, the list entries (matrix or data.frame) must all have the same dimensionality. The individual list entries represent either r measurement times or raters. If such a list object is used, first the item parameters are calculated across all r measurement points or raters and additionally a threshold parameter is given for each of the r measurement points or raters (e.g. rater severity or overal item shift).
For a graphic representation of the item 'estimates' the plotting S3 method plot.pair is available. For plotting the item category probabilities the function catprob can be used.
A (list) object of class "pair" containing the item category thresholds and difficulties sigma, also called item location.
Choppin, B. (1968). Item Bank using Sample-free Calibration. Nature, 219(5156), 870-872.
Choppin, B. (1985). A fully conditional estimation procedure for Rasch model parameters. Evaluation in Education, 9(1), 29-42.
Heine, J. H. & Tarnai, Ch. (2015). Pairwise Rasch model item parameter recovery under sparse data conditions. Psychological Test and Assessment Modeling, 57(1), 3–36.
Alexandrowicz, R. W. (2011). 'GANZ RASCH': A Free Software for Categorical Data Analysis. Social Science Computer Review, 30(3), 369-379.
Masters, G. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danmarks pædagogiske Institut.
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
Fischer, Gerhard H. 2006. "Rasch Models". Pp. 515–85 in Handbook of statistics (26): Psychometrics. Vol. 26, edited by C. R. Rao and S. Sinharay. Amsterdam: Elsevier.
data(bfiN) # loading example data set # calculating itemparameters for 5 neuroticism items with 6 answer categories (0-5). neuro_itempar<-pair(daten = bfiN, m = 6) summary(neuro_itempar) summary(neuro_itempar, sortdif=TRUE) # ordered by difficulty # plotting threshold profiles for 5 neuroticism items. plot(neuro_itempar) plot(neuro_itempar, sortdif=TRUE) # plotting ordered by difficulty ################ with unequal number of categories data(sim200x3) res<-pair(sim200x3) summary(res) plot(res)data(bfiN) # loading example data set # calculating itemparameters for 5 neuroticism items with 6 answer categories (0-5). neuro_itempar<-pair(daten = bfiN, m = 6) summary(neuro_itempar) summary(neuro_itempar, sortdif=TRUE) # ordered by difficulty # plotting threshold profiles for 5 neuroticism items. plot(neuro_itempar) plot(neuro_itempar, sortdif=TRUE) # plotting ordered by difficulty ################ with unequal number of categories data(sim200x3) res<-pair(sim200x3) summary(res) plot(res)
Calculation of the item parameters for dichotomous (difficulty) or polytomous items (thurstonian thresholds) and their standard errors (SE) respectively. All parameters are calculated using a generalization (see Heine & Tarnai, 2015) of the pairwise comparison algorithm (Choppin, 1968, 1985). Missing values up to an high amount in data matrix are allowed, as long as items are proper linked together.
pairSE( daten, m = NULL, w = NULL, nsample = 30, size = 0.5, seed = "no", pot = TRUE, zerocor = TRUE, verbose = TRUE, likelihood = NULL, pot2 = 2, delta = TRUE, conv = 1e-04, maxiter = 3000, progress = TRUE, init = NULL, zerosum = TRUE, ... )pairSE( daten, m = NULL, w = NULL, nsample = 30, size = 0.5, seed = "no", pot = TRUE, zerocor = TRUE, verbose = TRUE, likelihood = NULL, pot2 = 2, delta = TRUE, conv = 1e-04, maxiter = 3000, progress = TRUE, init = NULL, zerosum = TRUE, ... )
daten |
a data.frame or matrix with optionaly named colums (names of items), potentially with missing values, comprising polytomous or dichotomous (or mixted category numbers) responses of |
m |
an integer (will be recycled to a vector of length k) or a vector giving the number of response categories for all items - by default |
w |
an optional vector of case weights. |
nsample |
numeric specifying the number of subsamples sampled from data, which is the number of replications of the parameter calculation.
WARNING! specifying high values for |
size |
numeric with valid range between 0 and 1 (but not exactly 0 or 1) specifying the size of the subsample of |
seed |
numeric used for |
pot |
either a logical or an integer >= 2 defining the power to compute of the pairwise comparison matrix. If TRUE (default) a power of three of the pairwise comparison matrix is used for further calculations. If FALSE no powers are computed. |
zerocor |
either a logical or an numeric value between >0 and <=1. If (in case of a logical) zerocor is set to TRUE (default) unobserved combinations (1-0, 0-1) in the data for each pair of items are given a frequency of one conf. proposal by Alexandrowicz (2011, p.373). As an alternative option a numeric value between >0 and <=1 can be assigned to unobserved combinations (1-0, 0-1) in the data for each pair of items (conf. to personal communication with A. Robitzsch; 29-03-2021). |
verbose |
logical, if |
likelihood |
see |
pot2 |
see |
delta |
see |
conv |
see |
maxiter |
see |
progress |
see |
init |
see |
zerosum |
see |
... |
additional parameters passed through. |
Parameter calculation is based on the construction of a paired comparison matrix Mnicjc with entries ficjc, representing the number of respondents who answered to item i in category c and to item j in category c-1 widening Choppin's (1968, 1985) conditional pairwise algorithm to polytomous item response formats. This algorithm is simply realized by matrix multiplication.
Estimation of standard errors is done by repeated calculation of item parameters for sub samples of the given data.
