get.scores: Estimate factor scores based on Genuine Likelihood

In ThurMod: Thurstonian CFA and Thurstonian IRT Modeling

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

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.

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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)

ThurMod documentation built on Sept. 19, 2023, 5:07 p.m.