Type:	Package
Title:	Thurstonian CFA and Thurstonian IRT Modeling
Version:	1.1.11
Date:	2023-09-019
Description:	Fit Thurstonian forced-choice models (CFA (simple and factor) and IRT) in R. This package allows for the analysis of item response modeling (IRT) as well as confirmatory factor analysis (CFA) in the Thurstonian framework. Currently, estimation can be performed by 'Mplus' and 'lavaan'. References: Brown & Maydeu-Olivares (2011) <doi:10.1177/0013164410375112>; Jansen, M. T., & Schulze, R. (in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.; Maydeu-Olivares & Böckenholt (2005) <doi:10.1037/1082-989X.10.3.285>.
VignetteBuilder:	knitr
License:	GPL (≥ 3)
Depends:	R (≥ 3.5.0)
Imports:	stats, utils, mvtnorm, MASS, matrixStats, lavaan
Suggests:	rmarkdown, knitr
URL:	https://github.com/MarkusTJansen/ThurMod
BugReports:	https://github.com/MarkusTJansen/ThurMod/issues
Encoding:	UTF-8
NeedsCompilation:	no
RoxygenNote:	7.2.3
LazyData:	true
Packaged:	2023-09-19 10:58:18 UTC; Jansen
Author:	Markus Thomas Jansen [aut, cre]
Maintainer:	Markus Thomas Jansen <mjansen@uni-wuppertal.de>
Repository:	CRAN
Date/Publication:	2023-09-19 16:50:02 UTC

Paired comparisons of $N=15$ items from one factor/trait (Thurstonian modeling)

Description

This data set contains synthetic data of 1000 participants on all binary indicators of 15 items. For each paired comparison, participants had to rank the two alternative items according to their preference. It is assumed that transitivity holds (that is, the data comes from a ranking task). More details can be found in Brown and Maydeu-Olivares (2011), Jansen and Schulze (2023) and Maydeu-Olivares and Böckenholt (2005).

Usage

data(FC)

Format

A data frame with 1000 observations on 105 variables. For a variable ixiy, the result is the response preferences between item x and item y. It is coded a 1, if item x is preferred over item y, and 0 otherwise.

References

Brown, A, & Maydeu-Olivares, A. (2011). Item response modeling of forced-choice questionnaires. Educational and Psychological Measurement, 71(3), 460-502. doi:10.1177/0013164410375112

Jansen, M. T., & Schulze, R. (in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285.

Paired comparisons of $N=12$ items from one factor/trait (Thurstonian modeling)

Description

This data set contains synthetic data of 1000 participants on all binary indicators of 12 items. For each paired comparison, participants had to rank the two alternative items according to their preference. It is assumed that transitivity holds (that is, the data comes from a ranking task). More details can be found in Brown and Maydeu-Olivares (2011), Jansen and Schulze (2023) and Maydeu-Olivares and Böckenholt (2005).

Usage

data(FC12)

Format

A data frame with 1000 observations on 66 variables. For a variable ixiy, the result is the response preferences between item x and item y. It is coded a 1, if item x is preferred over item y, and 0 otherwise.

References

Brown, A, & Maydeu-Olivares, A. (2011). Item response modeling of forced-choice questionnaires. Educational and Psychological Measurement, 71(3), 460-502. doi:10.1177/0013164410375112

Jansen, M. T., & Schulze, R. (in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285.

Raw ranking data of $N=15$ items from three factors/traits (Thurstonian modeling)

Description

This data set contains synthetic raw data of 1000 participants on a ranking task on 15 items.

Usage

data(FC_raw)

Format

A data frame with 1000 observations on 15 variables.

Scores of the data set 'FC' from Mplus.

Description

This data set contains synthetic data of 1000 participants on all binary indicators of 15 items and their factor scores. For each paired comparison, participants had to rank the two alternative items according to their preference. It is assumed that transitivity holds (that is, the data comes from a ranking task). More details can be found in Brown and Maydeu-Olivares (2011), Jansen and Schulze (2023) and Maydeu-Olivares and Böckenholt (2005).

Usage

data(FC_scores)

Format

A data frame with 1000 observations on 111 variables. For a variable ixiy, the result is the response preferences between item x and item y. It is coded a 1, if item x is preferred over item y, and 0 otherwise. The last six variables are the resulting factor scores and the standard error of factor scores for three factors.