To avoid numerical problems with off diagonal zeros when constructing the pairwise comparison matrix Mnicjc, powers of the Mnicjc matrix, can be used (Choppin, 1968, 1985). Using powers k of Mnicjc, argument pot=TRUE (default), replaces the results of the direct comparisons between i and j with the sum of the indirect comparisons of i and j through an intermediate k.
In general, it is recommended to use the argument with default value pot=TRUE.
A (list) object of class c("pairSE","list") containing the item category thresholds, difficulties sigma and their standard errors.
Estimation of standard errors is done by repeated calculation of item parameters for subsamples of the given data. This procedure is mainly controlled by the arguments nsample and size (see arguments). With regard to calculation time, the argument nsample may be the 'time killer'. On the other hand, things (estimation of standard errors) will not necessarily get better when choosing large values for nsample. For example choosing nsample=400 will only result in minimal change for standard error estimation in comparison to (nsample=30) which is the default setting (see examples).
Choppin, B. (1968). Item Bank using Sample-free Calibration. Nature, 219(5156), 870-872.
Choppin, B. (1985). A fully conditional estimation procedure for Rasch model parameters. Evaluation in Education, 9(1), 29-42.
Heine, J. H. & Tarnai, Ch. (2015). Pairwise Rasch model item parameter recovery under sparse data conditions. Psychological Test and Assessment Modeling, 57(1), 3–36.
Alexandrowicz, R. W. (2011). 'GANZ RASCH': A Free Software for Categorical Data Analysis. Social Science Computer Review, 30(3), 369-379.
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
data(bfiN) # loading example data set # calculating item parameters and their SE for 5 neuroticism items with 6 answer categories (0-5). neuro_itempar<-pairSE(daten = bfiN, m = 6) summary(neuro_itempar) # summary for result # plotting item thresholds with with their CI = 95% plot(neuro_itempar) plot(neuro_itempar,sortdif=TRUE) ###### example from details section 'Some Notes on Standard Errors' ######## neuro_itempar_400<-pairSE(daten = bfiN, m = 6,nsample=400) plot(neuro_itempar) plot(neuro_itempar_400)data(bfiN) # loading example data set # calculating item parameters and their SE for 5 neuroticism items with 6 answer categories (0-5). neuro_itempar<-pairSE(daten = bfiN, m = 6) summary(neuro_itempar) # summary for result # plotting item thresholds with with their CI = 95% plot(neuro_itempar) plot(neuro_itempar,sortdif=TRUE) ###### example from details section 'Some Notes on Standard Errors' ######## neuro_itempar_400<-pairSE(daten = bfiN, m = 6,nsample=400) plot(neuro_itempar) plot(neuro_itempar_400)
function for calculating item fit indices. The procedures for calculating the fit indices are based on the formulas given in Wright & Masters, (1982, P. 100), with further clarification given in http://www.rasch.org/rmt/rmt34e.htm.
pairwise.item.fit(pers_obj, na_treat = NA)pairwise.item.fit(pers_obj, na_treat = NA)
pers_obj |
an object of class |
na_treat |
value to be assigned to residual cells which have missing data in the original response matrix. default is set to |
contrary to many IRT software using Ml based item parameter estimation, pairwise will not exclude persons, showing perfect response vectors (e.g. c(0,0,0) for dataset with three variables), prior to the scaling. Therefor the fit statistics computed with pairwise may deviate somewhat from the fit statistics produced by IRT software using Ml based item parameter estimation (e.g. R-package eRm), depending on the amount of persons with perfect response vectors in the data.
an object of class c("pifit", "data.frame") containing item fit indices.
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
Wright, B. D., & Masters, G. N. (1990). Computation of OUTFIT and INFIT Statistics. Rasch Measurement Transactions, 3(4), 84–85.
######## data(sim200x3) result <- pers(pair(sim200x3)) pairwise.item.fit(pers_obj=result) # item fit statistic######## data(sim200x3) result <- pers(pair(sim200x3)) pairwise.item.fit(pers_obj=result) # item fit statistic
function for calculating person fit indices. The procedures for calculating the fit indices are based on the formulas given in Wright & Masters, (1982, P. 100), with further clarification given in http://www.rasch.org/rmt/rmt34e.htm.
pairwise.person.fit(pers_obj, na_treat = NA)pairwise.person.fit(pers_obj, na_treat = NA)
pers_obj |
an object of class |
na_treat |
value to be assigned to residual cells which have missing data in the original response matrix. default is set to |
contrary to many IRT software using ML based item parameter estimation, pairwise will not exclude persons, showing perfect response vectors (e.g. c(0,0,0) for dataset with three variables), prior to scaling. Therefor the fit statistics computed with pairwise may deviate somewhat from the fit statistics produced by IRT software using ML based item parameter estimation (e.g. R-package eRm), depending on the amount of persons with perfect response vectors in the data.
an object of class c("ppfit", "data.frame") containing person fit indices
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
Wright, B. D., & Masters, G. N. (1990). Computation of OUTFIT and INFIT Statistics. Rasch Measurement Transactions, 3(4), 84–85.
