| Title: | Thurstonian CFA and Thurstonian IRT Modeling |
|---|---|
| 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>. |
| Authors: | Markus Thomas Jansen [aut, cre]
|
| Maintainer: | Markus Thomas Jansen <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.1.11 |
| Built: | 2025-02-11 03:26:11 UTC |
| Source: | https://github.com/markustjansen/thurmod |
This function sorts all items in a block into ascending order.
blocksort(blocks)blocksort(blocks)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns represent the number of items per block. |
Returns a matrix consisting of the blocks where all items per blocks are sorted in ascending order.
# Define 30 items divided by ten triplets as blocks blocks <- matrix(c(1:30), ncol = 3) # sort the blocks blocksort(blocks)# Define 30 items divided by ten triplets as blocks blocks <- matrix(c(1:30), ncol = 3) # sort the blocks blocksort(blocks)
This function calculates the number of paired comparisons needed to compare a set of N items.
count.combn(nitem)count.combn(nitem)
nitem |
Number of items. |
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
An integer corresponding to the number of paired comparisons.
# Number if paired comparisons for a set of 15 items = 105. count.combn(15)# Number if paired comparisons for a set of 15 items = 105. count.combn(15)
This function determines the minimal number of extra blocks needed in order to link all blocks.
count.xblocks(blocks)count.xblocks(blocks)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
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)
An integer corresponding to the number of extra blocks needed.
Jansen, M. T., & Schulze, R. (2023). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.
# Define a matrix of blocks blocks <- matrix(1:15,ncol=3, byrow=TRUE) # Determine the number of extra blocks needed count.xblocks(blocks)# Define a matrix of blocks blocks <- matrix(1:15,ncol=3, byrow=TRUE) # Determine the number of extra blocks needed count.xblocks(blocks)
Creates the Thurstonian design matrix for paired comparison and ranking data, given by blocks or the number of items.
designA(blocks = NULL, nitems = max(unique(blocks)))designA(blocks = NULL, nitems = max(unique(blocks)))
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
nitems |
The number of items that are included in the design. |
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).
Returns a design matrix which includes all paired comparisons derivable from the blocks.
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.
# Define a matrix of blocks blocks <- matrix(1:15,ncol=3, byrow=TRUE) # Get the design matrix loading_Matrix <- designA(blocks)# Define a matrix of blocks blocks <- matrix(1:15,ncol=3, byrow=TRUE) # Get the design matrix loading_Matrix <- designA(blocks)
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).
data(FC)data(FC)
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.
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.
This data set contains synthetic raw data of 1000 participants on a ranking task on 15 items.
data(FC_raw)data(FC_raw)
A data frame with 1000 observations on 15 variables.
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).
data(FC_scores)data(FC_scores)
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.
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.
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).
data(FC12)data(FC12)
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.
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.
Correct fit indices (RMSEA and CFI) by correcting the degrees of freedom after estimation a Thurstonian model.
fit.correct(n, blocks, chi2_mod, df_mod, chi2_base, df_base)fit.correct(n, blocks, chi2_mod, df_mod, chi2_base, df_base)
n |
The number of respondents. |
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
chi2_mod |
The |
df_mod |
The degrees of freedom of the estimated model. |
chi2_base |
The |
df_base |
The degrees of freedom of the baseline model. |
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).
Returns a vector containing corrected degrees of freedom, and the corrected RMSEA and CFI values.
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
# 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# 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
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.
fit.lavaan(blocks, itf, model, data = NULL, estimator = "ULSMV", rename_list = NULL)fit.lavaan(blocks, itf, model, data = NULL, estimator = "ULSMV", rename_list = NULL)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
model |
A descriptor for the model. Can be one of ''lmean'', ''uc'‘, '’irt'‘ or '’simple2'‘, '’simple3'‘ or '’simple5''. The Number behind the ''simple'' statement defines the Thurstone case. |
data |
A matrix or data frame including the binary indicators as columns and respondents as rows. |
estimator |
Which estimator should be used? All estimators that are available in ‘lavaan' can be used. Defaults to '’ULSMV''. |
rename_list |
A list with two vectors to rename the objects in the syntax. Vector one is the original names, vector two the new names. Defaults to 'NULL'. |
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')'.
Returns a lavaan object containing the specified results, after model analysis.
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.
# 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')# 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')
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.