References

Brown, A, & Maydeu-Olivares, A. (2011). Item response modeling of forced-choice questionnaires. Educational and Psychological Measurement, 71(3), 460-502. doi:10.1177/0013164410375112

Jansen, M. T., & Schulze, R. (in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285.

Sorts the blocks in ascending numbering

Description

This function sorts all items in a block into ascending order.

Usage

blocksort(blocks)

Arguments

Value

Returns a matrix consisting of the blocks where all items per blocks are sorted in ascending order.

Examples

# Define 30 items divided by ten triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

# sort the blocks
blocksort(blocks)

Count paired comparisons

Description

This function calculates the number of paired comparisons needed to compare a set of N items.

Usage

count.combn(nitem)

Arguments

Details

This function is only useful, if the number of paired comparisons of a full design, that is all possible paired comparisons, is of interest. Then the number is

\frac{N\times(N-1)}{2}

Value

An integer corresponding to the number of paired comparisons.

Examples

# Number if paired comparisons for a set of 15 items = 105.
count.combn(15)

Determine the number of extra blocks

Description

This function determines the minimal number of extra blocks needed in order to link all blocks.

Usage

count.xblocks(blocks)

Arguments

Details

The matrix of blocks must be constructed so that the number of columns corresponds to the number of items per block. The number of rows corresponds to the number of blocks for the specific measure. If $p$ is the number of blocks, and $k$ is the number of items per block (e.g. $k=3$ for triplets), then the number of extra blocks can be determined by (see also Jansen & Schulze, 2023)

\lceil\frac{p-1}{k-1}\rceil

Value

An integer corresponding to the number of extra blocks needed.

References

Jansen, M. T., & Schulze, R. (2023). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.

Examples

# Define a matrix of blocks
blocks <- matrix(1:15,ncol=3, byrow=TRUE)

# Determine the number of extra blocks needed
count.xblocks(blocks)

Create the Thurstonian design matrix for paired comparison and ranking data.

Description

Creates the Thurstonian design matrix for paired comparison and ranking data, given by blocks or the number of items.

Usage

designA(blocks = NULL, nitems = max(unique(blocks)))

Arguments

Details

Each Thurstonian design can be defined by blocks of at least two items. The function determines the fundamental design matrix A of the Thurstonian design, including all possible paired comparisons that can be derived by the blocks. For further information of the importance of the design matrix, see Jansen and Schulze (2023a,2023b).

Value

Returns a design matrix which includes all paired comparisons derivable from the blocks.

References

Jansen, M. T., & Schulze, R. (2023a). Linear factor analytic Thurstonian forced-choice models: Current status and issues. Manuscript submitted.

Jansen, M. T., & Schulze, R. (2023b). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.

Examples

# Define a matrix of blocks
blocks <- matrix(1:15,ncol=3, byrow=TRUE)

# Get the design matrix
loading_Matrix <- designA(blocks)

Correct degree of freedom and fit indices in Thurstonian block models

Description

Correct fit indices (RMSEA and CFI) by correcting the degrees of freedom after estimation a Thurstonian model.

Usage

fit.correct(n, blocks, chi2_mod, df_mod, chi2_base, df_base)

Arguments

Details

If a ranking design is used (variances of binary indicators is zero) there are redundancies among the thresholds and tetrachoric correlations to be estimated. This is the case, whenever the number of items per block is larger than two. In these cases the degrees of freedom must be corrected by subtracting the redundancies. For more details see Jansen and Schulze (2023) and Maydeu-Olivares (1999).

Value

Returns a vector containing corrected degrees of freedom, and the corrected RMSEA and CFI values.

References

Jansen, M. T., & Schulze, R. (in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Maydeu-Olivares, A. (1999). Thurstonian modeling of ranking data via mean and covariance structure analysis. Psychometrika, 64(3), 325-340. doi:10.1007/BF02294299

Examples

# Define 30 items divided by ten triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

# Assume the model yield the following fit, with 426 respondents
# chi2_mod = 224.456, df_mod = 59, chi2_base = 1056.566, df_base = 90

fit.correct(426,blocks,224.456,59,1056.566,90)

# The corrected values are rmsea = 0.0917892; cfi =  0.8184749

Performs lavaan estimation of the given model.