######## data(sim200x3) result <- pers(pair(sim200x3)) pairwise.person.fit(pers_obj=result) # item fit statistic######## data(sim200x3) result <- pers(pair(sim200x3)) pairwise.person.fit(pers_obj=result) # item fit statistic
This function calculates the S-statistic on item level proposed by Fischer and Scheiblechner (1970) on item level for dicho- or polytomous item response formats by splitting the data into two subsamples. For polytomous Items the test is performed on item category level. Several splitting options are available (see arguments). The S-statistic is also mentioned in van den Wollenberg, (1982) – an article in Psychometrika, which might be available more easily (see details).
pairwise.S( daten, m = NULL, split = "random", splitseed = "no", verbose = FALSE, ... )pairwise.S( daten, m = NULL, split = "random", splitseed = "no", verbose = FALSE, ... )
daten |
a data.frame or matrix with optionaly named colums (names of items), potentially with missing values, comprising polytomous or dichotomous (or mixed category numbers) responses of |
m |
an integer (will be recycled to a vector of length k) or a vector giving the number of response categories for all items - by default |
split |
Specifies the splitting criterion. Basically there are three different options available - each with several modes - which are controlled by passing the corresponding character expression to the argument. 1) Using the rawscore for splitting into subsamples with the following modes: 2) Dividing the persons in 3) The third option is using a manifest variable as a splitting criterion. In this case a vector with the same length as number of cases in |
splitseed |
numeric, used for |
verbose |
logical, if |
... |
additional arguments |
The data is splitted in two subsamples and then item thresholds, the parameter (Sigma) and their standard errors (SE) for the items according the PCM (or RM in case of dichotonimies) are calculated for each subsample. This function internaly calls the function pairSE. Additional arguments (see description of function pairSE) for parameter calculation are passed through.
This item fit statistic is also (perhaps misleadingly) namend as 'Wald test' in other R-packages. The S-statistic, as implemented in pairwise, is defined according to Fischer and Scheiblechner (1970); see also equation (3) in van den Wollenberg, (1982), p. 124 in the following equation:
where is the estimate of the item parameter of subsample 1, is the estimate of the item parameter of subsample 2 and and are the respective standard errors.
In Fischer (1974), p. 297, the resulting test statistic (as defined above) is labeled with , as it is asymtotically normally distributed. Contrary to the 'Wald-type' test statistic , which was drived by Glas and Verhelst (2005) from the (general) distributed test of statistical hypotheses concerning several parameters, which was introduced by Wald (1943).
A (list) object of class "pairS" containing the test statistic and item difficulty parameter sigma and their standard errors for the two or more subsamples.
Estimation of standard errors is done by repeated calculation of item parameters for subsamples of the given data. This procedure is mainly controlled by the arguments nsample and size (see arguments in pairSE). With regard to calculation time, the argument nsample is the 'time killer'. On the other hand, things (estimation of standard errors) will not necessarily get better when choosing large values for nsample. For example choosing nsample=400 will only result in minimal change for standard error estimation in comparison to (nsample=30) which is the default setting (see examples).
description of function pairSE{pairwise}.
Fischer, G. H., & Scheiblechner, H. (1970). Algorithmen und Programme fuer das probabilistische Testmodell von Rasch. Psychologische Beitrage, (12), 23–51.
van den Wollenberg, A. (1982). Two new test statistics for the rasch model. Psychometrika, 47(2), 123–140. https://doi.org/10.1007/BF02296270
Glas, C. A. W., & Verhelst, N. D. (1995). Testing the Rasch Model. In G. Fischer & I. Molenaar (Eds.), Rasch models: Foundations, recent developments, and applications. New York: Springer.
Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society, 54(3), 426–482. https://doi.org/10.1090/S0002-9947-1943-0012401-3
Fischer, G. H. (1974). Einführung in die Theorie psychologischer Tests. Bern: Huber.
########## data("kft5") S_ran_kft <- pairwise.S(daten = kft5,m = 2,split = "random") summary(S_ran_kft) summary(S_ran_kft,thres = FALSE) #### polytomous examples data(bfiN) # loading example data set data(bfi_cov) # loading covariates to bfiN data set # calculating itemparameters and SE for two subsamples by gender S_gen <- pairwise.S(daten=bfiN, split = bfi_cov$gender) summary(S_gen) summary(S_gen,thres = FALSE) # other splitting criteria ## Not run: S_med <- pairwise.S(daten=bfiN, split = "median") summary(S_med) S_ran<-pairwise.S(daten=bfiN, split = "random") summary(S_ran) S_ran.4<-pairwise.S(daten=bfiN, split = "random.4") summary(S_ran.4) # currently not displayed ###### example from details section 'Some Notes on Standard Errors' ######## S_def<-pairwise.S(daten=bfiN, split = "random",splitseed=13) summary(S_def) ###### S_400<-pairwise.S(daten=bfiN, split = "random", splitseed=13 ,nsample=400) summary(S_400) ## End(Not run)########## data("kft5") S_ran_kft <- pairwise.S(daten = kft5,m = 2,split = "random") summary(S_ran_kft) summary(S_ran_kft,thres = FALSE) #### polytomous examples data(bfiN) # loading example data set data(bfi_cov) # loading covariates to bfiN data set # calculating itemparameters and SE for two subsamples by gender S_gen <- pairwise.S(daten=bfiN, split = bfi_cov$gender) summary(S_gen) summary(S_gen,thres = FALSE) # other splitting criteria ## Not run: S_med <- pairwise.S(daten=bfiN, split = "median") summary(S_med) S_ran<-pairwise.S(daten=bfiN, split = "random") summary(S_ran) S_ran.4<-pairwise.S(daten=bfiN, split = "random.4") summary(S_ran.4) # currently not displayed ###### example from details section 'Some Notes on Standard Errors' ######## S_def<-pairwise.S(daten=bfiN, split = "random",splitseed=13) summary(S_def) ###### S_400<-pairwise.S(daten=bfiN, split = "random", splitseed=13 ,nsample=400) summary(S_400) ## End(Not run)
This function calculates an Index of Person Separation, that is the proportion of person variance that is not due to error.