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, ...)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, ...)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
model |
A descriptor for the model. Can be one of ''lmean'', ''uc'‘, '’irt'‘ or '’simple2'‘, '’simple3'‘ or '’simple5''. The Number behind the ''simple'' statement defines the Thurstone case. |
input_path |
Path to save the Mplus input file. Defaults to ''myFC_model.inp''. |
output_path |
Path to the Mplus output file. Defaults to ''myFC_model.out''. |
data_path |
Path of the data file for Mplus. Defaults to ''myDataFile.dat''. |
fscore_path |
Path to save the file of factor scores. Defaults to ''myFactorScores.dat''. |
title |
Title of the Mplus model. Defaults to ''myFC_model''. |
ID |
Logical. Should a ID variable be included? The ID must be the first variable in the data set. Defaults to 'FALSE'. |
byblock |
Logical. Should the order in Mplus variable statement be the same as in the blocks. Defaults to 'TRUE'. |
estimator |
Which estimator should be used? All Estimators that are available in Mplus can be used. Defaults to ''ULSMV''. |
data_full |
Logical. Are the data considered to be from a full design? Defaults to 'FALSE'. |
standardized |
Logical. Should standardized values be computed? Defaults to 'TRUE'. |
rename_list |
A list with two vectors to rename the objects in the syntax. Vector one is the original names, vector two the new names. Defaults to 'NULL'. |
... |
Further arguments passed to function 'read.mplus'. |
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')'.
Returns a list containing the specified results, after model analysis.
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.
# 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)# 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)
This function estimates factor scores based on genuine likelihood (Yousfi, 2019).
get.scores(dat, blocks, itf, fit, alg = mvtnorm::TVPACK(), log = TRUE, mp, sp, serr = TRUE, sv = NULL, blocks_ul = NULL, mplus = FALSE, ...)get.scores(dat, blocks, itf, fit, alg = mvtnorm::TVPACK(), log = TRUE, mp, sp, serr = TRUE, sv = NULL, blocks_ul = NULL, mplus = FALSE, ...)
dat |
A data.frame or matrix defining holding the binary coded and named response data. |
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
fit |
The fit object. In case of Mplus, this is the path to the Mplus output file. In case of lavaan this is the lavaan Object. |
alg |
The algorithm to use for numerical integration. See ?mvtnorm::pmvnorm. |
log |
logical. Should the log transformed results be returned. Defaults to TRUE. |
mp |
The means of prior distribution. Defaults to multivariate normal with means 0 and vars 1 |
sp |
The vars of prior distribution. Defaults to multivariate normal with means 0 and vars 1 |
serr |
Logical. Should the standard errors be returned. Defaults to TRUE. |
sv |
Starting values. Defaults to NULL. |
blocks_ul |
Similar to 'blocks', but only with the unlinked design. Useful for comparison with other functions based on R. |
mplus |
Logical. Are results read from mplus? Defaults to FALSE. |
... |
other arguments passed by get.scores for optim. |
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.
The result is a list with the factor scores and the standard errors per person and factor.
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.
# 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)# 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)
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).
get.xblocks(blocks, itf, multidim, item_not = NULL, min = FALSE, show.warnings = FALSE)get.xblocks(blocks, itf, multidim, item_not = NULL, min = FALSE, show.warnings = FALSE)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
multidim |
Logical. Should the items within each linking block be forced to be multidimensional? |
item_not |
The items that are differently keyed compared to the majority of items. |
min |
Logical. Should a minimal number of blocks contain mixed keyed items? |
show.warnings |
Logical. Should warnings be shown? |
The result is a matrix where the rows correspond to the specific extra blocks.
Jansen, M. T., & Schulze, R. (2023). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.
# 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)# 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)
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).
get.xblocks.any(blocks, itf, multidim)get.xblocks.any(blocks, itf, multidim)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
multidim |
Logical. Should the items within each linking block be forced to be multidimensional? |
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..
The result is a matrix where the rows correspond to the specific extra blocks.
Jansen, M. T., & Schulze, R. (2023). The Thurstonian linked block design: Improving Thurstonian modeling for paired comparison and ranking data. Manuscript submitted.
# 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)# 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)
This function creates names for paired comparisons in the ixiy scheme. If items 1 and 2 are compared, this corresponds to i1i2.
i.name(blocks)i.name(blocks)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
Returns a character vector, containing names for all binary indicators of a design.
# Define 30 items divided by ten triplets as blocks blocks <- matrix(c(1:30), ncol = 3) i.name(blocks)# Define 30 items divided by ten triplets as blocks blocks <- matrix(c(1:30), ncol = 3) i.name(blocks)
This function creates meta interlinked blocks within a Thurstonian design.
metablock(blocks)metablock(blocks)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
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.
Returns a list of items that form meta interlinked blocks.