Description

This function writes a lavaan syntax given the specifications of the Thurstonian forced choice model. Additionally it runs the code (given lavaan is installed) and returns the results.

Usage

fit.lavaan(blocks, itf, model, data = NULL, estimator = "ULSMV",
  rename_list = NULL)

Arguments

Details

The syntax currently is able to perform model analysis for the latent utility model (''simple'‘ and '’lmean''; Maydeu-Olivares & Böckenholt, 2005) the unconstrained factor model (''uc''; Maydeu-Olivares & Böckenholt, 2005) and the IRT model(''irt''; Maydeu-Olivares & Brown, 2010). Additionally, all model types can be performed with all types of forced choice designs (full, block, partially linked block, linked block). For an overview and review see Jansen and Schulze (2023a,2023b).

The standard naming procedure ixiy, for the comparison of items x and y, can be changed by specifying the 'rename_list' argument. The first vector of the schould be the vector of original names, for example ‘c(’i1i2','i1i3','i2i3','Trait1','Trait2','Trait3')' the second vector should contain the new names, for example ‘c(’A01E12','A01C13','E01C23','Agree','Extra','Consc')'.

Value

Returns a lavaan object containing the specified results, after model analysis.

References

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285

Maydeu-Olivares, A., & Brown, A. (2010). Item response modeling of paired comparison and ranking data. Multivariate Behavioural Research, 45(6), 935-974. doi:10.1080/00273171.2010.531231

Jansen, M. T., & Schulze, R. (2023a). Linear factor analytic Thurstonian forced-choice models: Current status and issues. Educational and Psychological Measurement.

Jansen, M. T., & Schulze, R. (2023b, in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Examples

# read and save data set FC
data(FC12)

# set seed and define blocks
blocks <- matrix(c(5,2,1,4,7,6,3,8,10,12,9,11), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,4)

# Create and run syntax
fit <- fit.lavaan(blocks, itf, 'irt', FC, estimator = 'ULSMV')

Performs Mplus estimation of the given model.

Description

This function writes the Mplus syntax given the specifications of a Thurstonian forced choice design. Additionally it runs the code (given Mplus is installed) and returns the results.

Usage

fit.mplus(blocks, itf, model, input_path, output_path = NULL,
  data_path = "myDataFile.dat", fscore_path = "myFactorScores.dat",
  title = "myFC_model", ID = FALSE, byblock = TRUE,
  estimator = "ULSMV", data_full = FALSE, standardized = TRUE,
  rename_list = NULL, ...)

Arguments

Details

The syntax currently is able to perform model analysis for the latent utility models (''simple'‘ and '’lmean''; Maydeu-Olivares & Böckenholt, 2005) the unconstrained factor model (''uc''; Maydeu-Olivares & Böckenholt, 2005) and the IRT model(''irt''; Maydeu-Olivares & Brown, 2010). Additionally, all model types can be performed with all types of forced choice designs (full, block, partially linked block, linked block). For an overview and review see Jansen and Schulze (2023a,2023b).

The function writes and saves the Mplus input files, keeps the output files and reads the results specified for the function 'read.mplus'.

The standard naming procedure ixiy, for the comparison of items x and y, can be changed by specifying the 'rename_list' argument. The first vector of the schould be the vector of original names, for example ‘c(’i1i2','i1i3','i2i3','Trait1','Trait2','Trait3')' the second vector should contain the new names, for example ‘c(’A01E12','A01C13','E01C23','Agree','Extra','Consc')'.

Value

Returns a list containing the specified results, after model analysis.

References

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285

Maydeu-Olivares, A., & Brown, A. (2010). Item response modeling of paired comparison and ranking data. Multivariate Behavioural Research, 45(6), 935-974. doi:10.1080/00273171.2010.531231

Jansen, M. T., & Schulze, R. (2023a). Linear factor analytic Thurstonian forced-choice models: Current status and issues. Educational and Psychological Measurement.

Jansen, M. T., & Schulze, R. (2023b, in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Examples

# read and save data set FC
data(FC)
write.table(FC,paste0(tempdir(),'/','my_data.dat'),quote=FALSE, sep=" ",
col.names = FALSE, row.names = FALSE)

# set seed and define blocks
set.seed(1)
blocks <- matrix(sample(1:15,15), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,5)

# perform analysis 
## Not run: 
fit.mplus(blocksort(blocks),itf,'irt',data_path = 'mydata.dat', data_full = TRUE,
input_path = paste0(tempdir(),'/','myFC_model'))

## End(Not run)

Estimate factor scores based on Genuine Likelihood

Description

This function estimates factor scores based on genuine likelihood (Yousfi, 2019).