pairwise.SepRel(pers_obj, na.rm = TRUE)pairwise.SepRel(pers_obj, na.rm = TRUE)
pers_obj |
an object of class |
na.rm |
a logical evaluating to TRUE or FALSE indicating whether NA values should be stripped before the computation proceeds. |
none
An object of class c("pairwiseSepRel","list").
Andrich, D. (1982). An index of person separation in latent trait theory, the traditional KR.20 index, and the Guttman scale response pattern. Education Research and Perspectives, 9(1), 95–104.
###################### ######## data(bfiN) # loading reponse data pers_obj <- pers(pair(bfiN)) result <- pairwise.SepRel(pers_obj) result str(result) # to see whats in ;-) ########################## ######## data(bfiN) # loading reponse data pers_obj <- pers(pair(bfiN)) result <- pairwise.SepRel(pers_obj) result str(result) # to see whats in ;-) ####
This is the (new) main function for calculation of person estimates based on answering dichotomous or polytomous items according theRasch Model (Rasch, 1960) and Partial Credit Model (Masters, 1982), given the item parameters (object of class "pair" - as a result of pair()) and and the datamatrix (argument daten) containing the person respose vectors (rows), using an WL approach, introduced by Warm (1989).
pers( itempar, daten = NULL, incidenz = NULL, na_treat = NULL, limit = 1e-05, iter = 50, Nrel = FALSE, tecout = FALSE )pers( itempar, daten = NULL, incidenz = NULL, na_treat = NULL, limit = 1e-05, iter = 50, Nrel = FALSE, tecout = FALSE )
itempar |
The item parameter prior calculated or estimated. A list object of class |
daten |
A |
incidenz |
This argument is only relevant when items are assigned to different booklets. For such a booklet-design a |
na_treat |
optionaly an integer (vector) defining the type of treatment to missing responses in the argument |
limit |
numeric giving the limit at which accuracy the WL-algorithm stops. |
iter |
numeric giving the maximum numer of iteration to perform. |
Nrel |
logical with default set to |
tecout |
logical default set to |
no detail in the moment.
An object of class c("pers", "data.frame") or a (very long) "list" (when setting on techout=TRUE) containing the person parameters.
Masters, G. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149–174.
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danmarks pædagogiske Institut.
Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54(3), 427–450.
############ data(sim200x3) result <- pers(itempar=pair(sim200x3)) summary(result) plot(result) logLik(result) # Log-Likelihood for 'estimated' model logLik(result, sat=TRUE) # Log-Likelihood for saturated model AIC(logLik(result)) # AIC for 'estimated' model AIC(logLik(result, sat=TRUE)) # AIC for saturated model BIC(logLik(result)) # BIC for 'estimated' model BIC(logLik(result, sat=TRUE)) # BIC for saturated model ###### following example requires package eRm ###### # require(eRm) # # itemparameter with eRm: # itempar_eRm <- thresholds(PCM(sim200x3))$ threshtable[[1]][,2:3] # # pairwise personparameter with eRm-itemparameter and data: # summary(pers(itempar=itempar_eRm,daten=sim200x3)) # # eRm personparameter: # person.parameter(PCM(sim200x3)) # # personparameter with pairwise: # summary(pers(pair(sim200x3)))############ data(sim200x3) result <- pers(itempar=pair(sim200x3)) summary(result) plot(result) logLik(result) # Log-Likelihood for 'estimated' model logLik(result, sat=TRUE) # Log-Likelihood for saturated model AIC(logLik(result)) # AIC for 'estimated' model AIC(logLik(result, sat=TRUE)) # AIC for saturated model BIC(logLik(result)) # BIC for 'estimated' model BIC(logLik(result, sat=TRUE)) # BIC for saturated model ###### following example requires package eRm ###### # require(eRm) # # itemparameter with eRm: # itempar_eRm <- thresholds(PCM(sim200x3))$ threshtable[[1]][,2:3] # # pairwise personparameter with eRm-itemparameter and data: # summary(pers(itempar=itempar_eRm,daten=sim200x3)) # # eRm personparameter: # person.parameter(PCM(sim200x3)) # # personparameter with pairwise: # summary(pers(pair(sim200x3)))
S3 plotting method for object of classc("grm","list")
## S3 method for class 'grm' plot( x, xymin = NULL, xymax = NULL, ci = 2, main = NULL, col.error = "blue", col.diag = "red", itemNames = TRUE, cex.names = 0.8, type = "b", xlab = NULL, ylab = NULL, pch = 43, las = 3, cex.axis = 0.5, ... )## S3 method for class 'grm' plot( x, xymin = NULL, xymax = NULL, ci = 2, main = NULL, col.error = "blue", col.diag = "red", itemNames = TRUE, cex.names = 0.8, type = "b", xlab = NULL, ylab = NULL, pch = 43, las = 3, cex.axis = 0.5, ... )
x |
object of class |
xymin |
optional lower limit for xy-axis |