# 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)# 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)
This function creates and returns model matrices of Thurstonian model equations.
mod.matrices(blocks, itf, model)mod.matrices(blocks, itf, model)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
model |
A descriptor for the model. Can be one of ''lmean'', ''uc'‘, '’irt'‘ or '’simple2'‘, '’simple3'‘ or '’simple5''. The Number behind the ''simple'' statement defines the Thurstone case. |
Returns a list of elements containing model matrix information.
# 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')# 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')
This function returns a matrix containing all paired comparisons defined by a design.
pair.combn(blocks, unique = TRUE)pair.combn(blocks, unique = TRUE)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
unique |
Logical. Should only unique paired comparisons be returned? |
Returns a matrix with all paired comparisons defined by a design.
#' # Define 30 items divided by three triplets as blocks blocks <- matrix(c(1:30), ncol = 3) # Get all blocks pair.combn(blocks)#' # Define 30 items divided by three triplets as blocks blocks <- matrix(c(1:30), ncol = 3) # Get all blocks pair.combn(blocks)
This function determines the rank of the fundamental design matrix defined by the blocks.
rankA(blocks)rankA(blocks)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
Returns the rank of the design matrix as an integer.
# 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)# 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)
This function reads and returns results from an Mplus output file.
read.mplus(blocks, itf, model, output_path, convergence = TRUE, fit.stat = TRUE, loading = TRUE, cor = TRUE, intercept = TRUE, threshold = TRUE, resvar = TRUE, standardized = FALSE)read.mplus(blocks, itf, model, output_path, convergence = TRUE, fit.stat = TRUE, loading = TRUE, cor = TRUE, intercept = TRUE, threshold = TRUE, resvar = TRUE, standardized = FALSE)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
model |
A descriptor for the model. Can be one of ''lmean'', ''uc'‘, '’irt'‘ or '’simple2'‘, '’simple3'‘ or '’simple5''. The Number behind the ''simple'' statement defines the Thurstone case. |
output_path |
Path to the Mplus output file. Defaults to ''myFC_model.out''. |
convergence |
Logical. Should a message for convergence be returned? Defaults to 'TRUE'. |
fit.stat |
Logical. Should fit statistics be returned? Defaults to 'TRUE'. |
loading |
Logical. Should loading estimates be returned? Defaults to 'TRUE'. |
cor |
Logical. Should latent correlation estimates be returned? Defaults to 'TRUE'. |
intercept |
Logical. Should intercepts be returned? Does only work for ‘model = ’lmean''. Defaults to 'TRUE'. |
threshold |
Logical. Should thresholds be returned? Does only work for ‘model = ’uc'‘ or '’irt''. Defaults to 'TRUE'. |
resvar |
Logical. Should residual variances be returned? Defaults to 'TRUE'. |
standardized |
Logical. Should standardized values be returned? Defaults to 'FALSE'. |
Returns a list containing the specified results, after model analysis, by reading the results from the 'output_path'.
# 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)# 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.
recode(var = var, vals = c(1, 2, 3, 4, 5), ct = c(5, 4, 3, 2, 1), cat = FALSE)recode(var = var, vals = c(1, 2, 3, 4, 5), ct = c(5, 4, 3, 2, 1), cat = FALSE)
var |
A variable/column of a data matrix/ data frame containing data to be recoded. |
vals |
A vector containing the original scores. If cat is TRUE, these are thresholds. |
ct |
A vector containing the desired scores. |
cat |
Logical. should the data be categorized? ### Outputs —- |
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.
Returns a vector with the recoded input values.
Markus Thomas Jansen
#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)#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)
This function determines the number of redundancies among the tetrachoric correlations and thresholds.
redundancies(blocks, warn = TRUE)redundancies(blocks, warn = TRUE)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
warn |
Logical. Should warning messages be returned? Defaults to 'TRUE'. |
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).
Returns an integer of the number of redundancies.
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
# 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)# 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)
This function returns a reliability estimate for factor scores estimated via the Thurstonian IRT models.
reliabiltyFS(scores, scores_se, method = "sub")reliabiltyFS(scores, scores_se, method = "sub")
scores |
A matrix with factor scores. Rows are respondents, columns are factors/traits. |
scores_se |
A matrix with the standard errors of the factor scores. Rows are respondents, columns are factors/traits. Factors/traits must be in the same order as for 'scores'. |
method |
Can be one of 'div' or 'sub'. See details. Defaults to 'sub'. |
The function returns the empirical reliability of factor scores. If
is the sample variance of the estimated scores and
is the average if the squared scores, that is
then the subtraction method, a classical reliability estimate similar to classical test theory is returned using 'sub' yields
for the reliability of the scores. If 'div' is chosen, and alternative division based approach is used.