Usage

get.scores(dat, blocks, itf, fit, alg = mvtnorm::TVPACK(), log = TRUE, mp,
  sp, serr = TRUE, sv = NULL, blocks_ul = NULL, mplus = FALSE, ...)

Arguments

Details

The function estimates factor scores based on the Thurstonian IRT model and based on genuine likelihood proposed by Yousfi (2019). The function allows for the estimation of factor scores under all block designs, limited only by numerical integration procedures. For items per block between 5 and 20 use 'alg=mvtnorm::Miwa()'. Additionally, all model types can be performed with all types of forced choice designs (full, block, partially linked block, linked block). For an overview and review see Jansen and Schulze (2023a,2023b).

The standard naming procedure ixiy, for the comparison of items x and y.

Value

The result is a list with the factor scores and the standard errors per person and factor.

References

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285

Maydeu-Olivares, A., & Brown, A. (2010). Item response modeling of paired comparison and ranking data. Multivariate Behavioural Research, 45(6), 935-974. doi:10.1080/00273171.2010.531231

Jansen, M. T., & Schulze, R. (2023a). Linear factor analytic Thurstonian forced-choice models: Current status and issues. Educational and Psychological Measurement.

Jansen, M. T., & Schulze, R. (2023b, in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Yousfi, S. (2019). Person Parameter Estimation for IRT Models of Forced-Choice Data: Merits and Perils of Pseudo-Likelihood Approaches. In: Wiberg, M., Molenaar, D., González, J., Böckenholt, U., Kim, JS. (eds) Quantitative Psychology. IMPS 2019. Springer Proceedings in Mathematics & Statistics, vol 322. Springer, Cham. doi:10.1007/978-3-030-43469-4_3.

Examples

# read and save data set FC
data(FC12)

# set seed and define blocks
blocks <- matrix(c(5,2,1,4,7,6,3,8,10,12,9,11), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,4)

# Create and run syntax
fit <- fit.lavaan(blocks, itf, 'irt', FC, estimator = 'ULSMV')

# get scores for the first two respondents
ests <- get.scores(dat=as.matrix(FC)[1:2,],itf=itf, blocks=blocks,
fit = fit,mp=rep(0,max(itf)), 
sp=diag(1,max(itf)),estimator="MAP",sv=NULL, alg=mvtnorm::Miwa(),log=TRUE, mplus=FALSE)

Get extra blocks in a Thurstonian design, that links all blocks.

Description

The function creates extra blocks for a Thurstonian design, that links all initial blocks with as few extra blocks as possible. The number of extra blocks is determined by 'count.xblocks' (see Jansen & Schulze, 2023).

Usage

get.xblocks(blocks, itf, multidim, item_not = NULL, min = FALSE,
  show.warnings = FALSE)

Arguments

Value

The result is a matrix where the rows correspond to the specific extra blocks.

References

Jansen, M. T., & Schulze, R. (2023). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.

Examples

# Define a matrix of blocks
blocks <- matrix(1:15,ncol=3, byrow=TRUE)

# define the item-to-factor relation
itf <- rep(1:3,5)
 
# Get the extra blocks for a completely linked design
get.xblocks(blocks, itf, FALSE)

Get extra blocks in a Thurstonian design, that links as few blocks as possible.

Description

The function creates extra blocks in a Thurstonian design, that links as few initial blocks as possible, with the number of blocks determined by 'count.xblocks'. This is only useful for comparisons between linked and partially linked block designs (Jansen & Schulze, 2023).

Usage

get.xblocks.any(blocks, itf, multidim)

Arguments

Details

The main strategy of the function is to create extra blocks that link as few blocks as possible, with the number of blocks determined by 'count.xblocks'. Therefore, first all combinations of additional blocks with the first two blocks are created. If more extra blocks are needed the function uses block three, four, etc..

Value

The result is a matrix where the rows correspond to the specific extra blocks.

References

Jansen, M. T., & Schulze, R. (2023). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.