xymax |
optional upper limit for xy-axis |
ci |
numeric defining confidence intervall for point estimator |
main |
see |
col.error |
vector of colors for error bars |
col.diag |
color for the diagonal of the plot |
itemNames |
logical wether to plot itemnames |
cex.names |
magnification factor for itemnames |
type |
see |
xlab |
see |
ylab |
see |
pch |
see |
las |
see |
cex.axis |
see |
... |
other parameters passed to plot |
S3 plotting method for object of class"pair"
## S3 method for class 'pair' plot( x, sortdif = FALSE, ra = "auto", main = NULL, col.lines = (1:dim(x$threshold)[2]), type = "b", xlab = "items", ylab = "logits", pch = (1:dim(x$threshold)[2]), las = 3, cex.axis = 0.8, ... )## S3 method for class 'pair' plot( x, sortdif = FALSE, ra = "auto", main = NULL, col.lines = (1:dim(x$threshold)[2]), type = "b", xlab = "items", ylab = "logits", pch = (1:dim(x$threshold)[2]), las = 3, cex.axis = 0.8, ... )
x |
object of class |
sortdif |
logical wether to order items by difficulty |
ra |
either the character |
main |
see |
col.lines |
vector of colors for threshold profile lines |
type |
see |
xlab |
see |
ylab |
see |
pch |
see |
las |
see |
cex.axis |
see |
... |
other parameters passed to plot |
S3 plotting method for object of classc("pairSE","list")
## S3 method for class 'pairSE' plot( x, ci = 2, sortdif = FALSE, ra = "auto", main = NULL, col.lines = 1:(dim(x$threshold)[2]), col.error = 1:(dim(x$threshold)[2]), type = "b", xlab = "items", ylab = "logits", pch = 20, las = 3, cex.axis = 0.8, ... )## S3 method for class 'pairSE' plot( x, ci = 2, sortdif = FALSE, ra = "auto", main = NULL, col.lines = 1:(dim(x$threshold)[2]), col.error = 1:(dim(x$threshold)[2]), type = "b", xlab = "items", ylab = "logits", pch = 20, las = 3, cex.axis = 0.8, ... )
x |
object of class |
ci |
numeric defining confidence intervall for point estimator |
sortdif |
logical wether to order items by difficulty |
ra |
either the character |
main |
see |
col.lines |
vector of colors for threshold profile lines |
col.error |
vector of colors for error bars |
type |
see |
xlab |
see |
ylab |
see |
pch |
see |
las |
see |
cex.axis |
see |
... |
other parameters passed to plot |
S3 plotting method for object of class"pers"
## S3 method for class 'pers' plot( x, ra = NULL, sortdif = FALSE, main = NULL, ylab = "Logits", itemNames = TRUE, fillCol = "grey60", lineCol = "grey40", cex = 0.7, pos = 4, breaks = "Sturges", pch = 1, ... )## S3 method for class 'pers' plot( x, ra = NULL, sortdif = FALSE, main = NULL, ylab = "Logits", itemNames = TRUE, fillCol = "grey60", lineCol = "grey40", cex = 0.7, pos = 4, breaks = "Sturges", pch = 1, ... )
x |
object of class |
ra |
an integer, defining the (logit) range for y-axis |
sortdif |
logical wether to order items by difficulty |
main |
see |
ylab |
see |
itemNames |
logical wether to use itemnames in the resulting plot |
fillCol |
color for bar filling of the ability histogram |
lineCol |
color for bar lines of the ability histogram |
cex |
see |
pos |
see |
breaks |
see |
pch |
see |
... |
S3 plotting Method for object of class"rfa"
## S3 method for class 'rfa' plot( x, com = 1, ra = "auto", main = NULL, labels = NULL, xlab = "logits", ylab = "loadings", srt = 0, cex.axis = 0.8, cex.text = 0.8, col.text = NULL, ... )## S3 method for class 'rfa' plot( x, com = 1, ra = "auto", main = NULL, labels = NULL, xlab = "logits", ylab = "loadings", srt = 0, cex.axis = 0.8, cex.text = 0.8, col.text = NULL, ... )
x |
object of class |
com |
an integer giving the number of the principal component used for plotting |
ra |
either the character |
main |
see |
labels |
a character vector specifying the plotting pattern to use. see |
xlab |
see |
ylab |
see |
srt |
|
cex.axis |
see |
cex.text |
see argument |
col.text |
see argument |
... |
other parameters passed through. |
Calculation of the point biserial correlations for dicho- or polytomous item categories with total scale (person parameter).
ptbis(y, daten = NULL)ptbis(y, daten = NULL)
y |
either an object of class |
daten |
if argument y is not an object of class |
no details in the moment.
An object of class c("data.frame", "ptbis") containing item statistics.
###################### ######## data(sim200x3) # loading reponse data y <- rowSums(sim200x3) ptbis(y=y, daten=sim200x3) #### result <- pers(pair(sim200x3)) ptbis(y= result)###################### ######## data(sim200x3) # loading reponse data y <- rowSums(sim200x3) ptbis(y=y, daten=sim200x3) #### result <- pers(pair(sim200x3)) ptbis(y= result)
function for calculating the person fit index Q, which was proposed by Tarnai and Rost (1990).