.
If 'irt' is chosen, a plot returning the standard error of the scores with the scores is returned per factor.
Returns the reliability value. If method = 'irt', the a plot with the reliability depending on the factorscore is returned.
# read and save data set FC data(FC_scores) # get reliability reliabiltyFS(FC_scores[,c(106,108,110)],FC_scores[,c(107,109,111)])# read and save data set FC data(FC_scores) # get reliability reliabiltyFS(FC_scores[,c(106,108,110)],FC_scores[,c(107,109,111)])
Simulates a data set of paired comparisons or ranking data based a Thurstonian latent utility model.
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)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)
nfactor |
The number of factors. Defaults to 1. |
nitem |
The number of items. |
nperson |
The number of data points (= respondents) to simulate. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
model |
The model class from which to simulate. Options are 'simple', 'factor', 'uc' and 'irt'. Defaults to 'factor'. |
variables |
A vector containing the names of paired comparison variables to return. If 'NULL' (default), all variables are returned. |
ints |
A vector defining the latent intercepts of item pairs. |
lmu |
A vector defining the latent means of items. |
ivarcov |
A matrix defining the variance-covariance matrix of the items. |
loadings |
A vector defining the loadings of items. |
varcov |
A matrix defining the variance-covariance matrix of the traits. |
graded |
Logical. Should a graded preference model be simulated? Defaults to 'FALSE'. |
ncat |
Numerical. The number of categories to specify for graded preference models. If graded = 'FALSE', ncat is 2. |
thres |
A vector of thresholds to categorize the latent difference response. If no thresholds are given, they are simulated from the distribution of the latent items. If graded = 'FALSE', the thresholds are all 0. |
transitive |
Logical. Should the data be transitive? If 'TRUE', ranking data is simulated, else paired comparison data is simulated. Defaults to 'TRUE'. |
var |
A vector containing the variances for each paired comparison. Defaults to 0. |
fvalues |
Logical. Should simulated factor values be returned? Defaults to 'FALSE'. |
sim |
Logical. Should the simulated data be returned? Defaults to 'TRUE'. |
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).
Returns a list containing the true factor scores and the data, or a matrix containing the data.
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)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)
This function writes a lavaan syntax given the specifications of the Thurstonian forced choice model.
syntax.lavaan(blocks, itf, model, rename_list = NULL)syntax.lavaan(blocks, itf, model, rename_list = NULL)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
model |
A descriptor for the model. Can be one of ''lmean'', ''uc'‘, '’irt'‘ or '’simple2'‘, '’simple3'‘ or '’simple5''. The Number behind the ''simple'' statement defines the Thurstone case. |
rename_list |
A list with two vectors to rename the objects in the syntax. Vector one is the original names, vector two the new names. Defaults to 'NULL'. |
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')'.
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.
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.
# 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')# 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')
This function writes and saves the Mplus syntax given the specifications of a Thurstonian forced choice design.
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)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)
blocks |
A matrix defining the blocks of the model. The number of rows must be the number of blocks, each row represents a block and contains the item numbers. The number of columns present the number of items per block. |
itf |
A vector defining the items-to-factor relation. For example 'c(1,1,1,2,2,2)' defines six items, the first three correspond to factor 1, the second three correspond to factor 2. |
model |
A descriptor for the model. Can be one of ''lmean'', ''uc'‘, '’irt'‘ or '’simple2'‘, '’simple3'‘ or '’simple5''. The Number behind the ''simple'' statement defines the Thurstone case. |
input_path |
Path to save the Mplus input file. Defaults to ''myFC_model.inp''. |
data_path |
Path of the data file for Mplus. Defaults to ''myDataFile.dat''. |
fscore_path |
Path to save the file of factor scores. Defaults to ''myFactorScores.dat''. |
title |
Title of the Mplus model. Defaults to ''myFC_model''. |
ID |
Logical. Should a ID variable be included? The ID must be the first variable in the data set. Defaults to 'FALSE'. |
byblock |
Logical. Should the order in Mplus variable statement be the same as in the blocks. Defaults to 'TRUE'. |
estimator |
Which estimator should be used? All Estimators that are available in Mplus can be used. Defaults to ''ULSMV''. |
data_full |
Logical. Are the data considered to be from a full design? Defaults to 'FALSE'. |
standardized |
Logical. Should standardized values be computed? Defaults to 'TRUE'. |
rename_list |
A list with two vectors to rename the objects in the syntax. Vector one is the original names, vector two the new names. Defaults to 'NULL'. |
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 —-
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'.
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.
# 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'))# 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'))