Examples

# Define a matrix of blocks
blocks <- matrix(1:15,ncol=3, byrow=TRUE)

# define the item-to-factor relation
itf <- rep(1:3,5)

# Get the extra blocks for a partially linked design
get.xblocks.any(blocks, itf, FALSE)

Creates names for paired comparisons of a given design.

Description

This function creates names for paired comparisons in the ixiy scheme. If items 1 and 2 are compared, this corresponds to i1i2.

Usage

i.name(blocks)

Arguments

Value

Returns a character vector, containing names for all binary indicators of a design.

Examples

# Define 30 items divided by ten triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

i.name(blocks)
    

Find all general blocks

Description

This function creates meta interlinked blocks within a Thurstonian design.

Usage

metablock(blocks)

Arguments

Details

This function creates meta interlinked blocks of a block design. These are blocks, that have at least one link from each of its items to any other of its items. If there is not such a link between every item, there are at least two meta blocks.

Value

Returns a list of items that form meta interlinked blocks.

Examples

# Define 30 items divided by ten triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

# Add one block to link the first three blocks.
blocks <- rbind(blocks,c(1,2,3))

# Find mata blocks
metablock(blocks)
  

Create model matrices for Thurstonian modeling

Description

This function creates and returns model matrices of Thurstonian model equations.

Usage

mod.matrices(blocks, itf, model)

Arguments

Value

Returns a list of elements containing model matrix information.

Examples

# set seed and define blocks
set.seed(1)
blocks <- matrix(sample(1:15,15), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,5)

mod.matrices(blocks,itf,'irt')
    

Determine all paired comparisons

Description

This function returns a matrix containing all paired comparisons defined by a design.

Usage

pair.combn(blocks, unique = TRUE)

Arguments

Value

Returns a matrix with all paired comparisons defined by a design.

Examples

#' # Define 30 items divided by three triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

# Get all blocks
pair.combn(blocks)
    

Determine the rank of the design matrix defined by the blocks.

Description

This function determines the rank of the fundamental design matrix defined by the blocks.

Usage

rankA(blocks)

Arguments

Value

Returns the rank of the design matrix as an integer.

Examples

# Define nine items divided by three triplets as blocks
blocks <- matrix(c(1:9), ncol = 3)

# Determine the rank of the design matrix
rankA(blocks)
    

Reads results from Mplus output file.

Description

This function reads and returns results from an Mplus output file.

Usage

read.mplus(blocks, itf, model, output_path, convergence = TRUE,
  fit.stat = TRUE, loading = TRUE, cor = TRUE, intercept = TRUE,
  threshold = TRUE, resvar = TRUE, standardized = FALSE)

Arguments

Value

Returns a list containing the specified results, after model analysis, by reading the results from the 'output_path'.

Examples

# read and save data set FC
data(FC)

write.table(FC,paste0(tempdir(),'/','my_data.dat'),quote=FALSE, sep=" ",
col.names = FALSE, row.names = FALSE)


# set seed and define blocks
set.seed(1)
blocks <- matrix(sample(1:15,15), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,5)

# perform analysis 
## Not run: 
fit.mplus(blocksort(blocks),itf,'irt',data_path = 'mydata.dat', data_full = TRUE,
input_path = paste0(tempdir(),'/','myFC_model'))


# After estimation
read.mplus(blocks,itf,'irt',output_path = paste0(tempdir(),'/','myFC_model.out'))

## End(Not run)

Recode variables.

Description

Recode variables.

Usage

recode(var = var, vals = c(1, 2, 3, 4, 5), ct = c(5, 4, 3, 2, 1),
  cat = FALSE)

Arguments

Details

This function is a simple recode function. It is possible to recode any value to any other value, as long as the class of values within a vector are equal. If an interval of numerical values should be categorized, for N categories, N-1 thresholds must be given. The first N-1 categories are constructed by using all values that are smaller or equal (<=) than the thresholds, the last category is constructed to be all values larger than the last threshold.

Value

Returns a vector with the recoded input values.