Q(obj = NULL, data = NULL, threshold = NULL, ...)Q(obj = NULL, data = NULL, threshold = NULL, ...)
obj |
an object of class |
data |
optional response data when object of class |
threshold |
optional in case that object of class |
... |
not used so far. |
The person Q-index proposed by Tarnai and Rost, (1990) is solely based on the empirical responses and the item parameters. Thus the computation of person parameters using the function pers is not required - see examples. But for convenience return objects of both functions are accepted in function Q.
a vector holding the Q-index for every person.
Tarnai, C., & Rost, J. (1990). Identifying aberrant response patterns in the Rasch model: the Q index. Münster: ISF.
####################### data(bfiN) # get some data ip <- pair(daten = bfiN,m = 6) # item parameters according the partial credit model Q(ip) ### with data an thresholds as external objects ##### threshold <- matrix(seq(-3,3,length.out = 9),ncol = 3) dimnames(threshold) <- list(c("I1","I2","I3"),c("1","2","2")) threshold resp_vec <- c(3,0,2,1,2,2,2,2,1,3,0,NA,NA,0,2,3,NA,2,NA,2,1,2,NA,1,2,2,NA) resp_emp <- matrix(resp_vec,ncol = 3,byrow = TRUE) colnames(resp_emp) <- c("I1","I2","I3") resp_emp Qindex <- Q(data = resp_emp,threshold = threshold) cbind(resp_emp,Qindex) #### unequal number of thresholds ################### threshold <- matrix(seq(-3,3,length.out = 9),ncol = 3) dimnames(threshold) <- list(c("I1","I2","I3"),c("1","2","2")) threshold[2,3] <- NA resp_vec <- c(3,0,2,1,2,2,2,2,1,3,0,NA,NA,0,2,3,NA,2,NA,2,1,2,NA,1,2,2,NA) resp_emp <- matrix(resp_vec,ncol = 3,byrow = TRUE) colnames(resp_emp) <- c("I1","I2","I3") resp_emp Qindex <- Q(data = resp_emp,threshold = threshold) cbind(resp_emp,Qindex)####################### data(bfiN) # get some data ip <- pair(daten = bfiN,m = 6) # item parameters according the partial credit model Q(ip) ### with data an thresholds as external objects ##### threshold <- matrix(seq(-3,3,length.out = 9),ncol = 3) dimnames(threshold) <- list(c("I1","I2","I3"),c("1","2","2")) threshold resp_vec <- c(3,0,2,1,2,2,2,2,1,3,0,NA,NA,0,2,3,NA,2,NA,2,1,2,NA,1,2,2,NA) resp_emp <- matrix(resp_vec,ncol = 3,byrow = TRUE) colnames(resp_emp) <- c("I1","I2","I3") resp_emp Qindex <- Q(data = resp_emp,threshold = threshold) cbind(resp_emp,Qindex) #### unequal number of thresholds ################### threshold <- matrix(seq(-3,3,length.out = 9),ncol = 3) dimnames(threshold) <- list(c("I1","I2","I3"),c("1","2","2")) threshold[2,3] <- NA resp_vec <- c(3,0,2,1,2,2,2,2,1,3,0,NA,NA,0,2,3,NA,2,NA,2,1,2,NA,1,2,2,NA) resp_emp <- matrix(resp_vec,ncol = 3,byrow = TRUE) colnames(resp_emp) <- c("I1","I2","I3") resp_emp Qindex <- Q(data = resp_emp,threshold = threshold) cbind(resp_emp,Qindex)
Calculation of Q3 fit statistic for the rasch model based on the residuals, which was proposed by Yen (1984).
q3( pers_obj, na_treat = 0, use = "complete.obs", res = "stdr", method = "pearson" )q3( pers_obj, na_treat = 0, use = "complete.obs", res = "stdr", method = "pearson" )
pers_obj |
an object of class |
na_treat |
value to be assigned to residual cells which have missing data in the original response matrix. default is set to |
use |
a character string as used in function |
res |
a character string defining which type of (rasch–) residual to analyze when computing the correlations. This must be (exactly) one of the strings "sr" for score residuals , "stdr" for standardised residuals, "srsq" for score residuals squared, or "stdrsq" for standardised residuals squared. The default is set to |
method |
a character string as used in function |
The lower level letter 'q' was used (intead of 'Q') for naming the function because the name 'Q3' was already used in another IRT package – namly TAM. As perhaps some users like to use both packages simultaniously, an alternative naming convention was choosen for 'pairwise'. No other details in the moment.
An object of class c("Q3","list").
Yen, W. M. (1984). Effects of Local Item Dependence on the Fit and Equating Performance of the Three-Parameter Logistic Model. Applied Psychological Measurement, 8(2), 125–145. https://doi.org/10.1177/014662168400800201
###################### ######## data(bfiN) # loading reponse data pers_obj <- pers(pair(bfiN)) result <- q3(pers_obj) str(result) # to see whats in ;-) ########################## ######## data(bfiN) # loading reponse data pers_obj <- pers(pair(bfiN)) result <- q3(pers_obj) str(result) # to see whats in ;-) ####
S3 residuals method to extract the (Rasch) residuals for object of class"pers"
## S3 method for class 'pers' residuals(object, res = "sr", na_treat = 0, ...)## S3 method for class 'pers' residuals(object, res = "sr", na_treat = 0, ...)
object |
object of class |
res |
a character string defining which type of (rasch–) residual to return. This must be (exactly) one of the strings "exp" for expected scores "sr" for score residuals (default), "stdr" for standardised residuals, "srsq" for score residuals squared, or "stdrsq" for standardised residuals squared. The default is set to res="sr". |
na_treat |
value to be assigned to residual cells which have missing data in the original response matrix. Default is set to na_treat=0 to set the residuals to 0, which implys that they are imputed as 'fitting data', i.e., zero residuals. This can attenuate contrasts (see. http://www.rasch.org/rmt/rmt142m.htm). An option is to set it to na_treat=NA. |
... |
not used jet. |
Calculation of the rasch residual factor analysis proposed by Wright (1996) and further discussed by Linacre (1998) to detect multidimensionality.
rfa( pers_obj, na_treat = 0, tr = FALSE, use = "complete.obs", res = "stdr", method = "pearson", cor = TRUE )rfa( pers_obj, na_treat = 0, tr = FALSE, use = "complete.obs", res = "stdr", method = "pearson", cor = TRUE )
pers_obj |
an object of class |
na_treat |
value to be assigned to residual cells which have missing data in the original response matrix. default is set to |
tr |
a logical value indicating whether the data (the residual matrix) is transposed prior to calculation. This would perform a person analysis rather than a item analysis. The default is set to item analysis. |
use |
a character string as used in function |
res |
a character string defining which type of (rasch–) residual to analyze when computing covariances or correlations. This must be (exactly) one of the strings "sr" for score residuals , "stdr" for standardised residuals, "srsq" for score residuals squared, or "stdrsq" for standardised residuals squared. The default is set to |
method |
a character string as used in function |
cor |
a logical value indicating whether the calculation should use the correlation matrix or the covariance matrix.The default is set to |
no details in the moment.
An object of class c("rfa","list").
Wright, B. D. (1996). Comparing Rasch measurement and factor analysis. Structural Equation Modeling: A Multidisciplinary Journal, 3(1), 3–24.
Linacre, J. M. (1998). Detecting multidimensionality: which residual data-type works best? Journal of outcome measurement, 2, 266–283.
###################### ######## data(bfiN) # loading reponse data pers_obj <- pers(pair(bfiN)) result <- rfa(pers_obj) summary(result) plot(result) ########################## ######## data(bfiN) # loading reponse data pers_obj <- pers(pair(bfiN)) result <- rfa(pers_obj) summary(result) plot(result) ####
Simulated data for 200 'subjects' 'answering' to 3 items with unequal number of categories – one dichotomous and two polytoumous items.
data(sim200x3)data(sim200x3)
A data.frame containing 3 variables and 200 obsevations.
This simulated data is used as an example in the rasch module of the 'ALMO - Statistiksystem'.
Holm, K. (2014). ALMO Statistik-System. P14.8 Das allgemeine ordinale Rasch-Modell http://www.almo-statistik.de/download/Ordinales_Rasch_Modell.pdf
data(sim200x3) dim(sim200x3) ############################################################## apply(sim200x3,2,table)data(sim200x3) dim(sim200x3) ############################################################## apply(sim200x3,2,table)
function for simulation of response patterns following the dichotomous and/or polytomous Rasch model based on the category probabilities given the model parameters.
At default, when just calling simra() 1 replication of responses to 5 items with difficulties -2, -1, 0, 1, 2 from 100 persons with ability drawn from N(0|1) are sampled.
simra( itempar = matrix(seq(-2, 2, length = 5)), theta = 100, pers_obj = NULL, replicate = 1, seed = seq(1, replicate, 1), ... )simra( itempar = matrix(seq(-2, 2, length = 5)), theta = 100, pers_obj = NULL, replicate = 1, seed = seq(1, replicate, 1), ... )
itempar |
a "matrix" with |
theta |
either one of the following (1) a numeric vector of length |
pers_obj |
an object of class |
replicate |
an integer defining how many replicates (data matrices) |
seed |
a numeric vector with legnth of number of replications used for |
... |
arguments passed through. |
no details in the moment.
an array with dim(n,k,r) response patterns (k items in colums n persons in rows and r replications in the third dimension).
######## simra() # 100 dichotomous probabilistic response pattern ### 100 polytomous response pattern (4 items; each 4 answer categories) v <- c(-1.0,-0.5,0.0,0.5,-0.75,-0.25,0.25,0.75,-0.5,0.0,0.5,1.0) itempar <- matrix(v,nrow = 4,ncol = 3) simra(itempar = itempar) simra(itempar = itempar,replicate = 10) # draw 10 replications######## simra() # 100 dichotomous probabilistic response pattern ### 100 polytomous response pattern (4 items; each 4 answer categories) v <- c(-1.0,-0.5,0.0,0.5,-0.75,-0.25,0.25,0.75,-0.5,0.0,0.5,1.0) itempar <- matrix(v,nrow = 4,ncol = 3) simra(itempar = itempar) simra(itempar = itempar,replicate = 10) # draw 10 replications
S3 summary method for object of classc("grm","list")
## S3 method for class 'grm' summary(object, ci = 2, ...)## S3 method for class 'grm' summary(object, ci = 2, ...)
object |
object of class |
ci |
numeric with default |
... |
other parameters passed trough |
S3 summary method for object of class"pair"
## S3 method for class 'pair' summary(object, sortdif = FALSE, ...)## S3 method for class 'pair' summary(object, sortdif = FALSE, ...)