Author(s)

Markus Thomas Jansen

Examples

#numerical
v <- rep(c(1:5),10)
v_r <- recode(v, c(1:5), c(5:1))

# character
v <- rep(c('a','b','d','e'),10)
v_r <- recode(v, c('a','b','d','e'), c('apple','1','dummy',TRUE))

# interval
set.seed(1)
v <- sample(runif(20,0,6))

# recode x <= 1.3 into 1
# recode x <= 2.6 into 2
# recode x <= 3.9 into 3
# recode x <= 5.2 into 4
# recode x > 5.1 into 5
v_r <- recode(v,c(1.3,2.6,3.9,5.2),c(1:5),cat=TRUE)

Determine the number of redundancies

Description

This function determines the number of redundancies among the tetrachoric correlations and thresholds.

Usage

redundancies(blocks, warn = TRUE)

Arguments

Details

If a ranking design is used (variances of binary indicators is zero) there are redundancies among the thresholds and tetrachoric correlations to be estimated. This is the case, whenever the number of items per block is larger than two. In these cases the degrees of freedom must be corrected by subtracting the redundancies. For more details see Jansen and Schulze (2023) and Maydeu-Olivares (1999).

Value

Returns an integer of the number of redundancies.

References

Jansen, M. T., & Schulze, R. (in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Maydeu-Olivares, A. (1999). Thurstonian modeling of ranking data via mean and covariance structure analysis. Psychometrika, 64(3), 325-340. doi:10.1007/BF02294299

Examples

# Define 30 items divided by ten triplets as blocks
blocks <- matrix(c(1:30), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,10)

# Determine the redundancies
redundancies(blocks)

Calculate reliability estimate for factor scores.

Description

This function returns a reliability estimate for factor scores estimated via the Thurstonian IRT models.

Usage

reliabiltyFS(scores, scores_se, method = "sub")

Arguments

Details

The function returns the empirical reliability of factor scores. If \sigma^2 is the sample variance of the estimated scores and \bar{sigma}^2_{error} is the average if the squared scores, that is

\bar{sigma}^2_{error}=\frac{1}{N}\sum^N_i=1 se_{scores}^2

then the subtraction method, a classical reliability estimate similar to classical test theory is returned using 'sub' yields

\frac{\sigma^2-\bar{sigma}^2_{error}}{\sigma^2}

for the reliability of the scores. If 'div' is chosen, and alternative division based approach is used.

\frac{\sigma^2}{\sigma^2+\bar{sigma}^2_{error}}

.

If 'irt' is chosen, a plot returning the standard error of the scores with the scores is returned per factor.

Value

Returns the reliability value. If method = 'irt', the a plot with the reliability depending on the factorscore is returned.

Examples

# read and save data set FC
data(FC_scores)

# get reliability
reliabiltyFS(FC_scores[,c(106,108,110)],FC_scores[,c(107,109,111)])

Create data based on Thurstonian model equations

Description

Simulates a data set of paired comparisons or ranking data based a Thurstonian latent utility model.

Usage

sim.data(nfactor = 1, nitem, nperson, itf, model = "factor",
  variables = NULL, ints = NULL, lmu = NULL, ivarcov = NULL,
  loadings = NULL, varcov = NULL, graded = FALSE, ncat = NULL,
  thres = NULL, transitive = TRUE, var = 0, fvalues = FALSE,
  sim = TRUE)

Arguments

Details

The syntax currently is able to simulate data from the latent utility model (''simple'‘ and '’factor''; Maydeu-Olivares & Böckenholt, 2005) the unconstrained factor model (''uc''; Maydeu-Olivares & Böckenholt, 2005) and the IRT model(''irt''; Maydeu-Olivares & Brown, 2010).

Value

Returns a list containing the true factor scores and the data, or a matrix containing the data.

Examples

nfactor <- 3
nitem <- 15
nperson <- 1000
itf <- rep(1:3,5)
varcov <- diag(1,3)

# latent utility means
set.seed(69)
lmu <- runif(nitem, -1, 1)
loadings <- runif(nitem, 0.30, 0.95)

FC <- sim.data(nfactor=nfactor, nitem=nitem, nperson=nperson, itf=itf, 
varcov = varcov, lmu = lmu, loadings=loadings)
    

Create lavaan syntax for Thurstonian forced choice analysis

Description

This function writes a lavaan syntax given the specifications of the Thurstonian forced choice model.