object |
object of class |
sortdif |
logical with default |
... |
other parameters passed trough |
S3 summary method for object of class"pairS"
## S3 method for class 'pairS' summary(object, thres = TRUE, ...)## S3 method for class 'pairS' summary(object, thres = TRUE, ...)
object |
object of class |
thres |
logical whether to output results based on the thresholds |
... |
other parameters passed trough |
S3 summary method for object of classc("pairSE","list")
## S3 method for class 'pairSE' summary(object, sortdif = FALSE, ...)## S3 method for class 'pairSE' summary(object, sortdif = FALSE, ...)
object |
object of class |
sortdif |
logical with default |
... |
other parameters passed trough |
S3 summary method for object of class"pairwiseSepRel"
## S3 method for class 'pairwiseSepRel' summary(object, ...)## S3 method for class 'pairwiseSepRel' summary(object, ...)
object |
object of class |
... |
other parameters passed trough |
S3 summary method for object of class"pers"
## S3 method for class 'pers' summary(object, short = TRUE, sortwle = FALSE, ...)## S3 method for class 'pers' summary(object, short = TRUE, sortwle = FALSE, ...)
object |
object of class |
short |
logical with default |
sortwle |
logical wether to order persons by ability - ignored when |
... |
other parameters passed trough |
S3 summary method for object of classc("pifit", "data.frame" )
## S3 method for class 'pifit' summary( object, sort = FALSE, by = "INFIT.ZSTD", decreasing = FALSE, relative = FALSE, ... )## S3 method for class 'pifit' summary( object, sort = FALSE, by = "INFIT.ZSTD", decreasing = FALSE, relative = FALSE, ... )
object |
object of class |
sort |
logical with default |
by |
character passing the type of Fit-Statistic to sort by - ignored when |
decreasing |
see |
relative |
logical with default |
... |
other parameters passed trough - see |
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
Wright, B. D., & Masters, G. N. (1990). Computation of OUTFIT and INFIT Statistics. Rasch Measurement Transactions, 3(4), 84–85.
S3 summary method for object of classc("ppfit", "data.frame" )
## S3 method for class 'ppfit' summary( object, sort = FALSE, by = "INFIT.ZSTD", decreasing = FALSE, relative = FALSE, ... )## S3 method for class 'ppfit' summary( object, sort = FALSE, by = "INFIT.ZSTD", decreasing = FALSE, relative = FALSE, ... )
object |
object of class |
sort |
logical with default |
by |
character passing the type of Fit-Statistic to sort by - ignored when |
decreasing |
see |
relative |
logical with default |
... |
other parameters passed trough - see |
Wright, B. D., & Masters, G. N. (1982). Rating Scale Analysis. Chicago: MESA Press.
Wright, B. D., & Masters, G. N. (1990). Computation of OUTFIT and INFIT Statistics. Rasch Measurement Transactions, 3(4), 84–85.
S3 summary method for object of class"q3"
## S3 method for class 'q3' summary(object, maxrc = 3, ...)## S3 method for class 'q3' summary(object, maxrc = 3, ...)
object |
object of class |
maxrc |
numerical with default |
... |
other parameters passed trough |
S3 summary method for object of class"pair"
## S3 method for class 'rfa' summary(object, sortdif = FALSE, ...)## S3 method for class 'rfa' summary(object, sortdif = FALSE, ...)
object |
object of class |
sortdif |
logical with default |
... |
other parameters passed trough |
plotting function for plotting the test information function (TIF).
tff( pair_obj, items = NULL, x = NULL, main = "Test Information Function", plot = TRUE, cat = FALSE, lwd = 2, col = 1, ... )tff( pair_obj, items = NULL, x = NULL, main = "Test Information Function", plot = TRUE, cat = FALSE, lwd = 2, col = 1, ... )
pair_obj |
an object of class |
items |
optional a vector (character or numeric) identifying the items (according their order in the data) to use for plotting the test information function. |
x |
The value(s) of the latent variable, at which the TIF will be evaluated. |
main |
see parameters for |
plot |
a logical (default |
cat |
a logical (default |
lwd |
see parameters for |
col |
see parameters for |
... |
arguments passed to plot |
no details in the moment.
a plot, a "data.frame" or a single numeric with values of the Test information function.
######## data(sim200x3) result <- pair(sim200x3) tff(pair_obj = result) # TIF plot tff(pair_obj = result, cat=TRUE) # TIF plot tff(pair_obj = result, items=c("V1","V3"), cat=TRUE) # TIF plot tff(pair_obj = result, x=0) # TIF at theta=0 tff(pair_obj = result, x=seq(0,4,.1)) # TIF for a given range of Thetas ##### examples with other data ... data(bfiN) result <- pair(bfiN) tff(pair_obj = result) tff(pair_obj = result, cat=TRUE) # TIF plot######## data(sim200x3) result <- pair(sim200x3) tff(pair_obj = result) # TIF plot tff(pair_obj = result, cat=TRUE) # TIF plot tff(pair_obj = result, items=c("V1","V3"), cat=TRUE) # TIF plot tff(pair_obj = result, x=0) # TIF at theta=0 tff(pair_obj = result, x=seq(0,4,.1)) # TIF for a given range of Thetas ##### examples with other data ... data(bfiN) result <- pair(bfiN) tff(pair_obj = result) tff(pair_obj = result, cat=TRUE) # TIF plot