Usage

syntax.lavaan(blocks, itf, model, rename_list = NULL)

Arguments

Details

The syntax currently is able to perform model analysis for the latent utility models (''simple'‘ and '’lmean''; Maydeu-Olivares & Böckenholt, 2005) the unconstrained factor model (''uc''; Maydeu-Olivares & Böckenholt, 2005) and the IRT model(''irt''; Maydeu-Olivares & Brown, 2010). Additionally, all model types can be performed with all types of forced choice designs (full, block, partially linked block, linked block). For an overview and review see Jansen and Schulze (2023a,2023b).

The standard naming procedure ixiy, for the comparison of items x and y, can be changed by specifying the 'rename_list' argument. The first vector of the schould be the vector of original names, for example ‘c(’i1i2','i1i3','i2i3','Trait1','Trait2','Trait3')' the second vector should contain the new names, for example ‘c(’A01E12','A01C13','E01C23','Agree','Extra','Consc')'.

Value

Returns a description of the user-specified model. Typically, the model is described using the lavaan model syntax. See 'lavaan::model.syntax' for more information.

References

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285

Maydeu-Olivares, A., & Brown, A. (2010). Item response modeling of paired comparison and ranking data. Multivariate Behavioural Research, 45(6), 935-974. doi:10.1080/00273171.2010.531231

Jansen, M. T., & Schulze, R. (2023a). Linear factor analytic Thurstonian forced-choice models: Current status and issues. Educational and Psychological Measurement.

Jansen, M. T., & Schulze, R. (2023b, in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Examples

# read data set FC
data(FC)

# set seed and define blocks
set.seed(1)
blocks <- matrix(sample(1:15,15), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,5)

# Create lavaan model syntax
syntax.lavaan(blocks,itf,'irt')

Create Mplus syntax for Thurstonian forced choice designs.

Description

This function writes and saves the Mplus syntax given the specifications of a Thurstonian forced choice design.

Usage

syntax.mplus(blocks, itf, model, input_path, data_path = "myDataFile.dat",
  fscore_path = "myFactorScores.dat", title = "myFC_model", ID = FALSE,
  byblock = TRUE, estimator = "ULSMV", data_full = FALSE,
  standardized = TRUE, rename_list = NULL)

Arguments

Details

The syntax currently is able to perform model analysis for the latent utility models (''simple'‘ and '’lmean''; Maydeu-Olivares & Böckenholt, 2005) the unconstrained factor model (''uc''; Maydeu-Olivares & Böckenholt, 2005) and the IRT model(''irt''; Maydeu-Olivares & Brown, 2010). Additionally, all model types can be performed with all types of forced choice designs (full, block, partially linked block, linked block). For an overview and review see Jansen and Schulze (2023a,2023b).

The function writes and saves the Mplus input files.

The standard naming procedure ixiy, for the comparison of items x and y, can be changed by specifying the 'rename_list' argument. The first vector of the schould be the vector of original names, for example ‘c(’i1i2','i1i3','i2i3','Trait1','Trait2','Trait3')' the second vector should contain the new names, for example ‘c(’A01E12','A01C13','E01C23','Agree','Extra','Consc')'.

### Outputs —-

Value

Returns a description of the user-specified model. Typically, the model is described using the lavaan model syntax. See 'lavaan::model.syntax' for more information.

Saves a list Mplus input file at 'input_path'.

References

Maydeu-Olivares, A., & Böckenholt, U. (2005). Structural equation modeling of paired-comparison and ranking data. Psychological Methods, 10(3), 285-304. doi:10.1037/1082-989X.10.3.285

Maydeu-Olivares, A., & Brown, A. (2010). Item response modeling of paired comparison and ranking data. Multivariate Behavioural Research, 45(6), 935-974. doi:10.1080/00273171.2010.531231

Jansen, M. T., & Schulze, R. (2023a). Linear factor analytic Thurstonian forced-choice models: Current status and issues. Educational and Psychological Measurement.

Jansen, M. T., & Schulze, R. (2023b, in review). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data.

Examples

# read and save data set FC
data(FC)
write.table(FC,paste0(tempdir(),'/','my_data.dat'),quote=FALSE, sep=" ",
col.names = FALSE, row.names = FALSE)

# set seed and define blocks
set.seed(1)
blocks <- matrix(sample(1:15,15), ncol = 3)

# define the item-to-factor relation
itf <- rep(1:3,5)

# Create and save Mplus syntax
syntax.mplus(blocks,itf,'lmean',data_path = 'my_data.dat', data_full = TRUE,
input_path = paste0(tempdir(),'/','myFC_model'))